Question

2071 Old Q.No.5 Person’s coefficient of skewness for a distribution is 0.4 and its coefficient of variation is 30%. If mode is 88, find mean and median.​

Answers

  1. Answer:

    Mean = 100

    Median = 96

    Step-by-step explanation:

    Given

    C_v = 30\% — coefficient of variation

    mode = 88

    Skp = 0.4

    Required

    The mean and the median

    The coefficient of variation is calculated using:

    C_v = \frac{\sigma}{\mu}

    Where:

    \mu \to mean

    So:

    30\% = \frac{\sigma}{\mu}

    Express percentage as decimal

    0.30 = \frac{\sigma}{\mu}

    Make \sigma the subject

    \sigma = 0.30\mu

    The coefficient of skewness is calculated using:

    Skp = \frac{\mu - Mode}{\sigma}

    This gives:

    0.4 = \frac{\mu - 88}{\sigma}

    Make \sigma the subject

    \sigma = \frac{\mu - 88}{0.4 }

    Equate both expressions for \sigma

    0.30\mu = \frac{\mu - 88}{0.4 }

    Cross multiply

    0.4*0.30\mu = \mu - 88

    0.12\mu = \mu - 88

    Collect like terms

    0.12\mu - \mu = - 88

    -0.88\mu = - 88

    Divide both sides by -0.88

    \mu = 100

    Hence:

    Mean = 100

    Calculate \sigma

    \sigma = 0.30\mu

    \sigma = 0.30 * 100

    \sigma = 30

    So:

    Also, the coefficient of skewness is calculated using:

    Skp = \frac{3 * (Mean - Median)}{\sigma}

    0.4= \frac{3 * (100 - Median)}{30}

    Multiply both sides by 30

    0.4*30= 3 * (100 - Median)

    Divide both sides by 3

    0.4*10= 100 - Median

    4= 100 - Median

    Collect like terms

    Median = 100 - 4

    Median = 96

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