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SPSS
) :
:
File.
Open.
Data..
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, (.. Excel file) Open..
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) Data View:
Variable View SPSS
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:
:
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(Bar Chart) (Histogram)
(Frequency Polygon) (Box Plot)
(Stem and Leaf Plot) (Pie chart) (Scatter plot)
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(Histogram)
-(Stem and Leaf Plot)
(Box-Plot)
(Bar Chart)
(Pie Chart)
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: 1993 . 1:, 2: , 3: , 4: , 5: , 6: . 42 (: , )
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Variable View
labels output
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:
Analyze.
Descriptive Statistics.
Frequencies
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:
:
Statistics.
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: Statistics
(.. , )
:
Continue. (.. , )
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: Charts
:
Continue.
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:
:
OK.
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:
Graphs.
Bar. :
:
Define..
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:
Category Axes
: OK
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Chart Editor
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Chart Editor
menu Chart editor , .. ,
Show properties window
Show data labels window
Transpose chart coordinates
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:
Graphs.
Pie.
:
summaries for groups of cases..
:
Define..
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:
:Define Slices by.
: OK
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Chart Editor
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Show properties window
Chart Editor
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: 1905 1993 (: , )
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Variable View ,
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:
Graphs.
Boxplot.
:
:
Define..
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:
:Boxes Represent.
: OK
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Q3+1.5(Q3- Q1)
3 (Q3)
(outliers)
1 (Q3)
Q3-1.5(Q3- Q1)
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:
Graphs.
Histogram.
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:
:Variable.
: OK
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Chart Editor
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-
:
Analyze.
Descriptive Statistics.
Descriptives
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:
/ / :Variable(s).
: Options..
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: Options
:
Continue
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:
Analyze.
Tables.
Custom Tables.
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.
Drug-and-Drop
columns
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columns
:
Summary statistics..
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:
drug-and-drop
apply to selection
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:
OK.
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-() 3 70, 65 90 . 85. 20% 40%
(: =79)
(b) Pearson : 2, 2, 2, 3, 5, 8, 12, 19, 22, 30
(: =0.993, CV=95.04%)
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(c) s. d;
x
(d) S. :
nXXX ,...,, 21 x(: )ssdxx =+= '' ,
SxxZ ii
= ni ,...,2,1=(: ()=0, Var(Z)=1)
(e) :5, 8, 12, 14, 15, 20, 25, 26 8, 12, 15, 23, 20, 37, 36, 29, 25
(: M1=14.5, M2=23)
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(f) , , 8, 5, 7 6 2. , .
(:==5)
(g) 11 : 52, 61, 78, 49, 79, 47, 54, 58, 62, 73, 72. , 1Q3Q
(: =61, =52 , =73)1Q 3Q
(h) 10 .
.
= 290x = 84692x
55.6,29 2 == sx(: )
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(i) :
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(j) 150 .
: , 32
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Bernoulli
Poisson
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Bernoulli [0,1]
Bernoulli Bernoulli
x=1( )
1 x=0p
P X xp
= = 0 1p
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,x=0n , n=1,2, q=1-p , X n p
( ) x n xn
P X x p qx
= = 0 1p
~ ( , )X Bin n p
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n=1,2,N=1,2,m=1,2,N
x=0,1,,min(m,n)
T ,n m .
( )
m N mx n x
P X xNn
= =
( ), ,X h N n m
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Poisson 0,1,2,3... Poisson (Po) :
:0,1, 2,3...x =
( )!
xeP X xx
= = 0 >
( ) = ( )Var X =
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. :
:
0,1, 2...x =
0 1p<
( , )X U a b
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:
,
1( ) , 0, 0x
Xf x e x = > >
exp( )X
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:
: ()= V(X)=
21 ( )21( ) , 0
2
x
Xf x e x
= <
2( , )X N 2
2( , )
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:
(,),
11( ) 0 , 0( )
xab
X af x e x x a bb = >
1
0
( ) (1) 1, ( ) ( 1)!x aa e x dx n n
= = =
( , )X a b
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:
(,)
1 1( )( ) (1 ) 0 1 0, 0( ) ( )
a bX
a bf x x x x a ba b
+= > >
( , )X eta a b
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(-):
n
2X
21
2 2
2
1( ) 0 1, 2,...2
2
x n
X nf x e x x nn = < =
2X2nX X
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t (t-student):
t
12 2
12( ) - 1, 2,...
