7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
1/270
=. Ogfdbaamrgtc - Nrupc \gfgjBNM_ 77
788
mjmrc
emormrc
kgrzc
gorba
?6?
Jgvmnum mj ag rml..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..... >=
Xgrg fckmjzgr!@vmjms y tmfjcacng..................... ..................... ..................... ..................... ..................... ..................... .......... >5
Ma kujlc lm ag mstglstbfg................... ..................... ..................... ..................... ..................... ..................... ..................... ........... >>
7. \goags lm pcrfmjtg`ms .................. ..................... ..................... ..................... ..................... ..................... ..................... ........... >>
?. Fafuac lm pcrfmjtg`ms mj tgoags mstglstbfgs .................... ..................... ..................... ..................... ..................... ..... 48
Ucfgouagrbc osbfc................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..... 46
_msukmj ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... .................... 46
Gutcfcjtrca ................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ................... 4
Xgrg fckmjzgr!Vbstmkg lm fccrlmjglgs fgrtmsbgjgs..................... ..................... ..................... ..................... ..................... . 44
Ma kujlc lm ag mstglstbfg.................... ..................... ..................... ..................... ..................... ..................... ..................... ........... 28
7. Nrefgs mstglstbfgs................... ..................... ..................... ..................... ..................... ..................... ..................... .............. 28 7.7 Lbgnrgkg lm ogrrgs ................... ..................... ..................... ...................... ..................... ..................... ..................... ... 28
7.? Lbgnrgkg lm ajmgs .................... ..................... ..................... ...................... ..................... ..................... ..................... ... 26
7.6 Lbgnrgkg lm smftcrms, fbrfuagr c pgstma ................... ..................... ..................... ..................... ..................... ........ 2=
Ucfgouagrbc osbfc..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..... 24
_msukmj ............................................................................................................................................................................................. 24
Gutcfcjtrca..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ................... 22
Jgvmnum mj ag rml................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ........ 788
_mvbsm su gprmjlbzg`m................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... . 788
Vmkgjg >Lbstrboufbj lm ermfumjfbgs (\) .............................................................................................................. 787
Xgrg fckmjzgr!Mamkmjtcs lm uj fuglrc pgrg vgrbgoams fugjtbtgtbvgs..................... ..................... ..................... .......... 78?
Ma kujlc lm ag mstglstbfg ................... ..................... ..................... ..................... ..................... ..................... ..................... ........... 786
7. Lbstrboufbj lm ermfumjfbgs ................... ..................... ..................... ..................... ..................... ..................... ..................... 786
?. Fcjstruffbj lm ujg lbstrboufbj lm ermfumjfbgs ..................... ..................... ..................... ..................... .................. 78=
M`mrfbfbc nubglc.................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ............ 785Ucfgouagrbc osbfc..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..... 782
_msukmj ................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... .. 782
Gutcfcjtrca..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ................... 778
Jgvmnum mj ag rml................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ........ 77?
_mvbsm su gprmjlbzg`m................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... . 77?
Vmkgjg 4
_mpgsc0 smkgjgs 7 g = ....................................................................................................................................... 776Xgrg fckmjzgr! ................................................................................................................................................................................. 77=
Amfturg ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... .................... 775
M`mrfbfbc nubglc .................................................................................................................................................................................. 774
_mvbsm su gprmjlbzg`m ...................................................................................................................................................................... 7?
Ma kujlc lm ag mstglstbfg .................. ..................... ..................... ..................... ..................... ..................... ..................... ............ 7?47. \goags mstglstbfgs pgrg vgrbgoams fugjtbtgtbvgs ..................... ..................... ..................... ..................... ..................... .. 7?4
7.7 Fcaukjg lm ermfumjfbgs gfukuaglgs ..................... ..................... ..................... ..................... ..................... .......... 7?4
7.? Fcaukjg lm ermfumjfbgs rmagtbvgs ................... ..................... ..................... ..................... ..................... .................... 768
7.6 Fcaukjg lm pcrfmjtg`ms ..................... ..................... ..................... ..................... ..................... ..................... .............. 76?
7.< Fcaukjg lm pcrfmjtg`ms gfukuaglcs .................... ..................... ..................... ..................... ..................... .......... 766
Ucfgouagrbc osbfc.................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ...... 765
Vmkgjg 76Kmlblgs lm pcsbfbj .................................................................................................................................................. 7>>
Xgrg fckmjzgr!_mpgsmkcs fkc sm fgafuag ag kmlbgjg.................. ..................... ..................... ..................... .................. 7>4
Amfturg0Xmrfmjtba lm tgaag y pmsc................... ..................... ..................... ..................... ..................... ..................... ..................... ... 7>2
Ma kujlc lm ag mstglstbfg.................... ..................... ..................... ..................... ...................... ..................... ..................... .......... 747
7. Kmlblgs lm pcsbfbj ..................... ..................... ..................... ..................... ...................... ..................... ..................... .......... 747
7.7 Xmrfmjtbams .................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... 74?
7.? Lmfbams .................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ........ 74
Gutcfcjtrca..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ................... 744
Jgvmnum mj ag rml................... ..................... ..................... ..................... ..................... ..................... ..................... ...................... ....... 728
_mvbsm su gprmjlbzg`m................... ..................... ..................... ..................... ..................... ..................... ...................... ..................... 728
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
10/270UBBMstglstbfg Lmsfrbptbvg jlbfm
Vmkgjg 7
Ucfgouagrbc osbfc.................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ...... ?88
_msukmj ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ?88
Gutcfcjtrca.................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... .................... ?87
Jgvmnum mj ag rml..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ...... ?8?
_mvbsm su gprmjlbzg`m..................... ..................... ..................... ..................... ..................... ..................... ..................... .................... ?8?
Vmkgjg 7=Xrcogobablglms ..................................................................................................................................................... ?86
Xgrg fckmjzgr! Vumrtm0jc tclc ms mjfcjtrgr uj troca lm fugtrc dc`gs..................... ..................... ..................... ....... ?8 4 2 78 77 7? 76 7< 7= 75 7>
]tbabzg ag bjecr-
kgfbj cotmjblgpcr kmlbc lmag gpabfgfbjlm lbemrmjtmsprcfmlbkbmjtcsmstglstbfcslmsfrbptbvcsmj ag tckg lmlmfbsbcjms.
Xgrg
fckmjzgr!
T T T T T T T T T T T T
Amfturg T T T T T T T T T T
Ma kujlc lm agmstglstbfg
T T T T T T T T T T T T T T T
M`mrfbfbc nubglc T T T
Ucfgouagrbcosbfc
T T T T T T T T T T T T T T T
_msukmj T T T T T T T T T T T T T T
Gutcfcjtrca T T T T T T T T T T T T T T T
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
14/2706Mstglstbfg Lmsfrbptbvg Obmjvmjblg y obmjvmjblc!
Fckpmtmjfbg
?Vmffbj lm aborc
Vmkgjg
7 ? 6 < = 5 > 4 2 78 77 7? 76 7< 7= 75 7>
Bjtmrprmtg agbjecrkgfbjmstglstbfglm lbemrmjtmseumjtms pgrgmjrbqumfmr suagocr.
Xgrgfckmjzgr!
T
Amfturg TT
T
T
T
T
Ma kujlc lm agmstglstbfg
T
T
T
T
T
T
T
M`mrfbfbc nubglcT
T T
Gutcfcjtrca T
T T
T
T
Fckpmtmjfbg
6Vmffbj lm aborc
Vmkgjg
7 ? 6 < = 5 > 4 2 78 77 7? 76 7< 7= 75 7>
]tbabzg ag tmfjc-acng lbspcjboammj ma gjabsbsmstglstbfc mjag tckg lmlmfbsbcjms.
Ma kujlc lm agmstglstbfg
T T T
M`mrfbfbc nubglc T T
Gutcfcjtrca T T T
Jgvmnummj ag rml
T T T T T T T T T T T T T T T
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
15/270? BNM_\gfgj
\goag7Fckpcrtgkbmjtclmagjgaegomtbskcpcrlmpgrtgkmjtc.Nugtmkgag,?87?(ergnkmjtc)
FlbncLmpgrtgkmjtc \ctga
Xcoagfbjlm7=gcsyks
Xcoagfbjgjgaegomtg
Xcrfmjtg`mlmgjgaegomtbskc
87Nugtmkgag
?744>>5 7786
Vgfgtmpqumz ?8?=58?687
7=28278=@gagpg
7>567?
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
20/2702Mstglstbfg Lmsfrbptbvg Obmjvmjblg y obmjvmjblc!
Aborc, fagsm rglbga y frfuac lm mstulbc
Vu mqubpc lm trgog`c!
Ma aborc, fcj smr ujg oumjg dmrrgkbmjtg, jc ac ms tclc. Xgrg qum ustml gafgjfm ma jbvma lm
fckpmtmjfbg lmsmglc,jumstrc sbstmkg pcjm g su lbspcsbfbj0 ma aborc, ag fagsm rglbga y ag
bjvbtgfbj g pgrtbfbpgr mj uj frfuac lm mstulbc.
Ag fagsm rglbga tbmjm fckc eujfbj prbjfbpga
mxpabfgr y egfbabtgr ag fckprmjsbj lm acs tmkgs
trgtglcs mj ma aborc. _mfumrlm qum pumlm nrgogr
ags fagsms rglbgams mj ujg kmkcrbg lm tmaecjc c
pumlm glqubrbr uj FL fcj mstgs fagsms nrgoglgs.
Xrmnujtm fkc dgfmrac ga mjfgrnglc lma frfuac
lm mstulbc c g su crbmjtglcr vcaujtgrbc. Nrgogr
ags fagsms rglbgams ms cptgtbvc, pmrc pumlm gyu-
lgram.
Ma frfuac lm mstulbcms ma aungr pgrg
fckpgrtbr y gprmjlmr `ujtcs. Gprcvm-fdm mstcs rmfurscs y gpymsm mj pmrsc-
jgs lm su fckujblgl pgrg rmscavmr sus
lulgs. _mfumrlm qum sbmkprm pumlm
fcjsuatgr scorm acs tmkgs qum am rmsua-
tmj lbefbams g su tutcr g lbstgjfbg.
Ma aborcfukpam fugtrc eujfbcjms0
g. \mxtc, mj ma qum mjfumjtrg ag bjecrkgfbj y ma
lmsgrrcaac lm acs fcjtmjblcs g mstulbgr.
o. Xbzgrrj, pgrg qum lurgjtm ag fagsm rglbga
suorgym blmgs bkpcrtgjtms c rmgabfm lbstbjtgs
gftbvblglms.
f. Fuglmrjc lm trgog`c, fcj m`mrfbfbcs pgrg prgf-
tbfgr ac gprmjlblc.
l. Dmrrgkbmjtg lm gutcmvgaugfbj, fugjlc rm-
sumavm su gutcfcjtrca fglg smkgjg.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
21/27078BNM_ \gfgj
Jumstrg kmtclcacng pgsc g pgsc
Xgrg egfbabtgr su gprmjlbzg`m y gprcvmfdgr ks y km`cr ma mstulbc fglg smkgjg, sbng mstcs
pgscs. Jc sm sgatm jbjnujc!
Amg ma fcjtmjblc lm ag smkgjg
Ammr ma fcjtmjblc jcs pmrkbtm tmjmr ujg blmg nmjmrga lma tmkg0 qu
sgomkcs, fcj qu ac rmagfbcjgkcs, mtf. Mstm prbkmr fcjtgftc tgkobj
jcs dgr fgmr mj ag fumjtg lma mseumrzc g rmgabzgr pgrg gprmjlmr ac jumvc
y jcs pcjlr mj cjlg pgrg ag fagsm rglbga.
7
Msfufdm ag fagsm rglbga
Fcj acs = smjtblcs
Ag fagsm rglbga ms jumstrg kgmstrg. Lm gd qum ma prcnrgkg sm aagkm "MaKgmstrc mj Fgsg". Ags kgmstrgs y kgmstrcs acfutcrms mxpabfgj ma fcjtm-
jblc, prcpcjmj m`mrfbfbcs y ctrcs m`mkpacs pgrg gkpabgr ma tmkg.
?
Lmspus lm ag fagsm rglbga, su trgog`c pmrscjga
Mstulbc y gutcfcjtrca
Ebjgabzglg ag fagsm rglbga ms ma kckmjtc lm su trgog`c pmrscjga. Lbstrbou-
yg su tbmkpc0 ms km`cr uj pcfc fglg lg, qum tclc ag vspmrg.
6
Fcjsuatm sus lulgs
]j mstulbgjtm bjtmabnmjtm sgom fujlc pmlbr gyulg
Fcjsuatm acs tmkgs qum jc am dgj qumlglc fagrcs mj ctrcs aborcs, mj
bjtmrjmt, fcj egkbabgrms c gkbncs. Vmnurc qum mjfcjtrgr pmrscjgs lbs-
pumstgs g gyulgram.
Mstglstbfg Lmsfrbptbvg Vmkgjg 7
7. Wu ms ag mstglstbfg3
Ag mstglstbfgms uj fcj`ujtc lm ktclcs pgrg rmfcamftgr lgtcs, crngjbzgracs,
bjtmrprmtgracs y aamngr g fcjfausbcjms fcj ogsm mj maacs.
Ms ujg rgkg lm ag kgtmktbfg qum surnb pcr ag jmfmsblgl lm acs ncomrjgjtms
lm fcjcfmr, pcr m`mkpac, fujtcs dgobtgjtms tmjg ujg fbulgl c rmnbj, fgafuagr
ag prcluffbj, sus tmrrbtcrbcs, mstbkgr ma tbmkpc qum tgrlgogj mj tmrkbjgr sus
fcjstruffbcjms, mstgoamfmr acs bkpumstcs y aumnc rmnbstrgr crlmjglgkmjtm tclg
mstg bjecrkgfbj.
Ag pgagorg mstglstbfgvbmjm lm ag pgagorg gamkgjgVtggt, qum sbnjbfg mstglc
cncobmrjc, pums mstm ms ma rmspcjsgoam lm rmprmsmjtgr, lmsfrbobr y fckpgrgr ag
sbtugfbj lm fglg rmnbj g su fgrnc.
Gftugakmjtm sm fcjsblmrg qum ma eujlglcr y crngjbzglcr lm ag mstglstbfg eum
ma gamkj Nclcermlc Gfdmjwgaa (7>72 7>>?), prcemscr y mfcjckbstg lm ag
]jbvmrsblgl lm Ambpzbn, Gamkgjbg.
Fcj ma tbmkpc, ag mstglstbfg dg blc mvcaufbcjgjlc0
Crbnbjgakmjtm sm us pgrg fcjtgr ag pcoagfbj lm uj pgs c ags prcpbmlglms
c obmjms lma Mstglc c lm acs ncobmrjcs.
Ks glmagjtm, sm gkpabgrcj sus eujfbcjms y sm mkpmz g usgr pgrg fgafuagr
ags prcogobablglms lm ngjgr mj acs `umncs lm gzgr (ruamtg, lglcs, mtftmrg).
Gftugakmjtm ms ujg fbmjfbg qum sm gpabfg g kufdgs gftbvblglms dukgjgs0lmslm ags fumjtgs qum aamvgj mj ujg tbmjlg, dgstg ags lm ujg mkprmsg c
bjstbtufbj kuy nrgjlm, ujg bjlustrbg, fccpmrgtbvg, msfumag y kufdgs ks.
Mj nmjmrga, ag mstglstbfg sm pumlm lmjbr fckc ag gpabfgfbj lm ag kgtmktbfg
ga fcj`ujtc lm tfjbfgs qum sm utbabzgj mj ma prcfmsgkbmjtc c gjabsbs lm lgtcs.
Vm utbabzg ag kgtmktbfg pgrg magocrgr prckmlbcs, tgoags y nrfgs fcj ma j lm
rmsukbr y gjgabzgr acs lgtcs pgrg ujg km`cr tckg lm lmfbsbcjms.
