Question

18. For a distribution Mean = 65, Median = 70 and S. D. = 25 find
i) Coefficient of Skewness.​

Answer 1

$\begin{gathered}\begin{gathered}\bf \:Given\:-\begin{cases} &\sf{Mean = 65} \\ &\sf{Median = 70}\\ &\sf{S. D. = 25} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:To\:find-\begin{cases} &\sf{Coefficient \: of \: Skewness}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline{\sf{Solution-}}$

Given that

• Mean = 65

• Median = 70

• S. D. = 25

We know that,

• Coefficient of Skewness is given by

$\rm :\longmapsto\:Coefficient \: of \: Skewness \: = \dfrac{3(Mean - Median)}{S. D.}$

$\rm :\longmapsto\:Coefficient \: of \: Skewness = \dfrac{3 \times (65 - 70)}{25}$

$\rm :\longmapsto\:Coefficient \: of \: Skewness =\dfrac{3 \times ( - 5)}{25}$

$\rm :\longmapsto\:Coefficient \: of \: Skewness = - \dfrac{3}{5}$

$\rm :\longmapsto\:Coefficient \: of \: Skewness = \: - \: 0.6$

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Additional Information :-

The coefficient of skewness is a measure of asymmetry in the distribution. A positive skew indicates a longer tail to the right, while a negative skew indicates a longer tail to the left. A perfectly symmetric distribution, like the normal distribution, has a skew equal to zero.

Interpretation :-

• If skewness is less than −1 or greater than +1, the distribution is highly skewed.

• If skewness is between −1 and −½ or between +½ and +1, the distribution is moderately skewed.

• If skewness is between −½ and +½, the distribution is approximately symmetric.