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    The Use Of StatisticsThe Use Of Statistics

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    There Are Two Branches OfThere Are Two Branches Of

    StatisticsStatistics

    Descriptive statistics refers to theDescriptive statistics refers to the

    methods for SUMMERAZINGmethods for SUMMERAZING

    information so that the informationinformation so that the informationis more useful or can be obtainedis more useful or can be obtained

    communicative or effectivecommunicative or effective

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    4 Examples Of DISCRIPTIVE4 Examples Of DISCRIPTIVE

    Statistic:Statistic:

    FRENQUECY TableFRENQUECY TablePercent DistributionPercent Distribution

    Bar GraphBar Graph

    Pie ChartPie Chart

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    Inferential StatisticsInferential Statistics

    Refers to the procedure used toRefers to the procedure used to

    make GENERALIZATIION from amake GENERALIZATIION from a

    sample to the larger population fromsample to the larger population from

    which the sample was drawnwhich the sample was drawn

    There are two DIFFENT types ofThere are two DIFFENT types of

    MESUREMENTSMESUREMENTS

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    Two Types Of Measurements:Two Types Of Measurements:

    Measure of centralMeasure of central

    tendency whichtendency which

    gives usgives us

    information aboutinformation aboutthe center of thethe center of the

    way data isway data is

    distributeddistributed

    MeanMean

    ModeMode

    MedianMedian

    Measurement ofMeasurement of

    dispersiondispersion

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    Sample QuestionsSample Questions

    How many people in your family,How many people in your family,

    other than you, have attendedother than you, have attended

    college?college?

    How many people in your familyHow many people in your family

    have graduated from college?have graduated from college?

    What is your grade point averageWhat is your grade point average

    (G.P.A)?(G.P.A)?

    Do you have a part time or full timeDo you have a part time or full time

    or no job?or no job?

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    How Many People in Your FamilyHow Many People in Your Family

    Graduated From College ?Graduated From College ?

    DescriptiveDescriptive

    statisticsstatistics

    Sample numbers:Sample numbers:

    0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,

    1,1,1,2,2,2,2,2,2,3,1,1,1,2,2,2,2,2,2,3,

    3,3,4,63,3,4,6

    Frequency tableFrequency table

    Bar graphBar graph

    Pie chartPie chart

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    Frequency TableFrequency Table

    4.2%1/6

    4.2%1/4

    8.3%2//3

    25%6///// /2

    20.8%5/////1

    37.5%9///// ////0

    PercentFrequency

    TallyCategory

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    01234

    567

    89

    0 1 2 3 4 6

    .

    .

    .

    .

    .

    .

    .

    ..

    .

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    Pie ChartPie Chart

    37.5

    20.825

    8.3

    4.2

    4.2

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    Do You Have a Part Time orDo You Have a Part Time or

    Full Time or No Job?Full Time or No Job?

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    Do You Have A Part Time FullDo You Have A Part Time Full

    Time or No Job?Time or No Job?

    40.74%11///// ///// /Full timejob

    37.04%10///// /////Part timejob

    22.22%6///// /No job

    percentFrequencyTallyCategories

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    Do You Have A Part Time orDo You Have A Part Time or

    Full Time or No Job?Full Time or No Job?

    0.00%

    5.00%10.00%

    15.00%

    20.00%

    25.00%

    30.00%

    35.00%

    40.00%

    45.00%

    No Job

    Part time job

    Full time job

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    Bar GraphBar Graph

    No Job

    Part Time Job

    Full Time Jo

    Slice 4

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    Frequency TableFrequency Table

    7.72//5

    3.81/4

    11.53///3

    34.69///// ////234.69///// ////1

    7.72//0

    PercentFrequencyTallyCategory

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    Bar GraphBar Graph

    0.00%

    5.00%

    10.00%

    15.00%

    20.00%

    25.00%

    30.00%

    35.00%

    0 1 2 3 4 5

    3-D Column 1

    3-D Column 2

    3-D Column 3

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    01

    2

    3

    4

    5

    Bar Graph

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    Inferential StatisticsInferential Statistics

    MeanMean

    MedianMedian

    ModeMode

    RangeRange

    Sample numbersSample numbers

    0,0,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,

    1,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,3,3,3,4,5,5.3,3,3,4,5,5.