M`mrfbfbc ?_mspcjlg0 Mj qu gftbvblglms lm ag vblg lbgrbg utbabzg ag mstglstbfg3
Ma kujlc lm ag mstglstbfg
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
29/27074BNM_ \gfgj
M`mrfbfbc 6
Amg ma sbnubmjtm fgsc m blmjtbqum ags eumjtms prbkgrbgs y ags eumjtms smfujlgrbgs lm bjvmstbngfbj.
Dgbt ms ma pgs fcj kgycr bjfblmjfbg lm tuomrfuacsbs mj Gkrbfg. Ma sbstmkg
lm vbnbagjfbg lm tuomrfuacsbs ms lm bkpcrtgjfbg mj ag lmtmffbj lm fgscs y mj
nmjmrgr bjecrkgfbj qum gpcym ma fcjtrca lm mstg mjemrkmlgl. Ag mvgaugfbj
(lma sbstmkg lm vbnbagjfbg) sm aamv g fgoc usgjlc ag nug lm mvgaugfbj lm
sbstmkgs lm vbnbagjfbg lm sgaul poabfg. Xgrg ag rmfcamffbj lm lgtcs, sm gpabf uj
fumstbcjgrbc g acs klbfcs y lbrbnmjtms lm bjstbtufbcjms fagvm. Glmks sm rmvbs
ma prctcfcac lm vbnbagjfbg y lma Xrcnrgkg Jgfbcjga lm tuomrfuacsbs lm gncstc ?878.
Ergnkmjtc glgptglc lma grtfuac magocrglc pcr Emjmacj Jgtgma y Lmay Xgtrbfi
7. Eumjtms prbkgrbgs0
?. Eumjtms smfujlgrbgs0
?. Ags eumjtms lm bjecrkgfbjAg bjecrkgfbj mstglstbfg pumlm cotmjmrsm lbrmftgkmjtm lm ag rmgablgl, ms
lmfbr, lm mjfumstgs, fumstbcjgrbcs, kmlbfbcjms y cosmrvgfbcjms lbrmftgs. Mstgs sm
aagkgj eumjtms prbkgrbgs lm bjecrkgfbj.
\gkobj pclmkcs cotmjmr bjecrkgfbj mstglstbfg lm fuglrcs, nrfgs,
tgoags m bjvmstbngfbcjms rmgabzglgs pcr ctrgs pmrscjgs. Mstgs sm aagkgj eumjtms
smfujlgrbgs lm bjecrkgfbj.
G fcjtbjugfbj, sm am prcpcrfbcjgj ganujcs sbtbcs poabfcs lcjlm pumlm
mjfcjtrgr bjecrkgfbj lm eumjtms smfujlgrbgs0
BJM0 dttp0//www.bjm.nco.nt/
Oboabctmfg lma Ogjfc lm Nugtmkgag0 dttp0//
ncc.na/CEgks8
Oboabctmfg lm ag ]jbvmrsblgl lm Vgj Fgracs lm
Nugtmkgag0 dttp0//ncc.na/fO=e4q Vmfrmtgrg lm Xagjbebfgfbj y Xrcnrgkgfbj lm
ag Xrmsblmjfbg, VMNMXAGJ0 dttp0//www.smnmpagj.
nco.nt/?.8/
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
30/27072Mstglstbfg Lmsfrbptbvg Vmkgjg 7
6. Ag prmnujtg lm bjvmstbngfbj y ag dbptmsbsAg mstglstbfg mj ag gftugablgl sm usg mj lbvmrsgs gftbvblglms. Vmnurgkmjtm, dg
vbstc qum acs prcluftcs mkpgfglcs qum sm vmjlmj mj ags tbmjlgs tbmjmj emfdg
lm vmjfbkbmjtc, c qum ganujcs prcluftcs fckc ags ockobaags tbmjmj bkprmsc
mj ma mkpgqum ma tbmkpc lm vblg tba c lm eujfbcjgkbmjtc. Ags mkprmsgs tbmjmjqum rmgabzgr ujg bjvmstbngfbj mstglstbfg pgrg lmtmrkbjgr fujtc lurgr fglg
prcluftc.
Fugjlc sm qubmrm pagjbfgr ujg bjvmstbngfbj ac prbkmrc qum dgy qum lmtmrkbjgr
ms fua ms ma prcoamkg qum sm lmsmg bjvmstbngr. Mstm prcoamkg sm pumlm msfrbobr
mj ecrkg lm prmnujtg c fckc ujg grkgfbj.
Xcr m`mkpac, mj ma fgsc lm ag amfdm mjvgsglg mj tmtrgpgfi, ag prmnujtg lm
bjvmstbngfbj pclrg smr0 fujtc tbmkpc tgrlg mj lmsfckpcjmrsm ma prbkmr abtrc
lm amfdm aumnc lm smr mkpgfglc3
Ctrcs m`mkpacs lm prmnujtg lm bjvmstbngfbj pumlmj smr0
g. Wu qubmrm ag kgycrg lm mstulbgjtms0 fcjstruffbj lm ujg fgjfdg lm
etoca c lm ogsqumtoca3
o. Wu pcrfmjtg`m lm mstulbgjtms cpbjg qum ma gtca lm ag rmegffbj tbmjm
oumj sgocr3
Ag prmnujtg, fckc pumlm vmrsm, lmom gfagrgr ac qum sm qubmrm mstulbgr.
Aumnc lm pagjtmgr ag prmnujtg, sm lmom lgr ujg rmspumstg tmjtgtbvg c pcsboam, g
ag fuga sm am aagkg dbptmsbs.
Ags dbptmsbs sm pagjtmgj ogsjlcsm mj ags mxpmrbmjfbgs qum ujc dg tmjblc. Xcr
m`mkpac, sb sm sgom qum mj ag fckujblgl jglbm tbmjm pmactgs lm ogsqumtoca y
jglbm `umng ogsqumtoca, mjtcjfms ag dbptmsbs pumlm smr0
Ag kgycrg lm mstulbgjtms prmebmrm ag fcjstruffbj lm ujg fgjfdg lm etoca.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
31/270?8BNM_ \gfgj
M`mrfbfbc 8 % lm ags pagjtgs lm fge lm uj fgemtga tmjg rcyg.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
33/270??BNM_ \gfgj
=. Ags vgrbgoams
Lm ag ujblgl lm gjabsbs "egkbabg" pclmkcs mstulbgr vgrbgs fgrgftmrstbfgs, tgams
fckc0 bjnrmsc, jkmrc lm bjtmnrgjtms lm ag egkbabg, tbpc lm fgsg qum tbmjm, mlgl
lma pglrm, msfcagrblgl lma pglrm, msfcagrblgl lm ag kglrm, mtftmrg. Fglg ujg
lm mstgs fgrgftmrstbfgs sm lmjckbjg vgrbgoam. Ugrbgoamms ag fgrgftmrstbfg qum
sm mstulbg lm ujg ujblgl lm gjabsbs. Ags vgrbgoams qum sm mstulbgj scj ags qumjmfmsbtgkcs pgrg tckgr lmfbsbcjms.
Lm ag ujblgl lm gjabsbs "pgjga"
pclmkcs mstulbgr ags vgrbgoams0 jkmrc
lm gom`gs, fgablgl lm kbma, fgjtblgl lm
kbma, mtftmrg.
]jblgl lm gjabsbs Ugrbgoam Fgtmncrgs
Gpbfuatcr Vmxc
Dckorm
? fgtmncrgs
Ku`mr
=.7 Ags vgrbgoams tbmjmj fgtmncrgs
Fugjlc sm dgoag lm vgrbgoams dgy qum lbstbjnubr lcs mamkmjtcs, g sgomr0
Ag vgrbgoam mj s y ags fgtmncrgs lm ag vgrbgoam.
Ags fgtmncrgsscj acs vgacrms qum ag vgrbgoam pumlm tckgr c qum ma bjvmstbnglcr
am gsbnjg. Mstgs fgtmncrgs ags lmjm ma bjvmstbnglcr.
Xgrg ag ujblgl lm gjabsbs gpbfuatcr, pclmkcs mstulbgr ags vgrbgoams0 smxc, jbvma
lm msfcagrblgl, jkmrc lm pgjgams qum tbmjm ma gpbfuatcr, jkmrc lm octmaags
lm kbma qum prclufm ma gpbfuatcr y fgablgl lm ag kbma qum prclufm ma gpbfuatcr,
mstgs fumjtgj fcj ags sbnubmjtms fgtmncrgs0
Vmxc lma gpbfuatcr. \bmjm ags fgtmncrgs0 dckorm y ku`mr, c smg lcs (?)
fgtmncrgs.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
34/270?6Mstglstbfg Lmsfrbptbvg Vmkgjg 7
Jbvma lm msfcagrblgl lma gpbfuatcr. Ags fgtmncrgs pclrgj smr0 sbj mstulbcs
ecrkgams, jbvma prbkgrbc bjfckpamtc, jbvma prbkgrbc fckpamtc, jbvma osbfc,
jbvma lbvmrsbfglc. C smg fbjfc (=) fgtmncrgs.
]jblgl lm gjabsbs Ugrbgoam Fgtmncrgs
GpbfuatcrJbvma lm
msfcagrblgl
Vbj mstulbcs ecrkgams
= fgtmncrgs
Jbvma prbkgrbc bjfckpamtc
Jbvma prbkgrbc fckpamtc
Jbvma osbfc
Jbvma lbvmrsbfglc
Jkmrc lm octmaags lm kbma qum prclufm ma gpbfuatcr. Ags fgtmncrgs pclrgj
smr lbmz (78), vmbjtm (?8), vmbjtbfbjfc (?=), mtftmrg. Ugrbgs fgtmncrgs.
]jblgl lm gjabsbs Ugrbgoam Fgtmncrgs
GpbfuatcrJkmrc lmoctmaags lm
kbma
78
Ugrbgsfgtmncrgs
?8
?=
Mtf.
]jblgl lm gjabsbs Ugrbgoam Fgtmncrgs
Gpbfuatcr Mstglc fbvba
Vcatmrc
6 fgtmncrgsFgsglc c ujblc
Ubulc
Mstglc fbvba lma gpbfuatcr. Ags fgtmncrgs pumlmj smr0 scatmrc, fgsglc, ujblc,
vbulc. C smg trms (6) fgtmncrgs.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
35/270?= % lm ags vgfgs prclufm ks lm < abtrcs lm amfdm pcr lg.
g. ]jblgl lm gjabsbs0
o. Ugrbgoam0
6. Mj ag gfglmkbg lm kmfgjcnrgeg, < lm fglg = gaukjcs msfrbomj ks lm =8 pgagorgs pcr kbjutc.
g. ]jblgl lm gjabsbs0
o. Ugrbgoam0
Fgablgl lm ag kbma qum vmjlm ma gpbfuatcr. Ags fgtmncrgs pumlmj smr0 oumjg,
rmnuagr, kgag. C smg, trms (6) fgtmncrgs.
]jblgl lm gjabsbs Ugrbgoam Fgtmncrgs
GpbfuatcrFgablgl lm ag
kbma
Oumjg
6 fgtmncrgs_mnuagr
Kgag
]jblgl lm gjabsbs Ugrbgoam Fgtmncrgs
GpbfuatcrJkmrc lm
pgjgams
Dgy vgrbgoams qum sm pumlmj kmlbr mj ecrkg fugabtgtbvg y fugjtbtgtbvg. Xcr m`mkpac0 sb sm prmnujtg matgkgc lm uj tmrrmjc, ag rmspumstgnrgjlm, kmlbgjccpmqumcsm rmmrm g ujg vgrbgoam fugabtgtbvg9pmrc sb ag rmspumstg ms mj jkmrc lm fumrlgs, orgzglgs, tgrmgs, kgjzgjgs, kmtrcs fuglrglcs, mtf.,sm rmmrm g ujg vgrbgoam fugjtbtgtbvg.
Kgrqum fcj ujg "x" sb ags vgrbgoams scj fugabtgtbvgs, fugjtbtgtbvgs c gkogs.
=.? Fagsbebfgfbj lm ags vgrbgoams
Ags vgrbgoams pumlm smr lm lcs tbpcs0 fugabtgtbvgs y fugjtbtgtbvgs.
Ugrbgoams fugabtgtbvgs
Vcj ags qum lmsfrbomj fgrgftmrstbfgs g ags qum jc sm pumlmj gsbnjgr jkmrcs mj ag
bjvmstbngfbj. Gqu sm lmpmjlm lm ac qum lbngj ags pmrscjgs g ags qum sm bjvmstbng.
Ags vgrbgoams smxc (dckorm, ku`mr), msfcagrblgl (sbj mstulbcs ecrkgams, jbvma
prbkgrbc bjfckpamtc, jbvma prbkgrbc fckpamtc, mtf.) y fgablgl lm ag kbma (oumjg,
rmnuagr c kgag) scj vgrbgoams fugabtgtbvgs.
Ugrbgoams fugjtbtgtbvgs
Vcj ags qum lmsfrbomj fgrgftmrstbfgs qum s sm pumlmj kmlbr utbabzgjlc jkmrcs.
Ag prbjfbpga fgrgftmrstbfg lm ags vgrbgoams fugjtbtgtbvgs ms qum mstj lglgs mj
ujblglms lm kmlbfbj, fckc kmtrcs, aborgs, abtrcs, dcrgs, mtf. Xcr m`mkpac0jkmrc lm pgjgams, fgjtblgl lm prcluffbj lm kbma, mtftmrg.
Ugrbgoam Fugabtgtbvg Fugjtbtgtbvg
7. Xmafuag egvcrbtg
?. \gkgc lm ag fgsg
6. Kmtrcs fuglrglcs lm fcjstruffbj
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
37/270?5BNM_ \gfgj
Ucfgouagrbc osbfcfgtmncrg0 scj acs vgacrms qum ag vgrbgoam pumlm tckgr c qum ma bjvmstbnglcr am gsbnjg. Xcr m`mkpac, mj
ag vgrbgoam mstgturgags fgtmncrgs pumlmj smr gatc y og`c9 mj ag vgrbgoam tmkpmrgturglma gnug aqublg, ag
fgtmncrg pclrg smr fugaqubmr tmkpmrgturg mjtrm 8 y 788 nrglcs Fmasbus.
fmjsc0fcamffbj lm lgtcs lm fglg mamkmjtc lm ujg pcoagfbj. Xcr m`mkpac, fugjlc ma ncobmrjc dgfm
uj fmjsc lm pcoagfbj, rmfcnm acs lgtcs qum am bjtmrmsg fcjcfmr lm tclcs acs dgobtgjtms. Mstcs lgtcs
pumlmj smr mlgl, smxc, bjnrmscs, jbvma lm msfcagrblgl y ctrcs.
dbptmsbs0 aumnc lm pagjtmgr ag prmnujtg sm lmom lgr ujg rmspumstg tmjtgtbvg c pcsboam, g mstg sm am
aagkg dbptmsbs.
prmnujtg lm bjvmstbngfbj0 fugjlc sm qubmrm pagjbfgr ujg bjvmstbngfbj ac prbkmrc qum dgy qum
lmtmrkbjgr ms fua ms ma prcoamkg qum sm lmsmg bjvmstbngr. Mstm prcoamkg sm pumlm msfrbobr mj ecrkg lmprmnujtg y mjtcjfms ms ag prmnujtg lm bjvmstbngfbj.
ujblgl lm gjabsbs0 ms ac qum sm vg g mstulbgr. Xcr m`mkpac, sb sm qubmrm sgomr scorm ag prcluffbj lm
dumvcs, ag ujblgl lm gjabsbs pumlm smr ag ngaabjg c ma ngaabjmrc, lmpmjlbmjlc lm sb sm qubmrm fcjcfmr ag
prcluffbj lm ag ngaabjg c lm tclgs ags ngaabjgs lma ngaabjmrc.
vgrbgoam0scj fgrgftmrstbfgs lm bjtmrs scorm fglg mamkmjtc bjlbvbluga lm ujg pcoagfbj c kumstrg, pcr
m`mkpac, ag mlgl lm ujg pmrscjg, su pmsc c su mstgturg.
