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    Statistics: Frequency Distributions

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    I have two questions. Please use Microsoft word to write out solution.

    1) The scores in Mathematics of 15 students are given below. Find range, sample variance and standard deviation.
    93 85 78 79 97 90 82 61 53 63 94 69 84 67 95
    Show and explain your steps.

    2) The following are the prices charged (in cents) for a can of chicken soup at 20 super markets.
    80 89 81 78 92 82 79 85 79 85 91 80 81 84 90 79 79 78 92 84
    a) Calculate the mean and standard deviation.
    b) What percentage of data lies in the interval μ ± σ ? In the interval μ ± 2σ ?

    © BrainMass Inc. brainmass.com December 24, 2021, 11:50 pm ad1c9bdddf
    https://brainmass.com/math/probability/statistics-frequency-distributions-607719

    SOLUTION This solution is FREE courtesy of BrainMass!

    1) The scores in Mathematics of 15 students are given below. Find range, sample variance and standard deviation.
    93 85 78 79 97 90 82 61 53 63 94 69 84 67 95
    Show and explain your steps.
    Answer
    X X - X̅ (X - X̅)2
    93 13.66666667 186.7777778
    85 5.666666667 32.11111111
    78 -1.333333333 1.777777778
    79 -0.333333333 0.111111111
    97 17.66666667 312.1111111
    90 10.66666667 113.7777778
    82 2.666666667 7.111111111
    61 -18.33333333 336.1111111
    53 -26.33333333 693.4444444
    63 -16.33333333 266.7777778
    94 14.66666667 215.1111111
    69 -10.33333333 106.7777778
    84 4.666666667 21.77777778
    67 -12.33333333 152.1111111
    95 15.66666667 245.4444444
    1190 2691.333333
    Range = Maximum value - Minimum value
    = 97 - 53
    = 44
    Sample variance = = 192.2380952
    Sample standard deviation = = 13.86499532

    2) The following are the prices charged (in cents) for a can of chicken soup at 20 super markets.
    80 89 81 78 92 82 79 85 79 85 91 80 81 84 90 79 79 78 92 84
    Answers
    a) Calculate the mean and standard deviation.
    X X - X̅ (X - X̅)2
    80 -3.4 11.56
    89 5.6 31.36
    81 -2.4 5.76
    78 -5.4 29.16
    92 8.6 73.96
    82 -1.4 1.96
    79 -4.4 19.36
    85 1.6 2.56
    79 -4.4 19.36
    85 1.6 2.56
    91 7.6 57.76
    80 -3.4 11.56
    81 -2.4 5.76
    84 0.6 0.36
    90 6.6 43.56
    79 -4.4 19.36
    79 -4.4 19.36
    78 -5.4 29.16
    92 8.6 73.96
    84 0.6 0.36
    1668 458.8
    Mean = = 83.4
    Sample standard deviation = = 4.913997194
    b) What percentage of data lies in the interval μ ± σ ? In the interval μ ± 2σ ?
    μ ± σ = 83.4 ± 4.91 = (78.49, 88.31)
    There are 13 observations lies in the interval μ ± σ.
    Hence the percentage of data lies in the interval μ ± σ = 13/20 = 65%
    Empirical rule states that for a normal distribution,
    About 68% (precisely 68.27%) of the values lie within 1 standard deviation of the mean.
    μ ± 2σ = 83.4 ± (2 * 4.91) = (73.58, 93.22)
    There are 20 observations lies in the interval μ ± 2σ.
    Hence the percentage of data lies in the interval μ ± σ = 20/20 = 100%
    Empirical rule states that for a normal distribution,
    About 95% (precisely 95.45%) of the values lie within 2 standard deviation of the mean.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 11:50 pm ad1c9bdddf>
    https://brainmass.com/math/probability/statistics-frequency-distributions-607719

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