The mean and variance of the distribution is 60 and 100 respectively. Find the mode and the median of the distribution if Skp = – 0.3. - Mathematics and Statistics

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The mean and variance of the distribution is 60 and 100 respectively. Find the mode and the median of the distribution if Skp = – 0.3.

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Solution

Given, Mean = 60, Variance = 100, Skp = – 0.3
∴ S.D. =`sqrt("Variance") = sqrt(100)` = 10
Skp = – 0.3
Pearsonian coefficient of skewness,

Skp = `("Mean"-"Mode")/"S.D."`

∴ – 0.3 = `(60 - "Mode")/(10)`

∴ – 3 = 60 – Mode
∴ Mode = 60 + 3 = 63

Mean – Mode = 3(Mean – Median)

∴ 60 – 63 = 3(60 – Median)

∴ – 3 = 180 – 3 Median

∴ 3 Median = 180 + 3 = 183

∴ Median = `183/3`

∴ Median = 61

Concept: Measures of Skewness - Karl Pearson’S Coefficient of Skewness (Pearsonian Coefficient of Skewness)
  Is there an error in this question or solution?
Chapter 3: Skewness - Exercise 3.1 [Page 43]
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