M`mrfbfbc nubglc
\ckgjlc ma m`mkpac lm ag kbma, dgrmkcs uj rmpgsc lma fcjtmjblc vbstc mj ag smkgjg, utbabzgjlc ag
vgrbgoam fugjtbtgtbvg.
Ma gpbgrbc lm ag fccpmrgtbvg lm ag galmg Xbpbatmpmqum Gog`c pcsmm 78 ngacjms lm kbma. Ags egkbabgs lm ag fccpmrgtbvg scj ags
mjfgrnglgs lma fublglc lm acs gpbgrbcs y lm sgfgr ag kbma lm acs pgjgams. Ag kbma qum vmjlmj jc ms
kmzfaglg fcj ctrcs bjnrmlbmjtms sbjc ms kbma purg, pcr ac qum su fgablgl ms mxfmamjtm. Xcr mxpmrbmjfbgacs prcluftcrms sgomj qum ujg fcakmjg prclufm uj kxbkc lm ?.= ngacjms, uj kjbkc lm 7.> ngacjms
y uj prckmlbc mstbkglc lm ? ngacjms lm kbma.
7. _mfcrlmkcs qum ag prmnujtg lm bjvmstbngfbj sm rmebmrm ga prcoamkg qum qumrmkcs bjvmstbngr,
pumlm pagjtmgrsm fckc gebrkgfbj c prmnujtg. Rg qum mstm m`mkpac ms scorm ag vgrbgoam fugjtbtgtbvg,
tmjmkcs qum tckgr mj fumjtg qum ag prmnujtg smr scorm fgrgftmrstbfgs qum sm pumlmj kmlbr
fugjtbtgtbvgkmjtm9 ms lmfbr, fcj jkmrcs.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
38/270?>Mstglstbfg Lmsfrbptbvg Vmkgjg 7
?. Ag dbptmsbs jcs lgr ujg rmspumstg pcsboam g jumstrg prmnujtg lm bjvmstbngfbj. Ag dbptmsbs
ag ogsgkcs mj jumstrg mxpmrbmjfbg, fcjcfbkbmjtc y cosmrvgfbj. Ag ecrkg mj qum sm pagjtmg ag
dbptmsbs jcs lmom egfbabtgr lmkcstrgrag.
6. Ag ujblgl lm gjabsbs ms ma co`mtc c fcsg qum sm vg g mstulbgr.
8 ngacjms lm kbma
Ma gpbgrbc
Fgjtblgl prclufblg
?>8 ngacjms lm kbma
Ugrbgoam fugjtbtgtbvg0
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
39/270?4BNM_ \gfgj
Gftbvblgl ?
Umgkcs ag sbnubmjtm jctbfbg lma gc ?878 scorm ma prmfbc lma tckgtm. Msfrbog ujg prmnujtg lm
bjvmstbngfbj, dbptmsbs, ujblgl lm gjabsbs, vgrbgoams (lmjbr qu tbpc lm vgrbgoam sm usg) y fgtmncrgs
lm fglg vgrbgoam.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
40/270?2Mstglstbfg Lmsfrbptbvg Vmkgjg 7
Eumjtm0Xrmjsg Aborm, ?7 lbfbmkorm ?878
7. Msfrbog ujg prmnujtg lm bjvmstbngfbj.
?. Magocrm ujg dbptmsbs qum rmspcjlg g ag prmnujtg.
6. Lmjg fua ms ag ujblgl lm gjabsbs.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
41/27068BNM_ \gfgj
_mvbsm su gprmjlbzg`m
Kgrqum fcj uj fdmqum ag fgsbaag qum km`cr bjlbqum su rmjlbkbmjtc. acnrglcmj
prcfmscjc
acnrglc
Lmspuslmmstulbgr... Fcjczfc ma crbnmj y ma usc lm ag mstglstbfg.
Mvgac ags eumjtms lm bjecrkgfbj.
Xagjtmc prmnujtgs lm bjvmstbngfbj m dbptmsbs.
Fagsbfc ags vgrbgoams.
Bjstbtutc Jgfbcjga lm Mstglstbfg (BJM)Ma Bjstbtutc Jgfbcjga lm Mstglstbfg (BJM) ms ag bjstbtufbj mjfgrnglg lm rmfcpbagr, prclufbr, gjgabzgr y
lbeujlbr mstglstbfgs fcjgoams. Mj su ogsm lm lgtcs sm mjfumjtrgj mstglstbfgs scfbclmkcnrfgs,
mfcjkbfgs, gkobmjtgams y lm smnurblgl y `ustbfbg.
Vb jmfmsbtg cotmjmr lgtcs mstglstbfcs scorm fugaqubmr aungr pcoaglc lma pgs, vbsbtm ag pnbjg0
www.bjm.nco.nt
Jgvmnum mj ag rml
Dcrbzcjtgams
6. \bpc lm vgrbgoam qum jc sm kblm fcj jkmrcs.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
42/270
Mstglstbfg Lmsfrbptbvg Vmkgjg ?
67
Fcjfmptcs osbfcs lm mstglstbfg
Wu mjfcjtrgr mstg smkgjg3
_mpgsmkcs acs fcjfmptcs osbfcs lm ag smkgjg 7
Fkc sm dgfm ujg mjfumstg3
Fagsbebfgfbj lm ags vgrbgoams, pcoagfbj, kumstrg y kumstrmc gamgtcrbc
Mstg smkgjg acnrgr0
Fagsbebfgr ags vgrbgoams fugabtgtbvgs y fugjtbtgtbvgs.
Lmtmrkbjgr ag pcoagfbj c ujbvmrsc lm ujg bjvmstbngfbj.
Vmamffbcjgr ujg kumstrg.
?
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
43/2706?BNM_ \gfgj
Xgrg fckmjzgr!
_mpgsmkcs acs fcjfmptcs osbfcslm ag smkgjg 7
Ag smkgjg pgsglg vbkcs acs mamkmjtcs qum lmomj tckgrsm mj fumjtg pgrgrmgabzgr ujg bjvmstbngfbj.
Ma prbkmr pgsc ms lmjbr glmfuglgkmjtm ma prcoamkg qum vg g bjvmstbngrsm. Mstm
sm pumlm pagjtmgr g trgvs lm ujg grkgfbj c prmnujtg lm bjvmstbngfbj.
Ma sbnubmjtm pgsc ms pagjtmgr ujg pcsboam rmspumstg g ag prmnujtg lm bjvmstbngfbj,
msg pcsboam rmspumstg sm fcjcfm fckc dbptmsbs.
Ctrcs mamkmjtcs qum scj pgrtm lm ag bjvmstbngfbj mstglstbfg scj0 ag ujblgl lm
gjabsbs, ags vgrbgoams y ags fgtmncrgs lm ag vgrbgoam. \gkobj ms bkpcrtgjtm sgomr
fagsbfgr ujg vgrbgoam fckc fugabtgtbvg c fugjtbtgtbvg.
Umgkcs uj m`mkpac0
]j mxgkmj lm kgtmktbfg sm mjtrmng g uj nrupc lm mstulbgjtms pgrg sgomr ma
fcjcfbkbmjtc qum tbmjmj gfmrfg lm ag sukg.
Ag prmnujtg lm bjvmstbngfbj ms0
Wu tgjtc sgomj sukgr acs mstulbgjtms3
Fckc sm kmjfbcj ag smkgjg gjtmrbcr, ag dbptmsbs jc sbmkprm ms jmfmsgrbg.
Vm pagjtmg ujg dbptmsbs jbfgkmjtm fugjlc sm qubmrm lmkcstrgr ganc, mj mstm
fgsc jc sm qubmrm lmkcstrgr jglg, sbjc jbfgkmjtm kmlbr ma fcjcfbkbmjtc lmacs mstulbgjtms.
Dbptmsbs0
]jblgl lm gjabsbs0
Fgtmncrgs0
Jc ms jmfmsgrbg
Mstulbgjtms
Xujtmc mj ma mxgkmj
Fgabfgfbcjms lm 8 g 788
Ugrbgoam fugjtbtgtbvg0
Ag vgrbgoam ms fugjtbtgtbvg pcrqum ags fgtmncrgs sm rmprmsmjtgj fcj jkmrcs.
Vb jc fcjczfc ujg fcsg, ag bjvmstbngr.
Acubs Xgstmur
Xgrg rmemxbcjgr0
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
44/270
Mstglstbfg Lmsfrbptbvg Vmkgjg ?
66
Amfturg
Fkc rmgabzgr ujg mjfumstg3
Ag mjfumstg ms ujg dmrrgkbmjtg kuy utbabzglg mj tclgs ags lbsfbpabjgs scfbgams, qum pmrkbtm rmfc-amftgr nrgj fgjtblgl lm lgtcs. Mstg tfjbfg lm bjvmstbngfbj sbrvm, mjtrm ctrgs fcsgs, pgrg rmfgogrbjecrkgfbj fckpgrgoam scorm ags cpbjbcjms lm ujg fgjtblgl bkpcrtgjtm lm pmrscjgs.
Magocrgfbj lm mjfumstgs
Ma prbkmr pgsc pgrg crngjbzgr ujg mjfumstg ms magocrgr fcj fagrblgl qu qumrmkcs gvmrbnugr yfuams scj acs co`mtbvcs lm jumstrg bjvmstbngfbj.
Mj uj smnujlc kckmjtc dgy qum lmjbr, mj eujfbj lm acs co`mtbvcs, g qubjms qumrmkcs mjfumstgr.Mstc ms ma ujbvmrsc. Vb mstm ujbvmrsc ms kuy nrgjlm sm smamffbcjg ujg kumstrg, qum ms uj nrupcsbnjbfgtbvc lma ujbvmrsc, c tctga.
Aumnc lm pagjtmgr acs co`mtbvcs y lmfblbr fcj qu kumstrg sm vg g rmgabzgr ag mjfumstg, ma tmrfmr pgscms ag fcjemffbj lma fumstbcjgrbc. Mstm lmom magocrgrsm g pgrtbr lm acs co`mtbvcs lm ag bjvmstbngfbj.Lmomkcs prcfurgr qum ags prmnujtgs qum ecrkuamkcs jc sm supmrpcjngj, mstj obmj crlmjglgs y
pumlgj smr fagrgkmjtm mjtmjlblgs pcr acs mjfumstglcs.
\gkobj ms bkpcrtgrtm tmjmr mj fumjtg ma tgkgc lma fumstbcjgrbc. Ms pcsboam qum ujc lmkgsbglcfcrtc jc jcs orbjlm ag bjecrkgfbj jmfmsgrbg pgrg jumstrcs co`mtbvcs, pmrc ujg abstg kuy agrng lm
prmnujtgs dgfm lbefba kgjtmjmr ma jbvma lm bjtmrs mj acs mjfumstglcs.
Vb ma mjfumstglcr scac pblm ga mjfumstglc dgfmr ujg kgrfg pgrg bjlbfgr fua eum ag cpfbj mamnblg,ma fumstbcjgrbc sm aagkg "mstrufturglc". Ag kgrfg pumlm smr, pcr m`mkpac, ujg T mj ag fgsbaag lmrmspumstg g ag prmnujtg c grkgfbj lma fumstbcjgrbc.
Ma fumstbcjgrbc mstrufturglc sbkpabfg ma gjabsbs lm acs lgtcs. \gkobj sm sbkpabfg ma gjabsbsfugjlc ma mjtrmvbstglc lmom mamnbr scac ujg lm ags cpfbcjms prcpumstgs mj ma fumstbcjgrbc. Vbmkprmdgy qum bjfaubr, glmks, ujg cpfbj pgrg acs qum jc sgomj qu fcjtmstgr c jc qubmrmj dgfmrac,fcjcfblg fckc jc sgom/jc fcjtmstg.
Xcr ctrg pgrtm, ms bkpcrtgjtm qum ags prbkmrgs prmnujtgs orbjlmj bjecrkgfbj scorm ganujgs fg-rgftmrstbfgs lm acs mjfumstglcs, fckc smxc, mlgl, jbvma lm bjstruffbj u ctrgs qum smgj bkpcrtgjtms
pgrg ag bjvmstbngfbj.
]jg pmqumg bjtrcluffbj qum fcjtmjngj qubjms sckcs y pcr qu mstgkcs dgfbmjlc ag mjfumstgegfbabtg ma trgog`c, yg qum nmjmrg fcjgjzg y jcs rmsuatgr ks efba cotmjmr ag bjecrkgfbj qum
ousfgkcs.
Ga jgabzgr ag mjfumstg dgy qum lmspmlbrsm gkgoamkmjtm lma mjfumstglc y fckprcogr qum tmjmkcsacs lgtcs lm fcjtgftc lm ag bjstbtufbj vbsbtglg, pcr m`mkpac, ujg eorbfg c ujg msfumag lcjlm smrmgabzg ag bjvmstbngfbj.
\ckglc lm0dttp0//ncc.na/r_MuU
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
45/2706? 8,??6?4 8,?68 8,544 ?8 8,?>< 8,78> 78 8,67> 8,>6< 7= 8,?57 8,2?4 68 8,6 ?= 8,666 8,566 ?5 8,64= 8,77772 8,? 8,4 8,?5> 8,228 84 8,6 8,45 ?? 8,6>4 8,>2? 84 8,7 8,>84 7< 8,=77 8,242 8? 8, 8,64> 8,45= ?< 8,6 8,?6> ?> 8,6>2 8,2=2 74 8,6 8,>64 ?5 8,= 8, 8,55 ?8 8,= 8,>57 72 8, 8,=4> 8,552 75 8,=82 8, 82 8,57> 8,87 ?? 8,55< 8,?27 86 8,5?= 8,>>> ?5 8,>86 8,5?? 74 8,5>8 8,28< 75 8,542 8,66274 8,=58 8,> 68 8,56> 8,6>< 8< 8,554 8,4=5 84 8,5=7 8,>28 ?2 8,>62 8,62< 77 8,>77 8,?=6 85 8,>?> 8,?24?5 8,=>= 8,42? 7< 8,>7< 8,65< 72 8,>7> 8,?6? 7? 8,>7= 8,=22 ?= 8,>=2 8,645 87 8,>28 8,62? 8< 8,>67 8,47 8,4
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
53/270
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
54/270
Mstglstbfg Lmsfrbptbvg Vmkgjg ?
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
55/270
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
56/270
Mstglstbfg Lmsfrbptbvg Vmkgjg ?
4
2
78
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
57/270
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
58/270Mstglstbfg Lmsfrbptbvg Vmkgjg 6
Fkc smamffbcjgr ujg kumstrg3Wu mjfcjtrgr mstg smkgjg3
Kblbmjlc ag emabfblgl
Fkc rmgabzgr ujg mjfumstg3 (smnujlg pgrtm)
Kumstrmc pcr fcjnackmrglcs y kumstrmc mstrgtbebfglc
Mstg smkgjg acnrgr0
Fcjcfmr acs pgscs pgrg rmgabzgr ujg mjfumstg.
Gpabfgr ma usc lm kumstrmc pcr fcjnackmrglcs.
Gpabfgr ma usc lm kumstrmc mstrgtbebfglc.
Lbemrmjfbgr mjtrm mstglstbfg lmsfrbptbvg y mstglstbfg bjemrmjfbga.
_mfcjcfmr sb uj lgtc ms uj mstglstbfc c uj pgrkmtrc.
