SPSS

) :

:

File.

Open.

Data..

, (.. Excel file) Open..

) Data View:

Variable View SPSS

:

:

(Bar Chart) (Histogram)

(Frequency Polygon) (Box Plot)

(Stem and Leaf Plot) (Pie chart) (Scatter plot)

(Histogram)

-(Stem and Leaf Plot)

(Box-Plot)

(Bar Chart)

(Pie Chart)

: 1993 . 1:, 2: , 3: , 4: , 5: , 6: . 42 (: , )

Variable View

labels output

:

Analyze.

Descriptive Statistics.

Frequencies

:

:

Statistics.

: Statistics

(.. , )

:

Continue. (.. , )

: Charts

:

Continue.

:

:

OK.

:

Graphs.

Bar. :

:

Define..

:

Category Axes

: OK

Chart Editor

Chart Editor

menu Chart editor , .. ,

Show properties window

Show data labels window

Transpose chart coordinates

:

Graphs.

Pie.

:

summaries for groups of cases..

:

Define..

:

:Define Slices by.

: OK

Chart Editor

Show properties window

Chart Editor

: 1905 1993 (: , )

Variable View ,

-

:

Graphs.

Boxplot.

:

:

Define..

:

:Boxes Represent.

: OK

-

Q3+1.5(Q3- Q1)

3 (Q3)

(outliers)

1 (Q3)

Q3-1.5(Q3- Q1)

:

Graphs.

Histogram.

:

:Variable.

: OK

Chart Editor

-

:

Analyze.

Descriptive Statistics.

Descriptives

:

/ / :Variable(s).

: Options..

: Options

:

Continue

-

:

Analyze.

Tables.

Custom Tables.

.

Drug-and-Drop

columns

columns

:

Summary statistics..

:

drug-and-drop

apply to selection

:

OK.

-() 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%)

(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)

(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(: )

(i) :

(j) 150 .

: , 32

Bernoulli

Poisson

-

Bernoulli [0,1]

Bernoulli Bernoulli

x=1( )

1 x=0p

P X xp

= = 0 1p

,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

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

Poisson 0,1,2,3... Poisson (Po) :

:0,1, 2,3...x =

( )!

xeP X xx

= = 0 >

( ) = ( )Var X =

. :

:

0,1, 2...x =

0 1p<

( , )X U a b

:

,

1( ) , 0, 0x

Xf x e x = > >

exp( )X

:

: ()= V(X)=

21 ( )21( ) , 0

2

x

Xf x e x

= <

2( , )X N 2

2( , )

:

(,),

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

:

(,)

1 1( )( ) (1 ) 0 1 0, 0( ) ( )

a bX

a bf x x x x a ba b

+= > >

( , )X eta a b

(-):

n

2X

21

2 2

2

1( ) 0 1, 2,...2

2

x n

X nf x e x x nn = < =

2X2nX X

t (t-student):

t

12 2

12( ) - 1, 2,...

12

n

n

f x x nn xn

n

+

+ = < < = +

( )X t n

Minitab

menu :

Calc

Probability Distributions..

Data Editor / / /. . (=2) 2 c1

:

Binomial

: f(x)=P(X=x)

F(x)=P(Xx)

n

p

/

OK.

: 68% . 15 ) 3 ) 4

p=0.68 n=15. : f(x)=P(X=3) F(x)=P(X4). Minitab :

POISSON

:

Poisson

:

f(x)=P(X=x)

F(x)=P(Xx)

Poisson

/

OK.

:

: 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 :

:

Exponential

:

f(x)=P(X=x)

F(x)=P(Xx)

/

OK.

: 6 . . ) 10 , ) 15 ) 20 ;

, =6 F(X)=(x) x=10, 15, 20. Minitab :

:

Normal

:

f(x)=P(X=x)

F(x)=P(Xx)

( )

OK.

/

: 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

:

Uniform

:

f(x)=P(X=x)

F(x)=P(Xx)

OK.

/

: ~U(3,6) (>5)

(X>5)=1-P(X5), Minitab F(5)=(5)

, (>5)=1-0,6667=0,333

-

:

Chi-square

:

f(x)=P(X=x)

F(x)=P(Xx)

n -

/

OK.

-

~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)

7 . 6

(: P(X>5)=0.0001)

, 30% . 10 : ) 3 , ) 8

(: P(X=3)=0.2668, P(X>8)=0.0001)

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)

~Bin(10,p) p

-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. (

~Bin(200,0.006), Poisson : ) (5) (: (3)=0,9662, (>5)=0,0015)

500. 0.002. 2 (: (=2)=0,1839)

, 0.75 . ;(: P(X2)=0.8008)

200 , 3.2 . 5 ;(: P(X=0)=1.12 )710

-

0.6. , () P(X4) () (>5)

(: P(X4)=0.9744, (>5)=0,064)

. 10 . p, p(: p=0.1)

-

~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) ) () ) (

. : ( ) atat eetTtP //21 21 = , 2 , Poisson. : )

(: ()=2)

3 . , , (: (>1=0.050))

-

~(300,25). : ) (>305) ) (305)=0.1587, ()=0.974 (: =18.171)

~(0,1) (||

~(0,1) : () (0.345

~(100, ) (