Q.For a distribution the mean is $40$, the median is $42$ and Karl Pearson's coefficient of skewness is $-0.3$. Find the standard deviation and state the type of skewness.

The mean and median are given, so use the median form $Sk_p = 3(\bar{x} - M)/\sigma$ and solve for $\sigma$.

Given: Mean $\bar{x} = 40$, Median $M = 42$, $Sk_p = -0.3$; the standard deviation is required.

Using the median form $Sk_p = \frac{3(\bar{x} - M)}{\sigma} \quad\Rightarrow\quad \sigma = \frac{3(\bar{x} - M)}{Sk_p} = \frac{3(40 - 42)}{-0.3} = \frac{-6}{-0.3} = 20.$ A standard deviation must be positive, and $20$ is indeed positive, so the value is admissible. The negative coefficient shows the distribution is negatively (left) skewed. …

Mishandling the double negative: $-6$ divided by $-0.3$ is $+20$, not $-20$. A negative standard deviation is impossible, so a negative answer here is an …