6
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
59/270
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
60/270
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
61/270=8BNM_ \gfgj
7. _mpgsgjlc fcjfmptcs osbfcs
Mj ag vblg, ganujgs vmfms sm prmsmjtgj cpcrtujblglms pgrg rmgabzgr bjvmstbngfbcjms. Acs
tmkgs vgrgj y ag bjvmstbngfbj pclrg smr scorm prcluftcs fckc gabkmjtcs, grtfuacspgrg omaamzg, fgazglc, kmlbfbjg. Mj ctrgs cfgsbcjms, pclrg smr scorm gspmftcs scfbgams
fckc acs jlbfms lm mkpamc, bjnrmscs, mlufgfbj, sgaul y ctrcs kufdcs ks.
Ag mstglstbfg sm utbabzg mj bjvmstbngfbcjms lm lbemrmjtm tbpc pgrg crlmjgr y prcfmsgr
lgtcs, ac fuga pmrkbtm gjgabzgracs lm km`cr kgjmrg. Vbrvm pgrg acs fcjtmcs ks sbkpams,
pmrc tgkobj pgrg acs ks fckpam`cs. Fugjtc ks y km`cr ag fckprmjlgkcs, km`crms
uscs pclrmkcs lgram.
Ag mstglstbfg ms kuy bkpcrtgjtm, pcrqum prcpcrfbcjg bjecrkgfbj rmspgalglg, qum ag
dgfm fcjgoam. Ag bjecrkgfbj mst rmspgalglg pcrqum sm ogsg mj mstulbcs co`mtbvcs9 ms
lmfbr, mj acs qum jc mjtrg ag cpbjbj lma bjvmstbnglcr, jb sus fcjsblmrgfbcjms suo`mtbvgs.
Lm gfumrlc fcj ac vbstc ag smkgjg pgsglg, mj ujg bjvmstbngfbj sm pgrtm lm ag prmnujtg
lm bjvmstbngfbj pgrg aumnc magocrgr ag dbptmsbs, qum ms ujg pcsboam rmspumstg g ag
prmnujtg.
Dgy ctrcs mamkmjtcs qum scj bkpcrtgjtms pgrg ma trgog`c lm ag mstglstbfg0 ag ujblgl
lm gjabsbs, ags vgrbgoams y ags fgtmncrgs lm ag vgrbgoam (rmfcrlmkcs qum ms bkpcrtgjtm
sgomr fagsbfgr ujg vgrbgoam fckc fugabtgtbvg c fugjtbtgtbvg).
M`mkpac0
Vm gpabfg uj mxgkmj lm kgtmktbfg g uj nrupc lm ?= mstulbgjtms lm ag MC_Klm Ma Xg`gr.
Acs mstulbgjtms eumrcj mamnblcs pcr ma ktclc lm kumstrmc gamgtcrbc sbkpam. Ma mxgkmjvg g kmlbr ma jbvma lm fcjcfbkbmjtc lma tmkg sukg.
Xrmnujtg lm bjvmstbngfbj0 Fujtc sgomj acs mstulbgjtms scorm ag sukg3
Dbptmsbs0
Ugrbgoam0
Fagsbebfgfbj c tbpc lm vgrbgoam0
Xcoagfbj0
Kumstrg0
Ktclc lm kumstrmc0
Jc ms jmfmsgrbg
Fcjcfbkbmjtc9 pumlm trgog`grsm fcj ma jckorm lm0a Xcrfmjtg`m lm fcjcfbkbmjtca Xujtmc mj ma mxgkmj
Fgabfgfbcjms lm 8 g 788
Fugjtbtgtbvg0 ags fgtmncrgs sm rmprmsmjtgj pcr jkmrcs
\clcs acs mstulbgjtms lm ag MC_Klm Ma Xg`gr
Acs ?= mstulbgjtms
Ag kumstrg sm smamffbcj mj ecrkg gamgtcrbg sbkpam
Fgtmncrgs0
Ma kujlc lm ag mstglstbfg
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
62/270=7Mstglstbfg Lmsfrbptbvg Vmkgjg 6
?. Ecrkgs lm smamffbcjgr ujg kumstrg (fcjtbjugfbj lm ag smkgjg ?)
Fckc vbkcs ag smkgjg gjtmrbcr, ag kumstrg pumlm smr cotmjblg mj ecrkg
gamgtcrbg sbkpam y ecrkg gamgtcrbg sbstmktbfg.
Mstg smkgjg vmrmkcs lcs jumvcs ktclcs lm kumstrmc gamgtcrbc0
Kumstrmc pcr fcjnackmrglcs
Kumstrmc mstrgtbebfglc
?.7 Kumstrmc pcr fcjnackmrglcs c rgfbkcs
Wu ms uj fcjnackmrglc3
]j fcjnackmrglcms ujg smffbj c nrupc ecrkglc pcr lbvmrscs mamkmjtcs.Mstm ktclc tgkobj sm fcjcfm fckc kumstrmc pcr rgfbkcs c fkuacs. Xgrg ag
kumstrg sm jmfmsbtg fcjtgr fcj ujg pcoagfbj qum sm qubmrm bjvmstbngr.
Ag pcoagfbj pumlm mstgr fcjecrkglg pcr pmrscjgs, gjbkgams u co`mtcs.
Fkc sm rmgabzg uj kumstrmc pcr fcjnackmrglcs3
Xgrg rmgabzgr uj kumstrmc pcr fcjnackmrglcs c rgfbkcs, prbkmrc sm lbvblm
ma rmg lm ag pcoagfbj mj smffbcjms c fcjnackmrglcs, aumnc sm smamffbcjgj
gamgtcrbgkmjtm ganujcs lm mstcs fcjnackmrglcs, utbabzgjlc pgrg ag kumstrg
tclcs acs mamkmjtcs lm acs fcjnackmrglcs smamffbcjglcs. M`mkpac0
Vm pumlm lbvblbr g tclg ag pcoagfbj lm fbulglgjcs (pcr m`mkpac,
pcoagfbj lm Nugtmkgag) mj lbemrmjtms fcjnackmrglcs (qum pumlmj smr acs
lmpgrtgkmjtcs lma pgs).
Vm smamffbcjg ujg smrbm lm fcjnackmrglcs lm gfumrlc fcj ac qum bjtmrmsg
pgrg ag bjvmstbngfbj. Mstg smamffbj sm dgfm pcr kmlbc lm uj kumstrmc
gamgtcrbc sbkpam c sbstmktbfc.
Fugjlc sm tbmjmj acs fcjnackmrglcs smamffbcjglcs (pclrg smr acslmpgrtgkmjtcs lma pgs smamffbcjglcs ga gzgr), sm lmom bjfaubr, pcr m`mkpac,
g tclcs acs mstulbgjtms lm prbkgrbg fckc mamkmjtcs lm ag kumstrg.
Fugjlc ags pcoagfbcjms qum sm qubmrm bjvmstbngr scj kuy nrgjlms, ujg ecrkg
ks ogrgtg y efba lm cotmjmr ags kumstrgs ms pcr nrupcs c fcjnackmrglcs.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
63/270=?BNM_ \gfgj
M`mkpac0
Xgrg dgfmr ujg bjvmstbngfbj scorm ujg pagjtgfbj lm gnugfgtms,
sm pumlm smamffbcjgr pcr ma ktclc lm kumstrmc gamgtcrbc
sbkpam, ac qum bkpabfgrg mamnbr gnugfgtms ga gzgr pcr tclg ag
pagjtgfbj.
Xmrc tgkobj sm pumlmj smamffbcjgr rocams lm gnugfgtm gagzgr mj tclg ag pagjtgfbj fckc uj fcjnackmrglc, mj ma fuga
tclcs acs gnugfgtms lm fglg roca smamffbcjglc scj pgrtm lm
ag kumstrg. Mstm ktclc egfbabtgrg ma kumstrmc pgrg mstm fgsc.
Vb sm qubmrm bjvmstbngr fujtcs pgsg`mrcs trgjspcrtgj ags ajmgs lm ous mxtrgurogjc
lbgrbgkmjtm, ma trgog`c sm pumlm rmgabzgr fcj ujg kumstrg gamgtcrbg sbkpam c
gamgtcrbg sbstmktbfg, yg qum ag pcoagfbj lm ousms ms nrgjlm.
Vb sm usg fckc ktclc ag kumstrg pcr fcjnackmrglc utbabzgjlc ma kumstrmc
gamgtcrbc sbkpam, sm smamffbcjgj ga gzgr mkprmsgs lm ousms lm tclgs ags qum
mxbstmj mj Nugtmkgag. \clcs acs ousms lm fglg mkprmsg smamffbcjglg scj
mjtcjfms pgrtm lm ag kumstrg.
M`mrfbfbc 7
Ag lbrmftcrg lm ag msfumag lm jbgs Ag Gurcrg lmsmg fcjcfmr fujtgs jbgs lm ag fckujblgl jc
gsbstmj g fagsms. Ag fckujblgl tbmjm 288 dcngrms lbstrboublcs mj > fgsmrcs. Lmoblc g ag egatg lm
ecjlcs, pagjmg rmgabzgr ujg mjfumstg y jmfmsbtg fcjcfmr ma tgkgc lm su kumstrg.7. Wu lmom tckgr mj fumjtg pgrg rmgabzgr ujg kumstrg gamgtcrbg3
?. Wu lmom tckgr mj fumjtg pgrg rmgabzgr ujg kumstrg pcr fcjnackmrglcs3
6. Wu tbpc lm kumstrg am rmfckmjlgrg g ag lbrmftcrg pgrg rmgabzgr ag mjfumstg y pcr qu3
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
64/270=6Mstglstbfg Lmsfrbptbvg Vmkgjg 6
?.? Kumstrmc mstrgtbebfglc
Wu ms mstrgtbefglc3
Ag pgagorg mstrgtbfglc vbmjm lm mstrgtbfgfbj, trkbjc qum sm rmmrm g ag
fagsbfgfbj lm ujg pcoagfbj mj lbemrmjtms mstrgtcs c jbvmams. ]j mstrgtc c jbvma
tbmjm fgrgftmrstbfgs qum ac lbemrmjfbgj lma rmstc lm jbvmams.
Ag prbjfbpga eujfbj ga mstgoamfmr mstrgtcs c jbvmams ms fagsbfgr mamkmjtcs,
fbrfujstgjfbgs c emjkmjcs.
Fkc sm rmgabzg uj kumstrmc mstrgtbefglc3
Xgrg rmgabzgr uj kumstrmc mstrgtbfglc c pcr mstrgtc, sm lbvblm g ag pcoagfbj
mj nrupcs lm fgrgftmrstbfgs dckcnjmgs c sbkbagrms qum bjtmrmsgj pgrg ag
bjvmstbngfbj.
Vb ac qum sm qubmrm bjvmstbngr scj acs sgagrbcs mj Nugtmkgag, ag vgrbgoam
smrg sgagrbc.
Xgrg mstgoamfmr ag kumstrg, sm lbvblmj acs nrupcs pcr sus fgrgftmrstbfgs0
sgagrbc gatc, sgagrbc kmlbc y sgagrbc og`c. Fglg ujc lm mstcs nrupcs ms uj
mstrgtc.
Lm fglg mstrgtc sm smamffbcjg ujg kumstrg.
M`mkpac0
Vb sm qubmrm cotmjmr ma pmsc lm tclcs acs mstulbgjtms lm ujg msfumag, sm pumlm lbvblbr
g acs mstulbgjtms mj lcs mstrgtcs0 dckorms y ku`mrms. Lm fglg nrupc (mstrgtc) smsmamffbcjg ujg kumstrg ga gzgr pcr kmlbc lma kumstrmc gamgtcrbc sbkpam.
Ag prbjfbpga lbemrmjfbg mjtrm ma kumstrmc pcr
fcjnackmrglcs y ma kumstrmc mstrgtbfglc ms
qum mj ma prbkmrc pgsgj g ecrkgr pgrtm lm ag
kumstrg tclcs acs mamkmjtcs qum fcjecrkgj
ma fcjnackmrglc9 mj fgkobc, mj ma kumstrmc
mstrgtbfglc sm kumstrmgj acs mstrgtcs y sm
tckgj scagkmjtm ganujcs mamkmjtcs lm fglg
mstrgtc fckc pgrtm lm ag kumstrg.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
65/270=8 rcs _cs fcjtgkbjglcs 7? rcs
Xgrkmtrc(cotmjblclm ag pcoagfbj)
4= % lm acs rcsfcjtgkbjglcs
Mstglstbfc cmstglnrgec (cotmjblc
lm ag kumstrg)
48 % lm acs rcsfcjtgkbjglc
M`mkpac0
Ag lbemrmjfbg mjtrm uj mstglstbfc y uj pgrkmtrc ms lm ljlm sm cotbmjm.
Fugjlc sm cotbmjmj lgtcs y scac sm lmsfrbomj acs rmsuatglcs qum sm mjfcjtrgrcj,
sm utbabzgj acs kclmacs lm mstglstbfg lmsfrbptbvg.
Vb ma co`mtbvc ms nmjmrgabzgr ag kumstrg gpabfgjlc acs rmsuatglcs g ag pcoagfbj
tctga, acs kclmacs qum sm utbabzgj scj lm mstglstbfg bjemrmjfbga.
Ugrbgoam fugjtbtgtbvg0 pagjtgs lm fge fcj rcyg
Xcoagfbj 688 kujbfbpbcs Kumstrg 78 kujbfbpbcs
Kujbfbpbcs fcj fge
=8 888 rocams fcj
rcyg Fcj rcyg 6888 rocams
Xgrkmtrc75> (prckmlbc lm
rocams fcj rcyg pcrkujbfbpbc)
Mstglstbfc cmstglnrgec
Xrckmlbc lm 688rocams fcj rcyg
pcr kujbfbpbc
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
68/270=>Mstglstbfg Lmsfrbptbvg Vmkgjg 6
Ucfgouagrbc osbfc
mstglstbfc0 ms ag kmlblg cotmjblg lm ujg kumstrg fcj ma co`mtbvc lm mstbkgr c bjemrbr fgrgftmrstbfgs lm
ujg pcoagfbj c kclmac mstglstbfc.
mstrgtc0 fcj`ujtc lm mamkmjtcs fcj lmtmrkbjglcs fgrgftmrms fckujms, qum sm lbemrmjfbgj lm ctrcs
fcj`ujtcs.
bjemrmjfbg mstglstbfg0 ms ma prcfmsc lm sgfgr fcjfausbcjms lm ujg pcoagfbj, ogsjlcjcs mj acs
rmsuatglcs cotmjblcs lm ujg kumstrg.
kumstrmc pcr fcjnackmrglcs0 ms uj kumstrmc gamgtcrbc lcjlm fglg fcjnackmrglc lm kumstrmc
fckprmjlm g vgrbgs ujblglms. Ag kumstrg sm cotbmjm smamffbcjgjlc fcjnackmrglcs pcr uj ktclc lm
kumstrmc gamgtcrbc sbkpam.
kumstrmc mstrgtbefglc0ms gquma mj ma qum sm lbvblm ag pcoagfbj mj suopcoagfbcjms c mstrgtcs, lm
gfumrlc fcj frbtmrbcs qum pumlmj smr bkpcrtgjtms mj ma mstulbc c bjvmstbngfbj. Xcstmrbcrkmjtm sm
rmgabzg uj kumstrmc gamgtcrbc sbkpam lm fglg mstrgtc.
pgrkmtrc0 ms ujg kmlblg qum rmprmsmjtg ujg fgrgftmrstbfg lm ujg pcoagfbj.
_msukmj
Ctrcs ktclcs lm kumstrmc gamgtcrbc scj0 kumstrmc pcr fcjnackmrglcs c rgfbkcs y kumstrmc
mstrgtbfglc.
Ma kumstrmc pcr fcjnackmrglcs sm rmgabzg prbkmrc lbvblbmjlc ag pcoagfbj mj smffbcjms c
fcjnackmrglcs y aumnc, smamffbcjgjlc acs fcjnackmrglcs ga gzgr. Vm utbabzg fckc kumstrg tclcs
acs mamkmjtcs lm acs fcjnackmrglcs smamffbcjglcs.
