Q.Karl Pearson's coefficient of skewness of a distribution is $0.4$, its mean is $48$ and its standard deviation is $10$. Find the mode.

Rearrange the mode form to make the mode the subject: $Z = \bar{x} - Sk_p \times \sigma$.

Given: $Sk_p = 0.4$, Mean $\bar{x} = 48$, $\sigma = 10$; find the mode.

From $Sk_p = \frac{\bar{x} - Z}{\sigma} \quad\Rightarrow\quad \bar{x} - Z = Sk_p \times \sigma = 0.4 \times 10 = 4,$ so $Z = \bar{x} - 4 = 48 - 4 = 44.$ …

Adding instead of subtracting: since the coefficient is positive the mean exceeds the mode, so the mode must be SMALLER than the mean. Getting a mo …