Q.State what is meant by skewness of a frequency distribution, and distinguish between a symmetric distribution and a positively skewed one in terms of the mean, median and mode.

Skewness is the lack of symmetry of a distribution — whether one tail is longer than the other.

Meaning of skewness. Skewness is the lack of symmetry in a frequency distribution. Whereas a measure of dispersion tells us how widely the data are spread, skewness tells us whether that spread is one-sided — whether one tail of the distribution is drawn out longer than the other. It carries a direction (the side of the longer tail) and a degree (how far the distribution departs from symmetry), and is measured by a pure number that is $0$ for a symmetric distribution and non-zero for a skewed one.

Symmetric distribution. The frequencies are balanced about the central value, so the left half is a mirror image of the right half and there is no longer tail on either side. The three averages coincide: $\text{Mean} = \text{Median} = \text{Mode},$ and every coefficient of skewness is $0$. …

Describing skewness as a measure of spread. Spread (dispersion) and symmetry (skewness) are different properties: two distributions can have the same spread but opposite skewness. Al …