Ma kumstrmc mstrgtbefglcrmqubmrm qum prbkmrc sm fagsbqum ag pcoagfbj mj mstrgtcs c fagsms
smnj ags fgrgftmrstbfgs qum bjtmrmsgj pgrg ag bjvmstbngfbj. Aumnc, sm smamffbcjg ujg kumstrg lm
fglg mstrgtc. Mstm ktclc sm utbabzg fugjlc ms lbefba trgog`gr fcj ag pcoagfbj tctga.
Ag bjemrmjfbg mstglstbfgmstulbg fkc cotmjmr fcjfausbcjms nmjmrgams pgrg tclg ag pcoagfbj
g pgrtbr lma mstulbc lm ujg kumstrg. Gsbkbskc, mstulbg ma jbvma lm fcjgjzg lm acs rmsuatglcs
cotmjblcs.
Ma prckmlbcc pcrfmjtg`m cotmjblc lm ujg kumstrg sm aagkg mstglstbfc c mstglnrgec. ]j
mstglstbfc ms ujg kmlbfbj jukrbfg qum lmsfrbom ganujg fgrgftmrstbfg lm ujg kumstrg.
Vb ma prckmlbc c pcrfmjtg`m sm rmmrm g tclg ag pcoagfbj sm am lmjckbjg pgrkmtrc. ]jpgrkmtrc
ms ujg kmlbfbj jukrbfg qum lmsfrbom ganujg fgrgftmrstbfg lm ujg pcoagfbj.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
69/270=4BNM_ \gfgj
Xrmnujtg lm bjvmstbngfbj0 Wu pcrfmjtg`m lm pmrscjgs lm ag fckujblgl mst lm gfumrlc fcj ag
fcjstruffbj lm ag dblrcmaftrbfg3
Dbptmsbs0
]jblgl lm gjabsbs0
\bpc lm vgrbgoam0
Jbvma lm kmlblg0
Xcoagfbj0
Kumstrg0
\bpcs lm kumstrg0
Ks lma =8 % jc mst lm gfumrlc fcj ag fcjstruffbj lm ag dblrcmaftrbfg
Dgobtgjtms lm ag fckujblgl
Gfumrlc c jc fcj fcjstruffbj lm dblrcmaftrbfg
Fugabtgtbvg (tbmjm lcs fgtmncrgs0 gfumrlc, jc gfumrlc)
Jckbjga
\clcs acs dgobtgjtms lm ag fckujblgl
Acs dgobtgjtms lm ags fgsgs smamffbcjglgs g qubmjms sm dbzc ag prmnujtg
Vm smamffbcj sbstmktbfgkmjtm (sm mabnb ujg lm fglg = fgsgs), y pcr fcj-nackmrglcs(sm cotuvc nrupcs lm pmrscjgs, mj fglg fgsg).Ma pcrfmjtg`m (%) ms uj mstglstbfc pcrqum sm cotuvc lm ujg kumstrg
Ugrbgoam0
M`mrfbfbc nubglc
Gjtms lm bjbfbgr acs m`mrfbfbcs, rmpgsm acs fcjfmptcs fcj mstcs m`mkpacs.
G. Vm qubmrm mstulbgr qu pbmjsgj acs dgobtgjtms lm ag galmg Fdgj Fdgj scorm ag fcjstruffbj lm ujgdblrcmaftrbfg mj su fckujblgl. Xgrg dgfmrac smamffbcjgj 68 fgsgs lm ag fckujblgl, mj ujg lm fglg
= sm dgfm ag prmnujtg0 mst ustml lm gfumrlc fcj qum sm fcjstruyg ag dblrcmaftrbfg3
Fckc ma co`mtbvc ms lmtmrkbjgr ma nrglc lm gfumrlc lm tclg ag fckujblgl, sm utbabzgr mstglstbfgbjemrmjfbga.
O. Ma FCK]LMlma kujbfbpbc lm Vgj Kgjuma Fdgpgrrj, @gagpg, lmsmg fcjcfmr ma bjnrmsc sgagrbga lm acs
`mems(gs) lm dcngr lma kujbfbpbc. \gjtc lma rmg rurga fckc urogjg, sm smamffbcjgj =8 dcngrms (tctga788), utbabzgjlc jkmrcs gamgtcrbcs.
Ma lgtc qum sm cotmjlr ms uj mstglnrgecc mstglstbfc(sm cotmjlr lm ag kumstrg). Vm utbabzgr ms-tglstbfg bjemrmjfbga. (Vm qubmrm sgomr ma sgagrbc lm acs `mems(gs) lm dcngr lma kujbfbpbc g pgrtbr lm agkumstrg).
Xrmnujtg lm bjvmstbngfbj0 Fua ms ma bjnrmsc sgagrbga prckmlbc lm acs `mems(gs) lm dcngr lma kujbfbpbc3
Dbptmsbs0
]jblgl lm gjabsbs0
\bpc lm vgrbgoam0
Xcoagfbj0
Kumstrg0
\bpcs lm kumstrg0
Vmamffbj lm kumstrg0
Ma bjnrmsc sgagrbga prckmlbc ms kgycr g W?,=88.88 kmjsugams
@mem(g) lm dcngr
Bjnrmsc sgagrbga c sgagrbc
Fugjtbtgtbvg
@mems(gs) lm dcngr lma kujbfbpbc lm Vgj Kgjuma Fdgpgrrj
Acs 788 mems(gs) lm dcngr smamffbcjglcs (cosmrvm qum jcscj acs dcngrms)
Ag pcoagfbj sm lbvblb mj lcs mstrgtcs0 urogjc y rurga
Gamgtcrbg sbkpam (jkmrcs gamgtcrbcs)
Ugrbgoam0
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
70/270=2Mstglstbfg Lmsfrbptbvg Vmkgjg 6
Gftbvblgl 7
Vm dgr ujg bjvmstbngfbj scorm ag fgablgl lm fge prclufblc mj ags jfgs lm ks lm ujg kgjzgjg mj
ma kujbfbpbc lm Vgj Gjtcjbc ag Xgz. Ma fge sm fagsbfgr fckc0 kuy oumjc, oumjc, rmnuagr y kgac. Xgrgdgfmrac sm smamffbcjgj 68 jfgs qum sm mjfumjtrgj g jc ks lm 78 ik lma fgsfc urogjc, pcr smr ags lm
ks efba gffmsc.
7. Xrmnujtg lm bjvmstbngfbj0
?. Dbptmsbs0
6. ]jblgl lm gjabsbs0
. Fua ms ag pcoagfbj3
4. Fua ms ag kumstrg3
2. Ma pcrfmjtg`m lm kuy oumjc, oumjc, rmnuagr y kgac, ms uj mstglstbfc c uj pgrkmtrc3
78. Wu tbpc lm mstglstbfg sm utbabzgr3
Gutcfcjtrca
Gftbvblgl ?
Mj ujg bjvmstbngfbj scorm ag fgjtblgl lm amfdm qum lgj ags vgfgs mj ag galmg Vgj Ergjfbsfc @cfctga sm
mjfcjtr qum ma prckmlbc lm ag kumstrg smamffbcjglg eum lm 72 abtrcs lbgrbcs. Ag kumstrg sm smamffbcj
fcjtgjlc ujg lm fglg 78 vgfgs qum sm mjfcjtrgogj pgstgjlc mj acs fcrrgams lm ag galmg.
7. Xrmnujtg lm bjvmstbngfbj0
?. Dbptmsbs0
6. ]jblgl lm gjabsbs0
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
71/27058BNM_ \gfgj
_mvbsm su gprmjlbzg`m
Kgrqum fcj uj fdmqum ag fgsbaag qum km`cr bjlbqum su rmjlbkbmjtc. acnrglcmj
prcfmscjc
acnrglc
Lmspuslmmstulbgr... Fcjczfc acs pgscs pgrg rmgabzgr ujg mjfumstg.
Gpabfc ma usc lm kumstrmc pcr fcjnackmrglcs.
Gpabfc ma usc lm kumstrmc mstrgtbebfglc.
Lbemrmjfbc mjtrm mstglstbfg lmsfrbptbvg y mstglstbfg bjemrmjfbga.
_mfcjczfc sb uj lgtc ms uj mstglstbfc c uj pgrkmtrc.
Kbjbstmrbc lm Mlufgfbj (KBJML]F)
Ma Kbjbstmrbc lm Mlufgfbj rmfcamftg pmrblbfgkmjtm lgtcs lm tclcs acs mstgoamfbkbmjtcs mlufgtbvcs
lma pgs (cfbgams, prbvglcs, kujbfbpgams y pcr fccpmrgtbvg), lm tclcs acs jbvmams mlufgtbvcs (prbkgrbg,
smfujlgrbg y lbvmrsbfglc). Ma prcfmsgkbmjtc lm ag bjecrkgfbj rmfcamftglg prcvmm ga Kbjbstmrbc lm
Mlufgfbj y usugrbcs mj nmjmrga, bjecrkgfbj gftugabzglg, fcjgoam y cpcrtujg, pgrg ag tckg lm
lmfbsbcjms, mjtrmng lm smrvbfbcs lm gpcyc, lmjbfbj lm pcatbfgs y lbsmc lm pagjbfgfbj lm ag
mlufgfbj jgfbcjga.
Vb lmsmg fcjcfmr lgtcs scorm ma mstglc lm ag mlufgfbj mj Nugtmkgag, vbsbtm ag pnbjg lma Kbjbstmrbc lm
Mlufgfbj0 www.kbjmluf.nco.nt
Jgvmnum mj ag rml...
5. Fua ms ag pcoagfbj3
>. Fua ms ag kumstrg3
4. Fkc sm smamffbcj ag kumstrg3
2. Ma prckmlbc lm 72 abtrcs, ms uj mstglstbfc c uj pgrkmtrc3
78. Wu tbpc lm mstglstbfg sm utbabzgr3
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
72/27057Mstglstbfg Lmsfrbptbvg Vmkgjg = j; 5?
% ;5?
7>= 788 ; 8.6==7=88 788 ; 8.?= 788 ; ?= %
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
77/27055BNM_ \gfgj
M`mrfbfbc nubglc
Amg ag sbnubmjtm jctbfbg qum gpgrmfb mj uj pmrblbfc lma pgs. Aumnc, fcrrcocrm ags cpmrgfbcjms pgrg
sgomr fkc sm mstgoamfb ma pcrfmjtg`m qum bjlbfg ma ttuac lm ag jctbfbg.
Eumjtm0maXmrblbfc, 6 kgyc ?87Mstglstbfg Lmsfrbptbvg Vmkgjg 575
Dumdumtmjgjnc 7 ?8< 6? 72?
Fdbkgatmjgjnc 5
Vufdbtmpqumz =?< 8=2
\ctcjbfgpj =85 =6>
Vcaca
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
79/27054BNM_ \gfgj
?.7 Mamkmjtcs lm ags tgoags
Ags tgoags tgkobj sm fcjcfmj fckc fuglrcs. Ms bkpcrtgjtm tckgr mj fumjtgqum fugjlc sm rmgabzg uj trgog`c mj ma qum sm prmsmjtgj tgoags c fuglrcs,sbmkprm sm lmom lmfblbr qu smffbcjms vg g fcjtmjmr.
g. Jkmrc lm tgoag Mj uj lcfukmjtc, tclgs ags tgoags lmomj smr jukmrglgs fcrrmagtbvgkmjtmpgrg qum smg efba blmjtbebfgrags. Xgrg blmjtbebfgrags sm pumlmj utbabzgr jkmrcsc amtrgs, tga fckc gpgrmfm mj ma m`mkpac lm ag pnbjg gjtmrbcr.
o. \tuac lm ag tgoag
\clg tgoag aamvg uj ttuac qum lmom fcjtmstgr g ags prmnujtgs0 qu, fkc,ljlm y fujlc. Ma ttuac lm ag tgoag gjtmrbcr fcjtmstg g ags prmnujtgssbnubmjtms0
Wu3 Ms ujg tgoag lm pcoagfbj. Acs jkmrcs qum fcjtbmjm ag tgoag
fcrrmspcjlmj g ag pcoagfbj lm fglg lmpgrtgkmjtc.
Fkc3Vcj ags vgrbgoams qum mstj mj ag tgoag9 mj mstm fgsc, lmpgrtgkmjtcslm Nugtmkgag.
Ljlm3Vm rmebmrm ga aungr mj lcjlm sm lbmrcj acs lgtcs, mj mstm fgsc,Nugtmkgag.
Fujlc3Vm rmebmrm g ag emfdg, gc, kms c pcfg mj qum sm lbmrcj acslgtcs9 mj mstm fgsc, ?876.
f. Eumjtm
Xgrg qum ag bjecrkgfbj lm ujg tgoag tmjng frmlbobablgl, ms kuy bkpcrtgjtmbjlbfgr lm ljlm sm cotuvbmrcj acs lgtcs. ]sugakmjtm sm msfrbom ag pgagorg"eumjtm" y aumnc sm bjlbfg lm ljlm sm cotuvc ag bjecrkgfbj. Mj ma m`mkpacgjtmrbcr, ag eumjtm ms ma Bjstbtutc Jgfbcjga lm Mstglstbfg (BJM).
Ganujgs vmfms, acs lgtcs prcvbmjmj lm mjfumstgs qum rmgabzg ma bjvmstbnglcr.Mj mstcs fgscs, sm fcacfg fckc eumjtm ujg mxpabfgfbj fckc ag sbnubmjtm0"Magocrgfbj prcpbg fcj lgtcs lm mjfumstg".
l. \tuacs lm ebag y fcaukjg
Vcj acs tmxtcs qum lmsfrbomj acs fcjtmjblcs lm ags ebags c fcaukjgs. Mj mam`mkpac gjtmrbcr, acs ttuacs lm fcaukjg scj "Lmpgrtgkmjtc" y "Xcoagfbjsmnj BJM" y ma jckorm lm fglg lmpgrtgkmjtc ms ma ttuac lm ebag.
m. Fmalgs lm bjecrkgfbj
Ags fmalgs lm bjecrkgfbj fcjtbmjmj acs lgtcs (pcr m`mkpac, ma jkmrc lmdgobtgjtms).
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
80/27052Mstglstbfg Lmsfrbptbvg Vmkgjg 74.64 % ?588 6=.>6 % 626> =7 2.?? % 2> 7.66 % >54 78.== %
Nugtmkgag. ?885
M`mkpac0
Ma BJM rmgabzg pmrblbfgkmjtm ujg mjfumstg lm fcjlbfbcjms lm vblg g jbvmajgfbcjga. Mj mstg mjfumstg sm rmfcnm ag bjecrkgfbj sbnubmjtm0
Ag prcfmlmjfbg lma mjfumstglc, ms lmfbr, sb ms dgobtgjtm lma rmg urogjg
c rurga.
Ag sbtugfbj mfcjkbfg lma mjfumstglc, sb pmrtmjmfm g ganujg lm agssbnubmjtms fgtmncrgs0 jc pcorm c pcorm mxtrmkc.
Mstcs lgtcs sm gnrupgj pcr prcfmlmjfbg y fgtmncrg. Aumnc, sm fgafuagj fckcpcrfmjtg`ms. \clg mstg bjecrkgfbj sm prmsmjtg mj ujg tgoag fckc ag sbnubmjtm0
Acs lgtcs lma m`mkpac gjtmrbcr scj rmgams y sm cotuvbmrcj lm ujg mjfumstg lmaBJMlma gc ?885.
Mamkmjtcs lm ag tgoag0
Xmrscjgs
Jc pcorm, pcorm mxtrmkc
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
81/270>8BNM_ \gfgj
M`mrfbfbc 6Lm ags mstbkgfbcjms y prcymffbcjms lm pcoagfbj lma Bjstbtutc Jgfbcjga lm Mstglstbfg (BJM) sm
cotbmjmj acs sbnubmjtms lgtcs pgrg ma lmpgrtgkmjtc lm @utbgpg0 lma tctga lm ag pcoagfbj, ma .8 %scj dckorms y =6.8 % scj ku`mrms. Acs dgobtgjtms scj kgycrbtgrbgkmjtm lma rmg rurga, lmoblc gqum ma 5>.6 % lm ags pmrscjgs dgobtgj mj msg rmg.
