2010 - 2011

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Transcript of 2010 - 2011

  • &

    /

    :

    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