Question

For a moderately skewed distribution, what is the empirical relationship between Mean, Median and Mode ?
1. Median - Mean = 3(Mean - Mode)
2. Mean - Mode = 3(Mode - Median)
3. Mean - Mode = 3(Mean - Median)
4. Mean - Mode = 3(Median - Mean)

Answer 1

Correct Answer - Option 3 : Mean - Mode = 3(Mean - Median)

To find the relationship between mean, median, and mode for a moderately skewed distribution, we should express this relationship by Karl Pearson’s formula. It is defined as the distance

between the mean and the median is about one-third the distance between the mean and the mode. We can write this as,

1/3(Mean – Mode) = (Mean – Median)

⇒ Mean – Mode = 3(Mean – Median)

∴ The required answer is Mean – Mode = 3(Mean – Median)