MAT 1272 Statistics, SP2014

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  • #13691

    Ezra Halleck
    Participant

    The following data give the annual earnings (in thousands of dollars) of 20 low to moderate income families.
    32.5 29.7 49.0 17.4 31.7 67.9 27.4
    43.7 53.4 59.5 37.0 22.7 15.8 43.2
    19.5 24.0 44.5 62.7 47.5 54.7
    a. Order the data and create a table with columns x and x^2. Find their sums
    b. Find the mean and median incomes (include units) and use them to comment on any skewing of this data.
    c. Use the table to find the sample variance and standard deviation. Write the latter using units.

    #17693

    Ezra Halleck
    Participant

    posted by Tamisha Prou
    x x2

    15.8 249.64
    17.4 302.76
    19.5 380.25
    22.7 515.29
    24.0 576
    27.4 750.76
    29.7 882.09
    31.7 1004.89
    32.5 1056.25
    37.0 1369
    43.2 1866.24
    43.7 1909.69
    44.5 1980..25
    47.5 2256.25
    49.0 2401
    53.4 2851.56
    54.7 2992.09
    59.5 3540.25
    62.7 3931.29
    67.9 4610.41
    _____ _______

    703.1 35425.9

    mean 35.1
    median 40.1

    nEx2-E(x)2
    ___________
    n(n-1)

    20.35425.9- 703.1(2)
    __________________
    20(20-1)

    708518-494349.61
    ________________
    380

    214168.39
    __________
    380

    =563.6 sample variance
    =24.0 standard deviation

    #17702

    Ezra Halleck
    Participant

    Looks good Tamisha. Just remember the units which are in thousands of dollars.

    #17705

    Leonardo Calegare
    Participant

    The formula for the sample variance is incorrect. The top part reads nEx2-Ex(2) and it should read nEx2-(Ex)^2.

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