Q.For a distribution the mean is $29$, the median is $30$ and the standard deviation is $5$. The mode is ill-defined. Find Karl Pearson's coefficient of skewness.

With the mode ill-defined, use the median form $Sk_p = 3(\bar{x} - M)/\sigma$.

Here $3(29 - 30) = -3$, and dividing by $5$ gives $-0.6$.

Given: Mean $\bar{x} = 29$, Median $M = 30$, $\sigma = 5$; mode ill-defined.

$Sk_p = \frac{3(\bar{x} - M)}{\sigma} = \frac{3(29 - 30)}{5} = \frac{-3}{5} = -0.6.$ The negative value means the distribution is negatively skewed.

Verification (dual solve). Recover the mode from $Z = 3M - 2\bar{x} = 3(30) - 2(29) = 90 - 58 = 32$, then use the mode form: $Sk_p = \frac{\bar{x} - Z}{\sigma} = \frac{29 - 32}{5} = \frac{-3}{5} = -0.6,$ which matches. The order Mean $29 <$ Median $30 <$ Mode $32$ is the negatively-skewed pattern, confirming the sign.

Omitting the factor 3, or subtracting in the wrong order ($M - \bar{x}$ instead of $\bar{x} - M$), which flips the sign. Keep mean first, median second, and multiply by 3.