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    Probability & Statistic

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    Ahsan Ali
    This document discusses various statistical concepts such as deviation from the mean, mean absolute deviation, population variance, population standard deviation, sample variance, sample standard deviation, empirical rule, and coefficient of variation. It provides examples and formulas to demonstrate how to calculate each concept.

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    © All Rights Reserved
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    Probability & Statistic

    Uploaded by

    Ahsan Ali
    47 views10 pages
    This document discusses various statistical concepts such as deviation from the mean, mean absolute deviation, population variance, population standard deviation, sample variance, sample standard deviation, empirical rule, and coefficient of variation. It provides examples and formulas to demonstrate how to calculate each concept.

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    This document discusses various statistical concepts such as deviation from the mean, mean absolute deviation, population variance, population standard deviation, sample variance, sample standard deviation, empirical rule, and coefficient of variation. It provides examples and formulas to demonstrate how to calculate each concept.

    Copyright:

    © All Rights Reserved
    Download as PPT, PDF, TXT or read online from Scribd
    Download as ppt, pdf, or txt
    47 views10 pages

    Probability & Statistic

    Uploaded by

    Ahsan Ali
    This document discusses various statistical concepts such as deviation from the mean, mean absolute deviation, population variance, population standard deviation, sample variance, sample standard deviation, empirical rule, and coefficient of variation. It provides examples and formulas to demonstrate how to calculate each concept.

    Copyright:

    © All Rights Reserved
    Download as PPT, PDF, TXT or read online from Scribd
    Download as ppt, pdf, or txt
    of 10

    PROBABILITY & STATISTIC

    Presented To:
    Maam Amna
    Prepared By:
    Zain ul Abideen 13021598-002
    Muhammad Usama 13021598-030
    Khizer Butt 13021598-050
    Muhammad Asim 13021598-096

    Slide 3-1
    DEVIATION FROM THE MEAN


    Data set: 5, 9, 16, 17, 18
    Mean: X 65
    13
    N 5

    Deviations from the mean: -8, -4, 3, 4, 5


    Slide 3-2
    MEAN ABSOLUTE DEVIATION

    Average of the absolute deviations from the mean

    X X X X
    M . A. D.
    5 -8 +8 N
    9 -4 +4 24
    16 +3 +3
    17 +4 +4
    5
    18 +5 +5 4. 8
    0 24

    Slide 3-3
    POPULATION VARIANCE
    Average of the squared deviations from the arithmetic
    mean

    X X
    X X
    2
    2


    2
    5 -8 64
    9 -4 16 N
    16 +3 9 130

    17 +4 16 5
    18 +5 25 26.0
    0 130

    Slide 3-4
    POPULATION STANDARD DEVIATION
    Square root of the
    variance

    X X X
    X
    2
    2


    2
    5 -8 64
    N
    9 -4 16
    16 +3 9 130

    17 +4 16 5
    18 +5 25 26.0
    0 130

    2

    26.0
    51
    . Slide 3-5
    EMPIRICAL RULE
    Data are normally distributed (or approximately normal)

    Distance from Percentage of Values


    the Mean Falling Within Distance

    1 68
    2 95
    3 99.7
    Slide 3-6
    SAMPLE VARIANCE
    Average of the squared deviations from the arithmetic
    mean

    X X X X X X X
    2
    2

    2
    2,398 625 390,625 S
    n 1
    1,844 71 5,041
    1,539 -234 54,756 663,866

    1,311 -462 213,444 3
    7,092 0 663,866 221,288.67

    Slide 3-7
    SAMPLE STANDARD
    DEVIATION X X
    Square root of the sample 2

    variance 2
    S n 1
    X X X X X
    2

    663,866
    2,398 625 390,625
    1,844 71 5,041 3
    1,539 -234 54,756 221,288.67
    1,311 -462 213,444 2
    7,092 0 663,866 S S
    221,288.67
    470.41
    Slide 3-8
    COEFFICIENT OF VARIATION

    Ratio of the standard deviation to the mean, expressed


    as a percentage
    Measurement of relative dispersion


    C.V . 100

    Slide 3-9
    COEFFICIENT OF VARIATION
    1 29 2 84
    1
    4.6 2
    10
    100 100
    CV
    . .
    1
    1
    CV
    . .
    2
    2

    1 2

    4.6 10
    100 100
    29 84
    1586
    . 1190
    .
    Slide 3-10

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