Q.For a certain distribution the mean, median and mode are all equal to $60$. What is its coefficient of skewness, and what does this tell you about the shape of the distribution?

When all three averages coincide the numerator of Karl Pearson's coefficient is zero.

Given: Mean $=$ Median $=$ Mode $= 60$.

Karl Pearson's coefficient is $Sk_p = \frac{\bar{x} - Z}{\sigma} = \frac{60 - 60}{\sigma} = \frac{0}{\sigma} = 0,$ for any positive standard deviation $\sigma$. A zero coefficient means the distribution has no skewness in either direction: it is symmetric, with the two tails balanced and the single peak at the centre. …

Thinking the answer depends on the standard deviation. As long as $\sigma > 0$, a zero numerator forces a zero coefficient; the value of $ …