Chapter 3

CHAPTER 3MEASURES OF CENTRAL TENDENCYMEANOne of the simplest and most e!ient meas"#es of !ent#al tenden!$ is the mean% Mean & 't is the (al"e o)tained )$ addin* the (al"es in the dist#i)"tion and di(idin* the s"m )$ the total n"m)e# of (al"es%MEAN FOR UN+ROUPED DATAFo#m"la O# MEAN FOR UN+ROUPED DATA:E,ample- .% Conside# the follo/in* (al"es%0.1 .21 331 401 351 601 321 061 03Comp"te the mean0% The a*es of .6 st"dents in a !e#tain !lass /e#e ta7en and sho/n )elo/%.61 .81 .91 .31 .51 0.1 .81 031 041 .81 .31 .91 021 0.1 .51 dete#mine the mean a*e of the st"dents%:E'+HTED MEAN:The#e a#e some instan!es /he#e1 in the !omp"tation of the mean of set data1 ea!h (al"e in the dist#i)"tion is asso!iated /ith !e#tain /ei*ht o# de*#ee of impo#tan!e% :he#e , ; #ep#esents the item (al"e / ; #ep#esents the /ei*ht asso!iated to ,:E'+HTED MEANExample:1. Compute the weighted mean grade of the student as shown below.S") +#ade =,> . 3 0%20 3 3%23 6 .%064 . 3%26 0 0%63 3 0%6:E'+HTED MEANExample:2. A die was rolled 100 times and the results are shown below.O"t!ome =,> f#e?"en!$ =/> ..90 .43 02 4 .66 .6 3 .5MEAN FOR +ROUPED DATATo compute the value of the presented in a freuenc! distribution" we shall consider two methods:Midpoint Method #$ %$' T(#& )ET(*+"T(E )#+,*#$T *- EAC( C.A&& #$TE/0A. #& TA1E$ A& T(E /E,/E&E$TAT#0E *- EAC( C.A&&. T(E&E )#+,*#$T& A/E )%.T#,.#E+ 23 T(E#/ C*//E&,*$+#$' -/E4%E$C#E&. T(E ,/*+%CT& A/E A++E+ A$+ T(E &%) #& +#0#+E+ 23 T(E T*TA. $%)2E/ *- -/E4%E$C#E&.MEAN FOR +ROUPED DATA)idpoint method5heref 6 represents the freuenc! of each classx 6 the midpoint of each classn 6 the total number of freuencies or sample si7eMEAN FOR +ROUPED DATASteps-.% +et the midpoint of ea!h !lass%0% M"ltipl$ ea!h midpoint )$ its !o##espondin* f#e?"en!$%3% +et the s"m of the p#od"!ts in step 0% 4% Di(ide the s"m o)tained in step 3 )$ the total n"m)e# of f#e?"en!ies% The #es"lt shall )e #o"nded o@ to t/o de!imal pla!es%MEAN FOR +ROUPED DATA-)idpoint )ethod 8example9Compute the value of the mean for the freuenc! distribution below.Classesf11:22 ;2;:;< =;=: 11