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    Inferential StatisticsInferential Statistics

    Mean= 68/26=2.62Mean= 68/26=2.62

    Median= 2+2/2=4/2=2Median= 2+2/2=4/2=2

    Mode = 1,2Mode = 1,2Range =0+5/2= 2Range =0+5/2= 2

    (Xi X)^2Xi XXi

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    (-1.6)^2=2.561-2.61

    (-1.6)^2=2.56

    1-2.61

    (-1.6)^2=2.56

    1-2.61

    (-1.6)^2=2.56

    1-2.61

    (-1.6)^2=2.56

    1-2.61

    (-1.6)^2=2.56

    1-2.61

    (-1.6)^2=2.56

    1-2.61

    (-1.6)^2=2.56

    1-2.61

    (-1.6)^2=2.56

    1-2.61

    (-2.6)

    ^2=6.76

    0-2.60

    (-2.6)^2=6.76

    0-2.60

    (Xi X)^2Xi XXi

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    (-.4)^2=.163-2.63

    (-.4)^2=.163-2.63

    (-.4)^2=.163-2.63

    (-.6)^2=.362-2.62

    (-.6)^2=.362-2.62

    (-.6)^2=.362-2.62

    (-.6)^2=.362-2.62

    (-.6)^2=.362-2.62

    (-.6)^2=.362-2.62

    (-.6)^2=.362-2.62(-.6)^2=.362-2.62

    (-.6 )^2=.362-2.62

    (Xi-X)^2Xi-XXi

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    (2.4)^2=5.765-2.65

    (2.4)^2=5.764-2.65

    (1.4)^2=1.964-2.64

    (Xi-X)^2Xi-XXi

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    What Is Your Grade PointWhat Is Your Grade Point

    Average?Average?

    ExcellentExcellent

    GoodGood

    AverageAveragePoorPoor

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    What Is Your Grade PointWhat Is Your Grade Point

    Average?Average?RawRaw

    data:2.1,2.1,2.4,data:2.1,2.1,2.4,

    2.4,2.5,2.5,2.6,2.7,2.4,2.5,2.5,2.6,2.7,

    2.7,2.7,2.7,2.8,2.8,2.7,2.7,2.7,2.8,2.8,2.9,3.0,3.0,3.1,3.1,2.9,3.0,3.0,3.1,3.1,

    3.2,3.3,3.5,3.5,3.6,3.2,3.3,3.5,3.5,3.6,

    3.8,4.03.8,4.0

    DescriptiveDescriptive

    statisticsstatistics

    Inferential statisticsInferential statistics

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    Frequency TableFrequency Table

    8%2//2.4-1.5

    72%18///// ////////// ///

    3.49-2.5

    20%5/////4.0-3.5

    PercentFrequencyTallyCategories

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    Bar GraphBar Graph

    0%

    10%

    20%

    30%

    40%

    50%

    60%

    70%

    80%

    4.0-3.5 3.49-2.5 2.4-1.5

    3-D Column 1

    .

    .

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    Pie ChartPie Chart

    4.0-3.5

    3.49-2.5

    2.4-1.5

    Slice 4

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    Inferential StatisticsInferential Statistics

    Mean =Mean =Xi/n=2.9Xi/n=2.9

    Mode= 2.8Mode= 2.8

    Median=2.7Median=2.7

    (Xi X)^2Xi XXi

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    (-.1)^2=.12.8-2.92.8

    (-.2)^2=.42.7-2.92.7

    (-.2)^2=.42.7-2.92.7(-.2)^2=.42.7-2.92.7

    (-.2)^2=.42.7-2.92.7

    (-.3)^2=.92.6-2.92.6

    (-.4)^2=.162.5-2.92.5

    (-.4)^2=.162.5-2.92.5

    (-.5)^2=.252.4-2.92.4

    (-.5)^2=.252.4-2.92.4

    (-.8)^2=.642.1-2.92.1

    (-.8)^2=.642.1-2.92.1

    (Xi-X) 2Xi-XXi

    ( 1)^2 12 1 2 82 8

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    (.3)^2=.93.2-2.93.2

    (.9)^2=.813.8-2.93.8

    (1.1)^2=1.214.0-2.94.0

    (1)^2=13.6-2.93.6

    (.6)^2=.363.5-2.93.5

    (.6)^2=.363.5-2.93.5

    (.4)^2=.163.3-2.93.3

    (.2)^2=.43.1-2.93.1

    (.2)^2=.43.1-2.93.1

    (.1)^2=.13.0-2.93.0

    (.1)^2=.13.0-2.93.0

    (0)^2=02.1-2.92.9

    (-.1)^2=.12.1-2.82.8

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