7. Fcj acs lgtcs lm smxc, fckpamtm ag sbnubmjtm tgoag0
?. Fcj acs lgtcs lma rmg lcjlm vbvmj ags pmrscjgs, fckpamtm ag sbnubmjtm tgoag.
\goag 7.Xcrfmjtg`m lm dgobtgjtms pcr smxc. @utbgpg, ?88?
Vmxc Xcrfmjtg`m
Ku`mr
Dckorm
Eumjtm0 Bjstbtutc Jgfbcjga lm Mstglstbfg
\goag ?.
Xcrfmjtg`m lm dgobtgjtms pcr rmg lcjlm dgobtg. @utbgpg, ?88?rmg Xcrfmjtg`m
_urga
]rogjg
Eumjtm0 Bjstbtutc Jgfbcjga lm Mstglstbfg
Gjabsbs lm ag tgoag
Acs lgtcs lm ujg tgoag sbrvmj pgrg rmgabzgr gjabsbs scorm ag bjecrkgfbj qum smprmsmjtg.
Fcj rmspmftc g ag bjecrkgfbj lm ag \goag ?, lma tctga lm pmrscjgs mjtrmvbstglgs,mj ma rmg rurga ag kgycrg mst rmnbstrglg mj ag fgtmncrg jc pcorm y mj ma rmg
urogjg, tgkobj ag kgycrg mst rmnbstrglg mj ag fgtmncrg jc pcorm.Lm tclcs acs mjtrmvbstglcs, ma =
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
82/270>7Mstglstbfg Lmsfrbptbvg Vmkgjg ?BNM_ \gfgj
\goag 7Fckpcrtgkbmjtc lma gjgaegomtbskc pcr lmpgrtgkmjtc. Nugtmkgag, ?87?
(ergnkmjtc)
Flbnc Lmpgrtgkmjtc\ctga
Xcoagfbj lm7= gcs y ks
Xcoagfbjgjgaegomtg
Xcrfmjtg`mlm gjgaegomtbskc
87 Nugtmkgag ? 744 >>5 77
86 Vgfgtmpqumz ?8? =58 ?6 87 7=2 827
8= @gagpg 7>5 67?
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
84/270>6Mstglstbfg Lmsfrbptbvg Vmkgjg >?2 ?52 =7.?= %
Dckorm > 6=6 =5?
\ctga 7= 84? 467 788 %
Eumjtm0 dttp0//www.lgtcskgfrc.fck/lmkcnrgg/pcoagfbcj/nugtmkgag
Ma pcrfmjtg`m lm pcoagfbj lm ku`mrms sm fgafua lbvblbmjlc ma jkmrc lm ku`mrms, qum ms> >?2 ?52 mjtrm ma tctga lm ag pcoagfbj qum ms 7= 84? 467, y sm kuatbpabf pcr 788.
> >?2 ?527= 84? 467
; 8.=7?= 8.=7?= 788 ; =7.?= %
Gdcrg, fgafuam ma pcrfmjtg`m lm pcoagfbj lm dckorms y fcacqum ma lgtc mj ag fgsbaag fcrrmspcjlbmjtm.
_msumavg ma m`mrfbfbc, fgafuagjlc ma pcrfmjtg`m lm pcoagfbj lm dckorms.
Gftbvblgl 6
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
86/270
Mstglstbfg Lmsfrbptbvg Vmkgjg =
>=
Fafuac lm pcrfmjtg`ms mj tgoags
Wu mjfcjtrgr mstg smkgjg3
@vmjms y tmfjcacng
Fafuac lm pcrfmjtg`ms mj tgoags mstglstbfgs
Mstg smkgjg acnrgr0
Gjgabzgr lgtcs lm pcrfmjtg`ms prmsmjtglcs mj tgoags.
Fgafuagr pcrfmjtg`ms fcj lgtcs lm ujg tgoag.
Magocrgr tgoags fcj pcrfmjtg`ms.
=
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
87/270
BNM_ \gfgj
>5
Xgrg fckmjzgr!
Mj ujg mjfumstg rmgabzglg mj ma gc ?877, sm prmnujt g `vmjms gfmrfg lm ag utbablgl lm ags rmlms
scfbgams. Acs lgtcs cotmjblcs bjlbfgj qum ma >4 % utbabzg ags rmlms scfbgams pgrg fckujbfgfbj fcj
gkbstglms y gpmjgs ma ?? % pgrg dgfmr tgrmgs c trgog`cs fcj jms lm mstulbc.
R ustml, qu uscs am lg ga Bjtmrjmt3 Bjtmjtm mxprmsgrac mj pcrfmjtg`ms.
Mj Nugtmkgag, ma 54.2 % lm acs `vmjms lm 7= g ?2 gcs tbmjm uj fmauagr. Vbj mkogrnc, mj mstm smftcr
lm ag pcoagfbj pclmkcs jctgr lbemrmjfbgs smnj ma njmrc y ma nrupc tjbfc. Umgkcs0 Ma >6.= % lm acs
dckorms fumjtg fcj uj fmauagr, kbmjtrgs qum mj ma fgsc lm ags ku`mrms scac ma 5=.< % tbmjm ujc. Xcr
ctrg pgrtm, mjtrm ag pcoagfbj bjlnmjg scac ma =4 % fumjtg fcj fmauagr, kbmjtrgs qum mj ag pcoagfbj jc
bjlnmjg ma pcrfmjtg`m gukmjtg g >
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
88/270
Mstglstbfg Lmsfrbptbvg Vmkgjg =
>>
7. \goags lm pcrfmjtg`ms
Gjtms lm pcjmr kgjcs g ag corg, dgy qum rmfcrlgr qum ags tgoags mstj ecrkglgs pcr
fcaukjgs,eags yfmalgs.Mj prbkmr aungr, pclrmkcs cosmrvgr ags fcaukjgs lm ujgtgoag sb pgsgkcs jumstrg vbstg mj smjtblc vmrtbfga9 ms lmfbr, lm grrbog dgfbg gog`c ().
Ga dgfmr mstm m`mrfbfbc vmrmkcs fagrgkmjtm ags fcaukjgs, `ustc fckc sm fcacfgj ags
fcaukjgs mj ags fcjstruffbcjms lm ags fgsgs, mlbfbcs, pgagfbcs, mtf. Fglg fcaukjg sm
utbabzg pgrg gnrupgr bjecrkgfbj lm lbstbjtc tbpc lm kgjmrg crlmjglg. Gs sm egfbabtg ag
fckprmjsbj lm acs lgtcs qum jcs smrvbrj pgrg rmgabzgr fafuacs y aumnc gjabsbs.
Mj smnujlc aungr, agseags fcjtbmjmj bjecrkgfbj fcacfglg lm ecrkg dcrbzcjtga (),
ms lmfbr, lm ag kbskg kgjmrg qum sm vmj ags ags lm jbcs y jbgs mj ags msfumags c acs
surfcs lm ags sbmkorgs.
Xcr atbkc, agsfmalgssmrgj fckc acs aglrbaacs lm ujg pgrml, mj mstm fgsc msg pgrml msjumstrg tgoag. Fcj ags fmalgs sm ecrkgj ags fcaukjgs y ags ags, fglg ujg fcjtbmjm uj
lgtc, fckc pcr m`mkpac0 mlgl, smxc, jckorm, fgjtblgl, pcrfmjtg`m, mjtrm ctrcs.
Jc cavblm qum mj ags tgoags lmomkcs dgfmr ujg sukg fcj acs lgtcs jukrbfcs lm fglg
fcaukjg pgrg fgafuagr acs tctgams, pums mstg bjecrkgfbj ms jmfmsgrbg pgrg ma fafuac
lm pcrfmjtg`ms.
Gdcrg s, kgjcs g ag corg0 vmg fkc sm fgafuagj acs pcrfmjtg`ms mj ujg tgoag. Xgrg fgafuagr
acs pcrfmjtg`ms lm ags fmalgsqum ecrkgj ujg tgoag sm utbabzg ag sbnubmjtm erkuag0
Mstglc fbvba Mjtrmvbstglcs Xcrfmjtg`m
Vcatmrc ?=5 = %
Lbvcrfbglc 64 >.?2 %
]jblc 7= ?.44 %
\ctga =?7 788 %
% ;Ugacr lm ag fmalg
\ctga 788
Ma kujlc lm ag mstglstbfg
Mj ags prxbkgs pnbjgs gprmjlmrmkcs fkc gpabfgr mstg erkuag pgrg cotmjmr
pcrfmjtg`ms mj ujg tgoag.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
89/270
BNM_ \gfgj
>4
M`mrfbfbc 7Xgrg br mjtmjlbmjlc km`cr, pgsmkcs g ag prftbfg. G fcjtbjugfbj, am prmsmjtgkcs bjecrkgfbj tckglg
lm ag pnbjg lm Mkprmsgrbcs pcr ag Mlufgfbj(www.mkprmsgrbcspcragmlufgfbcj.crn).
Amg ags tgoags qum sm mjfumjtrgj g fcjtbjugfbj y trgtm lm blmjtbfgr acs mamkmjtcs lm ags tgoags qum
yg dmkcs mstulbglc.
=.
?.7.
6.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
90/270
Mstglstbfg Lmsfrbptbvg Vmkgjg =
>2
M`mrfbfbc ?Amg ag tgoag qum gpgrmfm g fcjtbjugfbj. Cosmrvm qum acs lgtcs mstj prmsmjtglcs jbfgkmjtm mj
pcrfmjtg`ms pgrg egfbabtgr ag fckpgrgfbj mjtrm ags vgrbgoams.
\goag ?0 Lmsmkpmc nrglugjlcs pcr fgrrmrg mj Amfturg y Kgtmktbfg (tclcs acs smftcrms)
Gjgabfm acs lgtcs lm ag tgoag, rmspcjlg ag prmnujtg y fckpamtm ag tgoag.
7. Fua ms ag ujblgl lm gjabsbs3
?. Fcj ag bjecrkgfbj lm ag tgoag gjtmrbcr, bjfauyg mj ma fuglrc sbnubmjtm ags fgtmncrgs lm gjabsbs.
Am prcpcrfbcjgkcs ags vgrbgoams.
Ugrbgoam Fgtmncrgs
Fgrrmrg
Xrumogs lm mvgaugfbj
Gc lm ags prumogs
Lmsmkpmc
Eumjtm0 dttp0//www.mkprmsgrbcspcragmlufgfbcj.crn/ms/mstglbstbfgs.pdp
Gc LmsmkpmcOgfdbaamrgtc Kgnbstmrbc Xmrbtc Vmfrmtgrbglc \fjbfc
Amfturg Kgtmktbfg Amfturg Kgtmktbfg Amfturg Kgtmktbfg Amfturg Kgtmktbfg Amfturg Kgtmktbfg
?88=Acnrc 7>.6% ?5.=% 7=.5% 4.?% 7?.4% 7% =.7% 77.8% 72.8%
Jc acnrc 4?.4% >6.=% 42.2% 2=.=% >% 28.=%
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
91/270
BNM_ \gfgj
48
?. Fafuac lm pcrfmjtg`ms mj tgoagsmstglstbfgs
Gjgabfmkcs pgsc g pgsc fkc fgafuagr pcrfmjtg`ms mj tgoags mstglstbfgs.
M`mkpac 70
Vmnj ag Mjfumstg lm Fcjlbfbcjms lm Ublg ?885 lma Bjstbtutc Jgfbcjga lm
Mstglstbfg, mj ujg kumstrg lm >?>5 mjfumstglcs sm cotuvbmrcj mstcs lgtcs0
626> jc pcorms, >54 pcorms mxtrmkcs y ?=>7 pcorms jc mxtrmkcs.
7. Crngjbzgr ag bjecrkgfbj mj ujg tgoag, ms lmfbr mj ebags y fcaukjgs,
bjfauymjlc sus ttuacs y ma fafuac lma tctga.
Jbvma lm pcormzg Fgjtblgl
Jc pcorms 626>
Xcorms mxtrmkcs >54
Xcorms jc mxtrmkcs ?=>7
\ctga >?>5
?. Fgafuagr acs pcrfmjtg`ms, pgrg fgafuagr ma pcrfmjtg`m lm fglg fmalg sm lbvblm
fglg lgtc mjtrm ma vgacr tctga, mj mstm fgsc >?>5, yg qum fcjstbtuym ma 788 %. Xcr
mstg rgzj, mj ag tgoag qum mst ga ebjga lm ag pnbjg gnrmngkcs ctrg fcaukjg
tbtuaglgpcrfmjtg`my fckprcogkcs qum ga sukgr acs pcrfmjtg`ms cotmjlrmkcs
ma 788 %.
Mjtcjfms utbabzgjlc ag erkuag qum yg fcjcfmkcs, acs rmsuatglcs qumlgrgj gs0
Xgrg ag prbkmrg fmalg
Xgrg ag smnujlg fmalg
Xgrg ag tmrfmrg fmalg
%;626>
>?>5788 ; 8.=?>5788 ; 8.78=5 788 ; 78.=5%
%;?=>7
>?>5788 ; 8.6=66 788 ; 6=.66%
Jbvma lm pcormzg Fgjtblgl Xcrfmjtg`m
Jc pcorms 626> =54 78.=5 %
Xcorms jc mxtrmkcs ?=>7 6=.66 %
\ctga >?>5 788 %
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
92/270
Mstglstbfg Lmsfrbptbvg Vmkgjg =
47
6. Fcacfgr ma ttuac y ag eumjtm lm ag tgoag, lgtcs bkpcrtgjtms pgrg bjlbfgr lm
qu sm trgtg ag bjecrkgfbj qum sm mst utbabzgjlc, qu vgrbgoams sm lmtgaagj,
fujlc sufmlbmrcj acs lgtcs, mj qu pgs, lmpgrtgkmjtc, kujbfbpbc c galmg
y pcr atbkc lm ljlm cotuvbkcs ag bjecrkgfbj, yg smg lm ujg bjstbtufbj,
mjfumstg, mtf.
Jbvma lm pcormzg Fgjtblgl Xcrfmjtg`m
Jc pcorms 626> =54 78.=5 %
Xcorms jc mxtrmkcs ?=>7 6=.66 %
\ctga >?>5 788 %
\goag ?
Dgobtgjtms pcr jbvma lm pcormzg y pcrfmjtg`ms. Nugtmkgag, ?885
Eumjtm0 Bjstbtutc Jgfbcjga lm Mstglstbfg
M`mkpac ?0
G fcjtbjugfbj mjfcjtrgr ma fuglrc lm pcoagfbj cfupglg smnj ma smxc, mlgl,
nrupc tjbfc, pcsbfbj mj ma dcngr y mstglc fcjyunga0
Eumjtm0 Bjstbtutc Jgfbcjga lm Mstglstbfg
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
93/270
BNM_ \gfgj
4?
Fckc pclmkcs cosmrvgr, ma fuglrc lm ag pnbjg gjtmrbcr fcjtbmjm ogstgjtm
bjecrkgfbj. Mjtcjfms pgrg mkpmzgr dgrmkcs ujg tgoag, tckgjlc jbfgkmjtm
ag vgrbgoam "smxc" lma tctga lm ag pcoagfbj jgfbcjga.
Mjtcjfms, sbnubmjlc acs pgscs vbstcs, prbkmrc sm mxtrgm ag bjecrkgfbj qum
bjtmrmsg, sm crlmjg mj ags y fcaukjgs, sm fgafuag ma tctga lm dckorms y ku`mrms,
sm gnrmng ujg fcaukjg tbtuaglg Xcrfmjtg`m, sm gpabfg ag erkuag, sm gjctgj acs
rmsuatglcs fcj ma skocac lm pcrfmjtg`m y jgakmjtm sm fcacfg ma ttuac y ageumjtm lm ag tgoag.
