&

/

:

BSc, MSc Statistics

2010

BSc MSc Statistics - /

2

(Normal)

t (Students t)

2

BSc MSc Statistics - /

;

3

;

BSc MSc Statistics 4 - /

..

.. : ,

,

..

; ;

BSc MSc Statistics 5 - /

:

(,

(, exit polls..)

( )

..

BSc MSc Statistics 6 - /

:

parking

; ;

;

;

(.. )

;

;

;

BSc MSc Statistics 7 - /

,

. ;

.

BSc MSc Statistics 8 - /

;

, ,

(Fisher)

BSc MSc Statistics 9 - /

;

.

BSc MSc Statistics 10 - /

;

BSc MSc Statistics 11 - /

(Descriptive Statistics)

(Experimental Design)

(Sampling Theory)

, ,

(Statistical Inference)

.

BSc MSc Statistics

12 - /

;

:

BSc MSc Statistics 13 - /

BSc MSc Statistics 14 - /

:

,

.

:

:

: .

:

:

..

:

..

BSc MSc Statistics 15 - /

:

(nominal data),

( ).

, ,

(dichotomous, binary)

()

,

(ordinal data)

BSc MSc Statistics 16 - /

:

.

(ranked data)

(discrete data)

(continuous data)

BSc MSc Statistics

17 - /

BSc MSc Statistics

18 - /

BSc MSc Statistics

19 - /

,

x1= x2=.

y1= , y2= , y3=

.

[0,120).

z1=

, z2= , z3=

/, z4=, z5= .

BSc MSc Statistics

20 - /

BSc MSc Statistics 21 - /

:

.

.

BSc MSc Statistics 22 - /

:

- 18

1900-1990

1900 54

1910 151

1920 665

1930 1.485

1940 1.976

1950 3.522

1960 4.171

1970 3985

1980 3851

1990 2.828

.

BSc MSc Statistics 23 - /

:

-

BSc MSc Statistics 24 - /

:

-

2.294 , , 1976-1980

(mg/100ml)

25-34

(%)

25-34

55-64

(%)

55-64

80-119 13 1,2 5 0,4

120-159 150 14,1 48 3,9

160-199 442 41,4 265 21,6

200-239 299 28,0 458 37,3

240-279 115 10,8 281 22,9

280-319 34 3,2 128 10,4

320-359 9 0,8 35 2,9

360-399 5 0,5 7 0,6

1.067 100,0 1.227 100,0

BSc MSc Statistics 25 - /

:

(mg/100ml)

25-34

(%)

25-34

(%) 25-34

80-119 13 1,2 1,2

120-159 150 14,1 15,3

160-199 442 41,4 56,7

200-239 299 28,0 84,7

240-279 115 10,8 95.5

280-319 34 3,2 98,7

320-359 9 0,8 99,5

360-399 5 0,5 100

1.067 100,0

BSc MSc Statistics 26 - /

:

0

500

1000

1500

2000

2500

3000

3500

4000

4500

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990

BSc MSc Statistics 27 - /

:

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45

80 - 119 120 - 159 160 - 199 200 - 239 240 - 279 280 - 319 320 - 359 360 - 399

(mg/100ml)

(%

)

BSc MSc Statistics 28 - /

:

0,00%

5,00%

10,00%

15,00%

20,00%

25,00%

30,00%

35,00%

40,00%

45,00%

80 - 119 120 - 159 160 - 199 200 - 239 240 - 279 280 - 319 320 - 359 360 - 399

(mg/100ml)

(%

)

25-34

55-64

BSc MSc Statistics 29 - /

:

0,00%

20,00%

40,00%

60,00%

80,00%

100,00%

120,00%

80 -

119

120 -

159

160 -

199

200 -

239

240 -

279

280 -

319

320 -

359

360 -

399

(mg/100ml)

(%

)

25-34

55-64

BSc MSc Statistics 30 - /

:

(Box Plots)

BSc MSc Statistics 31 - /

:

- Two way scatter plot

2

3

4

5

6

7

8

2 3 4 5 6 7 8

BSc MSc Statistics 32 - /

:

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20 25 30 35 40

BSc MSc Statistics 33 - /

:

,

.

. ..

,

6

8.5.

BSc MSc Statistics 34 - /

:

(arithmetic mean, average, mean)

n

1i

in1 xx

BSc MSc Statistics 35 - /

:

BSc MSc Statistics 36 - /

:

BSc MSc Statistics 37 - /

:

k

, :knnn ...,,, 21

k

i

i

k

i

ii

n

n

1

1

BSc MSc Statistics 38 - /

:

(median) - 50

:

2

1

:

2

122

BSc MSc Statistics 39 - /

:

BSc MSc Statistics 40 - /

:

(mode) -

. ,

.

. ..

.

BSc MSc Statistics 41 - /

:

(mode) -

, :

:

.

:

,

(bimodal).

BSc MSc Statistics 42 - /

:

(range) -

minmax R

BSc MSc Statistics 43 - /

:

BSc MSc Statistics 44 - /

:

(quantiles)-

%

(1-)%

(percentiles)

(deciles)

(quartiles)

9921 ...,,, ppp

902010 ...,,, ppp

375250125 ,, QpQpQp

BSc MSc Statistics 45 - /

:

(variance) & standard deviation-

2

1

2

1

22

1

1)(

1

1

i

i

i

is

2

1

2

1

2

1

1)(

1

1

i

i

i

is

BSc MSc Statistics 46 - /

:

BSc MSc Statistics 47 - /

:

Coefficient of Variation

%100

sCV

BSc MSc Statistics 48 - /

:

BSc MSc Statistics 49 - /

:

k

i i

k

i ii

f

fm

1

1

BSc MSc Statistics 50 - /

:

BSc MSc Statistics 51 - /

:

1)(

1

1

2

2

k

i i

k

i ii

f

fxms

BSc MSc Statistics 52 - /

:

BSc MSc Statistics 53 - /

BSc MSc Statistics 54 - /

,

.

.

.. : {,}

: {1,2,3,4,5,6}

. ={ , }

(event) .

.. = = {2,4,6}

BSc MSc Statistics 55 - /

, 2, 4, 6

= .. {2}

= { }, .

;

,

; ;

:

BSc MSc Statistics 56 - /

1.

.. {,} , .

{1,2,3,4,5,6} .

.

:

( )

P() = ( ) /

( )

.. ( / ) = 3/6 = 1/2.

BSc MSc Statistics 57 - /

2.

[ -

()]

.

:

()

()

() .

BSc MSc Statistics 58 - /

..

BSc MSc Statistics 59 - /

3.

. ;

,

, , .

.

.

BSc MSc Statistics 60 - /

:

(= )

.

A

BSc MSc Statistics 61 - /

:

(= )

.

A

BSc MSc Statistics 62 - /

:

=

=

.. : =

= 4

= {2,4,6}

={1,2,3,4}

= {2,4}

BSc MSc Statistics 63 - /

:

U ( )

BA

BSc MSc Statistics 64 - /

U = {1,2,3,4,6}

: 1. U =

2. U = U

3. U ( C) = (A U B) (A U C)

A (B U C) = (A B) U (A C)

BSc MSc Statistics 65 - /

:

, ,

.

=

A

BSc MSc Statistics 66 - /

.. , =

=

= {1,3,5}

= {2,4,6} =

= =>

.

BSc MSc Statistics 67 - /

: = -

=

A

BSc MSc Statistics 68 - /

c B = A