Q.The mean of a distribution is $32$, its mode is $35$ and its standard deviation is $6$. Find Karl Pearson's coefficient of skewness and state the type of skewness.

Apply the mode form $Sk_p = (\bar{x} - Z)/\sigma$ with the given values.

The numerator $32 - 35 = -3$ is negative, so the coefficient is negative.

Given: Mean $\bar{x} = 32$, Mode $Z = 35$, $\sigma = 6$.

$Sk_p = \frac{\bar{x} - Z}{\sigma} = \frac{32 - 35}{6} = \frac{-3}{6} = -0.5.$ The negative value shows the distribution is negatively (left) skewed.

Verification (dual solve). The sign is consistent with the averages: since $\bar{x} = 32 < Z = 35$, the mean lies below the mode, which is exactly the mean-below-mode pattern of a negatively skewed distribution. The magnitude $0.5$ lies well within the practical range $[-1, 1]$, so the result is admissible.

Dropping the negative sign and reporting $0.5$ (positive) loses the whole message — it would claim a right-skewed distribution when the data are actually left-skewed. The sign is the most important part of the answer.