Vmxc \ctga jgfbcjga Xcrfmjtg`m
Dckorm 6 >=8 822 5
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
94/270
Mstglstbfg Lmsfrbptbvg Vmkgjg =
46
%;Ugacr lm ag fmalg
\ctga 788
Ma pcrfmjtg`m ms tba pgrg fckpgrgr fgjtblglms. Mj ganujgs tgoags mstglstbfgs sm prmsmjtgj ags
fgjtblglms tctgams gfckpgglgs lm acs pcrfmjtg`ms pgrg qum pclgkcs fckpgrgrags y fckprmjlmr acs
lgtcs lm kgjmrg ks rpblg y smjfbaag.
Xgrg fgafuagr acs pcrfmjtg`ms lmjtrc lm ujg tgoag, sm gpabfg ag sbnubmjtm erkuag0
% ;Ugacr lm ag fmalg
\ctga 788
_msukmj
Ucfgouagrbc osbfc
fmalg0 ms ag ujblgl osbfg lm ujg tgoag, lcjlm sm bjtrclufmj lgtcs, vgacrms y erkuags.
fcaukjg0 fmalgs uobfglgs mj ecrkg vmrtbfga mj ujg tgoag.
eag0 fmalgs uobfglgs mj ecrkg dcrbzcjtga mj ujg tgoag.
eumjtm0sm rmmrm ga aungr c bjstbtufbj lm lcjlm sm cotuvbmrcj acs lgtcs. Vb ustml rmfcpba acs lgtcs,
mjtcjfms ag eumjtm lmom lmfbr0 magocrgfbj prcpbg.
pcrfmjtg`m0mxprmsg ag prcpcrfbj lm ujblglms lm fglg fbmj.
ttuac0ma ttuac lmom bjlbfgr qu, fkc, ljlm y fujlc sm cotuvbmrcj acs lgtcs prmsmjtglcs. Ma ttuac
tgkobj fcjtbmjm ma jkmrc qum ag tgoag tbmjm lmjtrc lma bjecrkm c bjvmstbngfbj, smnj ma crlmj mj
qum gpgrmfm.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
95/270
BNM_ \gfgj
4 7>
4 77 ??
7? 7= ?6
75 72 ?6
7. G fcjtbjugfbj sm prmsmjtgj acs lgtcs lm ag pcoagfbj bjegjtba y `uvmjba lm ag galmg Ma \goaj. Fgafuam
ma pcrfmjtg`m lm pmrscjgs lm fglg mlgl.
Gftbvblgl 7
Eumjtm0 Magocrgfbj prcpbg
\goag ?Umjtg lm vmdfuacs jumvcs mj Nugtmkgag. Mjmrc @ujbc ?878
?. Ag tgoag qum sm prmsmjtg g fcjtbjugfbj kumstrg ag fgjtblgl lm vmdfuacs jumvcs vmjlblcs mj
Nugtmkgag mj ma prbkmr smkmstrm lm ?878. Fcj acs lgtcs lm mstg tgoag fgafuam acs pcrfmjtg`ms.
Kgrfg Fgjtblgl Xcrfmjtg`m
Ibg 2=8
Jbssgj 27=
Kgzlg >85
Dyujlgb 77?7
\cyctg ??28
Eumjtm0 Vupmrbjtmjlmjfbg lm Ogjfcs
Gutcfcjtrca
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
96/270
Mstglstbfg Lmsfrbptbvg Vmkgjg =
4=
\goag 6_msuatglcs mj ag prumog lm Wukbfg
_msuatglcs Fgjtblgl Xcrfmjtg`m
Gprcoglcs ?>
_mprcoglcs 7?
\ctga 62
Amg acs fgscs sbnubmjtms y rmgabfm ags gftbvblglms.
7. ]j fgtmlrtbfc lm qukbfg gpabf ag prumog pgrfbga g acs mstulbgjtms. Mstcs eumrcj acs rmsuatglcs0 ?>
gaukjcs gprcogrcj y 7? rmprcogrcj.
Mjfumjtrm ma pcrfmjtg`m pgrg fglg fgsc y msfrogac mj ag fcaukjg lm ag tgoag sbnubmjtm.
Gftbvblgl ?
Eumjtm0 Magocrgfbj prcpbg
g. Xcrfmjtg`m lm mstulbgjtms gprcoglcs0
o. Xcrfmjtg`m lm mstulbgjtms rmprcoglcs0
Vmxc lm acs mstulbgjtms Fgjtblgl Xcrfmjtg`m
?. Ag fagsm lm 6. prbkgrbg lm ag msfumag "Ma Vgomr" dgr ujg mxfursbj ga zccanbfc Ag Gurcrg. Gjtms
lm suobr ga ous, ag kgmstrg fumjtg g acs gaukjcs qum tbmjmj pmrkbsc lm sus pglrms pgrg dgfmr mstg
vbsbtg. Jmfmsbtg sgomr fujtcs jbcs y fujtgs jbgs brj pgrg jc pmrlmracs lm vbstg mj ma zccanbfc.
Mstc ms bkpcrtgjtm, pums jc g tclcs acs gaukjcs lm msg fagsm rmgabzgrj ag vbsbtg.
Ma fcjtmc lbc fckc rmsuatglc0 Jbgs0 7= Jbcs0 7?
Magocrm ujg tgoag tckgjlc mj fumjtg ma smxc lm acs mstulbgjtms. Aumnc, fgafuam ma pcrfmjtg`m lm
fglg nrupc.
\goag 5
Jbcs y jbgs qum gsbstbrj ga zccanbfc
g. Xcrfmjtg`m lm jbgs0 o. Xcrfmjtg`m lm jbcs0
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
97/270
BNM_ \gfgj
45
_mvbsm su gprmjlbzg`m
Kgrqum fcj uj fdmqum ag fgsbaag qum km`cr bjlbqum su rmjlbkbmjtc. acnrglcmj
prcfmscjc
acnrglc
Lmspuslmmstulbgr...
Gjgabzc lgtcs lm pcrfmjtg`ms prmsmjtglcs mj tgoags.
Fgafuac pcrfmjtg`ms fcj lgtcs lm ujg tgoag.
Magocrc tgoags fcj pcrfmjtg`ms.
Kbjbstmrbc lm Vgaul Xoabfg y Gsbstmjfbg Vcfbga (KVXGV)
Ma Kbjbstmrbc lm Vgaul fumjtg fcj ma Vbstmkg lm Bjecrkgfbj Nmrmjfbga mj Vgaul (VBNVG), qum rmfcamftg
lgtcs scorm ag sbtugfbj lm sgaul mj ma pgs, acs fugams crngjbzg y gjgabzg pgrg nmjmrgr bjecrkgfbj qum
ngrgjtbfm ag sgaul lm acs dgobtgjtms. Ubsbtm ag pnbjg0 ncc.na/nPn
Jgvmnum mj ag rml...
\bpc lm fckoustboam Fgjtblgl Xcrfmjtg`m
Amg ma sbnubmjtm fgsc y magocrm ujg tgoag fcj acs lgtcs scabfbtglcs.
6. Mj ag ngscabjmrg lm Lcj @uabc sm vmjlb mj ujg smkgjg0 28 ngacjms lm lbmsma, 7?8 ngacjms lm
ngscabjg rmnuagr, 48 ngacjms lm ngscabjg spmr.
g. Lbmsma0
o. Ngscabjg rmnuagr0
f. Ngscabjg spmr0
Xcrfmjtg`m lm fckoustboam vmjlblc0
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
98/270
Mstglstbfg Lmsfrbptbvg Vmkgjg 5
4>
Nrfgs mstglstbfgs
Wu mjfcjtrgr mstg smkgjg3 Vbstmkg lm fccrlmjglgs fgrtmsbgjgs
Nrebfgs mstglstbfgs
Mstg smkgjg acnrgr0
Acfgabzgr pujtcs mj uj sbstmkg lm fccrlmjglgs fgrtmsbgjgs.
]tbabzgr ag bjecrkgfbj lm ags tgoags pgrg fcjstrubr lbgnrgkgs lm ogrrgs, lmajmgs y fbrfuagrms.
Fgafuagr nrglcs pgrg magocrgr uj lbgnrgkg fbrfuagr.
Ugacrgr ma usc lm nrebfgs pgrg prmsmjtgr lgtcs mstglstbfcs.
5
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
99/270
BNM_ \gfgj
44
Xgrg fckmjzgr!
Vbstmkg lm fccrlmjglgs fgrtmsbgjgs
Ags fccrlmjglgs fgrtmsbgjgs tckgj su jckorm mj dcjcr g _mj Lmsfgrtms
(7=25 75=8), kgtmktbfc, acsec y esbfc ergjfs, fcjsblmrglc fckc ujc lmacs bjtmamftugams ks lmstgfglcs lm ag rmvcaufbj fbmjtfg. Lmsfgrtms eum ma
prbkmrc mj usgr uj pagjc fgrtmsbgjc, fuyg eujfbj ms uobfgr fugaqubmr pujtc
mj uj pagjc.
]j sbstmkg lm fccrlmjglgs fgrtmsbgjgssm fckpcjm lm lcs ajmgs pmrpmjlb-fuagrms, qum ecrkgj fugtrc rmgs aagkglgs fuglrgjtms.
Ma pujtc mj lcjlm sm `ujtgj c bjtmrsmfgj ags lcs ajmgs sm lmjckbjg crbnmj y sm
rmprmsmjtg fcj ma fmrc (8). Lm kgjmrg qum acs jkmrcs pcsbtbvcs sm mjfumjtrgj
dgfbg ag lmrmfdg y dgfbg grrbog lma crbnmj y acs jkmrcs jmngtbvcs dgfbg ag
bzqubmrlg y dgfbg gog`c lma crbnmj. Xcr mstg rgzj, ags lcs ajmgs c m`ms scj rmftgsjukrbfgs.
Ag ajmg qum vg mj lbrmffbj dcrbzcjtga,sm lmjckbjg m`mxy ag ajmg qum vg mjlbrmffbj vmrtbfgasm lmjckbjg m`my. Lm mstg fumjtg, ags fccrlmjglgs fgrtmsbgjgssmgagj uj pujtc qum sm fckpcjm lm lcs fccrlmjglgs, y sm rmprmsmjtg (x, y).
78
4
5
.>4
`ujbc ?876 >.4?
`uabc ?876 >.4?
gncstc ?876 >.4=
smptbmkorm ?876 >.27
cftuorm ?876 >.2=
jcvbmkorm ?876 >.4>
lbfbmkorm ?876 >.4=
mjmrc ?87< >.48
emormrc ?87< >.>=
kgrzc ?87< >.>6
Xgrg rmgabzgr ag nrebfg lmomkcs0
Magocrgr uj sbstmkg lm fccrlmjglgsfcj acs m`ms pcsbtbvcs, ga bnuga qum malbgnrgkg lm ogrrgs.
Fcacfgr acs vgacrms mj ma m`m (y) c vmrtbfga. Xgrg ac fuga ms jmfmsgrbc blmjtbebfgrfua ms ma vgacr kmjcr y fua ma kgycr, mj mstm fgsc ma kmjcr ms >.>6 y ma kgycr
ms >.2=. Lm kgjmrg qum ma m`m (y) lmomr gogrfgr mscs vgacrms mj su jukmrgfbj.
Xgrg qum sm vmg km`cr ag nrebfg ms fcjvmjbmjtm fcacfgr vgacrms qum tmrkbjmj
mj fmrc. Mj mstm fgsc pumlm smr lmslm >.>8 dgstg 4.88. Ac bkpcrtgjtm ms qum
acs vgacrms kgycr y kmjcr mstj fcjtmjblcs mj mstm m`m.
Eumjtm0 OGJN]G\
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
105/270
BNM_ \gfgj
2.27>.2=
>.4>>.4=
>.48
>.>=>.>6
>.48
>.2=
4.88
>.28
>.4=
>.48
>.>=
>.>8
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
106/270
Mstglstbfg Lmsfrbptbvg Vmkgjg 5
2=
7.6 Lbgnrgkg lm smftcrms, fbrfuagr c pgstma
Ma lbgnrgkg lm smftcrms ms ujc lm acs ktclcs nrfcs ks sbkpams, lglc
qum pgrmfm uj pgstma rmlcjlc fcrtglc mj pmlgzcs qum `ujtcs sukgj ma 788
pcr fbmjtc. Mstg nrfg ms kuy tba pgrg vbsugabzgr ags lbemrmjtms ermfumjfbgs fcj
rmspmftc g uj tctga. Acs pgscs pgrg fcjstrubr scj0
Magocrgr ujg tgoag, ga bnuga qum ags ctrgs nrebfgs sm pgrtm lm ujg tgoag, pcrac tgjtc amgkcs ag bjecrkgfbj lma fuglrc sbnubmjtm0
\goag 2Jkmrc lm pmrscjgs smnj ma jbvma lm pcormzg. Nugtmkgag, ?885
Jbvma lm pcormzg Fgjtblgl
Jc pcorms 626>
Xcorms mxtrmkcs >54
Xcorms jc mxtrmkcs ?=>7
\ctga >?>5
Eumjtm0 Bjstbtutc Jgfbcjga lm Mstglstbfg (BJM),Mjfumstg Jgfbcjga lm Fcjlbfbcjms lm Ublg ?885 (MJFCUB?885)
Gvmrbnugr qu pcrfmjtg`m fcrrmspcjlm g fglg ujg lm ags fgjtblglms.Xcr ac tgjtc, tmjlmrmkcs qum lbvblbr 626> (fgjtblgl) mjtrm >?>5 (tctga) y
kuatbpabfgrac pcr 788, qum lg fckc rmsuatglc = =54 78.== %
Xcorms jc mxtrmkcs ?=>7 6=.6< %
\ctga >?>5 788.88 %
Fgafuagr fujtcs nrglcs am fcrrmspcjlm g fglg pcrfmjtg`m,gpabfgjlc agerkuag sbnubmjtm0
Jc. lm nrglcs% lm fgtmncrg 658
788;
Jc. lm nrglcs;% lm fgtmncrg 658
788
=
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
107/270
BNM_ \gfgj
25
Jbvma lm pcormzg Fgjtblgl Xcrfmjtg`m Nrglcs
Jc pcorms 626> =54 78.== % 64
Xcorms jc mxtrmkcs ?=>7 6=.6< % 7?>
\ctga >?>5 788.88 % 658
\ckm mj fumjtg qum ag sukg lm acs nrglcs pumlm lgr uj jkmrc lbemrmjtm lm
658 pcr ags gprcxbkgfbcjms qum sm lgj, ac fuga jc bjlbfg jbjnj prcoamkg.
Xgrg trgzgr fglg smftcr dgy qum utbabzgr uj trgjspcrtglcr.
\rgzgr ujg fbrfujemrmjfbg y fcacfgr ujg ajmg ogsmmj fugaqubmr lbrmffbj.
Am gnrmngkcs ujg fcaukjg g ag tgoag mj ag qum msfrbobkcs acs nrglcs.
Fcacfgr ma trgjspcrtglcr y kmlbr dgfbg grrbog acs nrglcs9mj mstm prbkmrfgsc, 72=.