12
n
n
f x x nn xn
n
+
+ = < < = +
( )X t n
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Minitab
menu :
Calc
Probability Distributions..
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Data Editor / / /. . (=2) 2 c1
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:
Binomial
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: f(x)=P(X=x)
F(x)=P(Xx)
n
p
/
OK.
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: 68% . 15 ) 3 ) 4
p=0.68 n=15. : f(x)=P(X=3) F(x)=P(X4). Minitab :
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POISSON
:
Poisson
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:
f(x)=P(X=x)
F(x)=P(Xx)
Poisson
/
OK.
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:
: 0,1,2,3,4,5
x 0 1 2 3 4 5
f 345 277 75 17 5 3 672
=== 69.0
672463
i
ii
fxf
x Poisson , :
f(x)=(=x) Poisson =0.69 =0,1,2,3,4,5. Minitab :
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:
Exponential
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:
f(x)=P(X=x)
F(x)=P(Xx)
/
OK.
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: 6 . . ) 10 , ) 15 ) 20 ;
, =6 F(X)=(x) x=10, 15, 20. Minitab :
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:
Normal
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:
f(x)=P(X=x)
F(x)=P(Xx)
( )
OK.
/
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: 11, 12 13 28 3 . 25 34
=28 =3. (25X34).
(25X34)=F(34)-F(25)=P(X 34)- P(X 25)
:
P(X 34) P(X 25)
, (25X34)=0,9772-0,1587=0,8185
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:
Uniform
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:
f(x)=P(X=x)
F(x)=P(Xx)
OK.
/
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: ~U(3,6) (>5)
(X>5)=1-P(X5), Minitab F(5)=(5)
, (>5)=1-0,6667=0,333
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:
Chi-square
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:
f(x)=P(X=x)
F(x)=P(Xx)
n -
/
OK.
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~Bin(6,1/3), : P(X=4), P(X 2)(: P(X=4)=0.0821, P(X2)=0.681)
~Bin(8,0.4), P(X=2), P(X=0) P(X>6)(: P(X=2)=0.209, P(X=0)=0.0168, P(X>6)=0.0085)
7 . 3
(: P(X=3)=0.0781)
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7 . 6
(: P(X>5)=0.0001)
, 30% . 10 : ) 3 , ) 8
(: P(X=3)=0.2668, P(X>8)=0.0001)
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6 . 4 (: P(X4)=0.8906)
~Bin(n,0.6) P(X1)=0.087, n(: n=5)
~Bin(n,p) ()=2, Var(X)=24/13. n, p.(: p=1/13, n=26)
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~Bin(10,p) p
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-POISSON ~Po(3.5) : a) P(X=0), b) P(X=4), c)
P(X2), d) P(X>1)
(: P(X=0)=0.0301, P(X=4)=0.1888, P(X2)=0.321, P(X>1)=0.864)
~Po(2.4) F(X) : a) F(0), b) F(1), c) F(2), d) F(3)
(: F(0)=0.0907, F(1)=0.3084, F(2)=0.5697, F(3)=0.7787)
Poisson 3. (
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~Bin(200,0.006), Poisson : ) (5) (: (3)=0,9662, (>5)=0,0015)
500. 0.002. 2 (: (=2)=0,1839)
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, 0.75 . ;(: P(X2)=0.8008)
200 , 3.2 . 5 ;(: P(X=0)=1.12 )710
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0.6. , () P(X4) () (>5)
(: P(X4)=0.9744, (>5)=0,064)
. 10 . p, p(: p=0.1)
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~U(6,9) P(7.2X8.4)
(: P(7.2X8.4)=0.4)
~U(0,/2) P(/3X/2)
(: P(/3X/2)=1/3)
: ( ) ( )
=
bxa
abxf0
1
-
(+)/2 . 1 4/3 : ) , () (0)
(: =-1, =3, (0)=0.25)
[,]. :
( )( )
-
-
f(x), . : ) (>0.5) ) () ) (
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. : ( ) atat eetTtP //21 21 = , 2 , Poisson. : )
(: ()=2)
3 . , , (: (>1=0.050))
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~(300,25). : ) (>305) ) (305)=0.1587, ()=0.974 (: =18.171)
~(0,1) (||
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~(0,1) : () (0.345
-
~(100, ) (
