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Question
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.
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
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