\rgzgr ag ajmg g acs 72= nrglcs y kcvmr ma trgjspcrtglcr dgfbg ag jumvgajmg ogsm y kmlbr acs sbnubmjtms nrglcs, (64).Fckc scac dgy trms fgtmnc-rgs, ag atbkg qumlgr fcj 7?> nrglcs, pcrqum ag sukg ms 658.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
108/270
Mstglstbfg Lmsfrbptbvg Vmkgjg 5
2>
Bjtmrprmtgfbj, fckc sm pumlm cosmrvgr ma
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
109/270
BNM_ \gfgj
24
_msukmj
]j sbstmkg lm fccrlmjglgs fgrtmsbgjgs mst fckpumstc pcr lcs ajmgs pmrpmjlbfuagrms qum smfruzgj mj uj pujtc lm crbnmj, ecrkgjlc fugtrc fuglrgjtms, fcj jkmrcs pcsbtbvcs dgfbg ag lmrmfdg
y dgfbg grrbog y jkmrcs jmngtbvcs dgfbg ag bzqubmrlg y dgfbg gog`c.
Ags nrfgs scj ag rmprmsmjtgfbj vbsuga lm ujg tgoag lm lgtcs. Acs trms tbpcs ks fckujms lmnrfgs scj0 lbgnrgkg lm ogrrgs, lbgnrgkg lm ajmgs y lbgnrgkg fbrfuagr c pgstma.
Ma lbgnrgkg lm ogrrgssm rmgabzg gsbnjgjlc ags vgrbgoams ga m`m (x) y acs pcrfmjtg`ms mj ma m`m ( y). Gfcjtbjugfbj, sm lmtmrkbjg ma gatc, sb ags ogrrgs scj vmrtbfgams, c ma agrnc, sb ags ogrrgs scj dcrbzcjtgams,
smnj ma vgacr lm fglg lgtc g rmprmsmjtgr.
Ma lbgnrgkg lm ajmgssm magocrg g pgrtbr lm ujg tgoag fcjtmjbmjlc ujg smrbm dbstrbfg lm lgtcs mj agqum fglg lgtc sm rmprmsmjtg pcr uj pujtc. Aumnc, sm ujmj tclcs acs pujtcs fcj ujg ajmg.
Ma lbgnrgkg fbrfuagrsm magocrg g pgrtbr lm ujg tgoag lm ermfumjfbg y rmprmsmjtg ma pcrfmjtg`m lm fglglgtc rmspmftc ga tctga. Xgrg lbou`gr ma smftcr c pcrfbj qum rmprmsmjtg fglg lgtc, sm utbabzg ag sbnubmjtm
erkuag0
Jc. lm nrglcs% lm fgtmncrg 658
788;
Ucfgouagrbc osbfc
lbgnrgkg lm ogrrgs0 nrfg qum utbabzg ogrrgs, mj pcsbfbj dcrbzcjtga c vmrtbfga, pgrg rmprmsmjtgrnrfgkmjtm uj fcj`ujtc lm lgtcs c vgacrms.
lbgnrgkg lm ajmgs0nrfg qum ujm kmlbgjtm ajmgs acs pujtcs lm ujg smrbm lm lgtcs pgrg kcstrgr mafckpcrtgkbmjtc lm ujg vgrbgoam g trgvs lma tbmkpc.
lbgnrgkg fbrfuagr0 nrfg mj ecrkg lm frfuac qum kumstrg ag prcpcrfbj lm acs lgtcs c vgrbgoamsrmspmftc g uj tclc.
nrfg0 tbpc lm rmprmsmjtgfbj lm lgtcs, nmjmrgakmjtm jukrbfcs, mj ecrkg lm ajmgs, vcakmjms,nurgs y supmrfbms qum egfbabtgj ag vbsugabzgfbj y fckpgrgfbj lm lgtcs.
sbstmkg lm fccrlmjglgs fgrtmsbgjgs0 pagjc fckpumstc pcr lcs ajmgs pmrpmjlbfuagrms qum sm fcrtgjmjtrm s ecrkgjlc uj pujtc lm crbnmj. Vbrvm pgrg trgzgr pujtcs mj uj pagjc.
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
110/270
Mstglstbfg Lmsfrbptbvg Vmkgjg 5
22
Gftbvblgl 7Magocrm mj su fuglmrjc ags tgoags jmfmsgrbgs pgrg rmgabzgr acs lbgnrgkgs scabfbtglcs mj fglg bjfbsc.
Amg fcj gtmjfbj ag bjecrkgfbj.
7. Mj ag Mjfumstg Jgfbcjga lm Fcjlbfbcjms lm Ublg ?885 (MJFCUB?885) sm am prmnujt g acs mjtrmvbstglcs
sb ag fgsg lcjlm vbvgj mrg prcpbg c jc. Acs lgtcs mj ag tgoag rmeam`gj qu fcjtmstgrcj ags pmrscjgs
mjtrmvbstglgs g ag prmnujtg gjtmrbcr.
Ag nrebfg lmom tmjmr tclcs acs mamkmjtcs0 ttuacs (nmjmrga, m`ms y smftcrms), eumjtm, mtf. _mgabfm0
lbgnrgkg lm ogrrgs
lbgnrgkg lm smftcrms
Gutcfcjtrca
?. Mj ag Mjfumstg Jgfbcjga lm Fcjlbfbcjms lm Ublg ?885 (Mjfcvb ?885) sm lmtmrkbj sb lcjlm vbvg
ag kgycrg lm pmrscjgs, mrg rmg rurga c urogjg. Acs lgtcs mj ag tgoag rmeam`gj qu fcjtmstgrcj ags
pmrscjgs mjtrmvbstglgs g ag prmnujtg gjtmrbcr.
_mgabfm ags nrebfgs scabfbtglgs, rmfumrlm qum lmom tmjmr tclcs acs mamkmjtcs0 ttuacs (nmjmrga, m`ms y
smftcrms), eumjtm, mtf.
lbgnrgkg lm ogrrgs
lbgnrgkg lm smftcrms
_nbkmj lm tmjmjfbg DcngrmsFgsg jc prcpbg 745
\goag 7\mjmjfbg lm dgobtgfbj
rmg Dcngrms
_urga 64=?
]rogjg 65
\goag ?rmg lcjlm vbvmj ags pmrscjgs mjtrmvbstglgs
6. Mj uj guag lm ag msfumag Ma Xcrvmjbr gsbstm ag sbnubmjtm fgjtblgl lm mstulbgjtms0 7= ku`mrms y 7>
dckorms.
Fcj ag bjecrkgfbj prcpcrfbcjglg rmgabfm mj su fuglmrjc acs lbgnrgkgs bjlbfglcs.
lbgnrgkg lm ogrrgs
lbgnrgkg lm smftcrms
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
111/270
BNM_ \gfgj
788
_mvbsm su gprmjlbzg`m
Kgrqum fcj uj fdmqum ag fgsbaag qum km`cr bjlbqum su rmjlbkbmjtc. acnrglcmj
prcfmscjc
acnrglc
Lmspuslmmstulbg
r... Acfgabzc pujtcs mj uj sbstmkg lm fccrlmjglgs fgrtmsbgjgs.
]tbabzc ag bjecrkgfbj lm ags tgoags pgrg fcjstrubr lbgnrgkgs lm
ogrrgs, lm ajmgs y fbrfuagrms.
Fgafuac nrglcs pgrg magocrgr uj lbgnrgkg fbrfuagr.
Ugacrc ma usc lm nrfgs pgrg prmsmjtgr lgtcs mstglstbfcs.
Bjstbtutc Nugtmkgatmfc lm \urbskc (BJN]G\)
Ma Bjstbtutc Nugtmkgatmfc lm \urbskc (BJN]G\) ms ag bjstbtufbj mjfgrnglg lm eckmjtgr y prckcvmr malmsgrrcaac turstbfc lm Nugtmkgag g jbvma jgfbcjga m bjtmrjgfbcjga. Ma turbskc nmjmrg mkpamcs m bjnrmscs
pgrg kufdcs nugtmkgatmfcs, mj ag ecrkg lm prmstgfbj lm smrvbfbcs lm dctmams, rmstgurgjtms, trgjspcrtm,
gs fckc magocrgfbj lm grtmsgjgs, mjtrm ctrcs. Ma turbskc glmks pmrkbtm ma bjnrmsc lm lbvbsgs, ms lm-
fbr kcjmlg lm ctrcs pgsms. Lmoblc g ag bkpcrtgjfbg lma turbskc mj ag mfcjckg jgfbcjga, ma BJN]G\aamvg
rmnbstrcs mstglstbfcs scorm ag cemrtg dctmamrg, ma bjnrmsc lm turbstgs ga tmrrbtcrbc jgfbcjga, acs tbpcs lm
vbg`mrcs qum jcs vbsbtgj, lm ljlm vbmjmj y ma lbjmrc qum lm`gj mj ma pgs. Vb lmsmg fcjcfmr ks lgtcs
scorm ma turbskc jgfbcjga m bjtmrjgfbcjga, vbsbtm ag pnbjg mamftrjbfg0
www.bjnugt.nco.nt/mstglbstbfgs.pdp
Jgvmnum mj ag rml...
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
112/270
Mstglstbfg Lmsfrbptbvg Vmkgjg >
787
Lbstrboufbj lm ermfumjfbgs (B)
Wu mjfcjtrgr mstg smkgjg3
Mamkmjtcs lm uj fuglrc pgrg vgrbgoam fugjtbtgtbvg
]sc lm bjtmrvgacs mj mjfumstgs
Lbstrboufbj lm ermfumjfbgs
Mstg smkgjg acnrgr0
Lbemrmjfbgr acs tbpcs lm tgoags smnj acs lgtcs qum prmsmjtgj.
Magocrgr tgoags fcj lgtcs fugjtbtgtbvcs.
Fcjstrubr ujg lbstrboufbj lm ermfumjfbgs.
>
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
113/270
BNM_ \gfgj
78?
Xgrg fckmjzgr!
Mamkmjtcs lm uj fuglrcpgrg vgrbgoams fugjtbtgtbvgs
Ag rmfcamffbj lm lgtcs fcjstbtuym ag kgtmrbg prbkg fcj qum sm trgog`g mj acsfafuacs mstglstbfcs, pcr ac tgjtc rmsuatg kuy bkpcrtgjtm ag ecrkg mj qum
crngjbzgkcs ag bjecrkgfbj pums pcr ac nmjmrga sm gjgabzg nrgj fgjtblgl lm
lgtcs.
Mj vgrbgs sbtugfbcjms lm ag vblg fctblbgjg fckc, pcr m`mkpac, acs grtmsgjcs
trgjsecrkgj ag kglmrg, ma ogrrc, ma kmtga y ctrcs kgtmrbgams mj kumoams, crmrcs,
msfuaturgs, mtf.9 tgkobj fugjlc fcfbjgkcs, lmspus lm vgrbcs prcfmlbkbmjtcs
acs gabkmjtcs frulcs sm fcjvbmrtmj mj pagtcs gpmtbtcscs qum sm sbrvmj mj ag kmsg.
G trgvs lm uj prcfmsc sbkbagr, ags bjvmstbnglcrgs m bjvmstbnglcrms fcj ag gyulg
lm "rmfmtgs" aagkglgs erkuags y tfjbfgs, bjtmjtgj trgjsecrkgr ag bjecrkgfbj
rmfcamftglg mj rmsuatglcs qum ams pmrkbtgj prcogr sus dbptmsbs y gkpabgr susfcjcfbkbmjtcs.
Mjtcjfms, qu dgfmr pgrg trgjsecrkgr nrgj fgjtblgl lm lgtcs mj uj rmsukmj
efba lm mjtmjlmr3
Vb acs lgtcs scj fugabtgtbvcs, pclmkcs fcjstrubr ujg tgoag fckc ags qum
gprmjlbkcs mj ag smkgjg 5. M`mkpac0
Vmxc Fgjtblgl
Dckorms 78
Ku`mrms ?8
\ctga 68
Vb acs lgtcs scj fugjtbtgtbvcs, pclmkcs fcjstrubr ujg lbstrboufbj lm ermfumjfbgs
mj ecrkg lm tgoag lm bjtmrvgacs. M`mkpac0
Fagsm Ermfumjfbg
8 7 =
? 6 4
< = 78
5 > 5
\ctga (j) ?2
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
114/270
Mstglstbfg Lmsfrbptbvg Vmkgjg >
786
7. Lbstrboufbj lm ermfumjfbgs
Ag lbstrboufbj lm ermfumjfbgs ms ujg crngjbzgfbj, mj ecrkg lm tgoag, lm lgtcs
mstglstbfcs gnrupglcs9 mj ag tgoag sm kumstrg ag ermfumjfbg fcj qum gpgrmfmj
acs lgtcs mj fglg bjtmrvgac. Vm utbabzg fugjlc sm tbmjmj lgtcs fugjtbtgtbvcs, tgams
fckc fgabfgfbcjms, pmsc, mstgturg, mlgl, sgagrbc c fugaqubmr lgtc qum pumlg
mxprmsgrsm lm ecrkg jukrbfg.
Ga bnuga qum ags tgoags pgrg vgrbgoams fugabtgtbvgs, mst ecrkglg pcr fcaukjgs y
ags. Ag prbkmrg fcaukjg fcjtbmjm ags fagsms c bjtmrvgacs y ag smnujlg kumstrg
fujtcs lgtcs dgy mj fglg bjtmrvgac, ms lmfbr, ag ermfumjfbg. Umgkcs uj m`mkpac
pgrg mjtmjlmr km`cr.
Vm gpabfg uj mxgkmj g 7?5 mstulbgjtms y sm fcjstruym ag lbstrboufbj lmermfumjfbgs pgrg ags fgabfgfbcjms.
Magocrgr uj fuglrc fckpumstc pcr lcs fcaukjgs. Ag prbkmrg fcaukjg
lmomr aamvgr ma ttuac"fagsm c bjtmrvgac"y ag smnujlg "ermfumjfbg e",fckc
sm cosmrvg mj ma fuglrc sbnubmjtm0
Fagsm c bjtmrvgac Ermfumjfbg e
82 78
7872 7=
?8?2 75
6862 7?
2 78
4842 2
2822 =
\ctga (j) 7?5
78 fagsms c bjtmrvgacs
Xrbkmrg eag c fagsm
Wubjtg eag c fagsm
Ma kujlc lm ag mstglstbfg
7/25/2019 Libro Tacan Estadstica Descriptiva 1er. Sem
115/270
BNM_ \gfgj
78
78=
?. Fcjstruffbj lm ujg lbstrboufbj lmermfumjfbgs
]jc lm acs prcfmlbkbmjtcs pgrg fcjstrubr ujg lbstrboufbj lm ermfumjfbgs ms ma
sbnubmjtm0
Fgafuagrag gkpabtul tctga lm acs lgtcs ; lgtc kgycr lgtc kmjcr
Lmfblbr fujtgs fagsms sm utbabzgrj.Vcorm mstm gspmftc, sm rmfckbmjlg utbabzgr
jckmjcs lm = fagsms c bjtmrvgacs, jb ks lm ?8. Mxbstmj erkuags pgrg gyulgr g
lmfblbr mj fujtgs fagsms sm dgr ag lbstrboufbj lm ermfumjfbgs0
Jc. fagsms ; 7 + 6.6 acn j
Mj lcjlm jms ma jkmrc lm lgtcs qum sm tbmjmj. Ma acngrbtkc (acn) sm fgafuag
utbabzgjlc ujg fgafuaglcrg fbmjtebfg.
Lbvblbr ag gkpabtul tctga mjtrm ma jkmrc lm fagsms lmfblblc,pgrg cotmjmruj tgkgc lm fagsm gprcxbkglc.
Lmfblbr ma tgkgc lm fagsm c bjtmrvgac gprcxbkgjlc ma vgacr cotmjblc
gjtmrbcrkmjtm.
Lmfblbr ljlm bjbfbgr ag lbstrboufbj. Ac jbfc bkpcrtgjtm ms qum ags
fagsms lmomj fcjtmjmr ga jkmrc ks pmqumc y ga jkmrc ks nrgjlm.
Jc jmfmsgrbgkmjtm sm lmom bjbfbgr mj maacs.
Msfrbobr ags fagsmsfcacfgjlc ma jkmrc lma akbtm bjemrbc