For a distribution with mean, median, mode and standard deviation 25, 24, 26 and 5 respectively, Karl Pearson's coefficient of skewness equals to:
-0.20
Karl Pearson's coefficient of skewness (using mode) is:
\[SK_P=\frac{\text{Mean}-\text{Mode}}{\sigma}\]
Substituting Mean = 25, Mode = 26, \(\sigma=5\):
\[SK_P=\frac{25-26}{5}=\frac{-1}{5}=-0.20\]
The negative value is consistent with Mode > Mean, indicating a slightly left-skewed distribution. Hence the coefficient is -0.20.
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For a distribution, the mean is 10, variance is 16, γ 1is + 1 and β 2is 4. The distribution is: