For a given frequency distribution, the mean is $28$ and the median is $30$. Using the empirical relationship between the measures of central tendency, find the mode of the distribution.

Step-by-step solution

1. Recall the empirical formula relating mean, median, and mode: $\text{Mode}=3\times \text{Median}-2\times \text{Mean}$.
2. Substitute the given values into the formula: $\text{Median}=30$ and $\text{Mean}=28$.
3. Calculate the value: $\text{Mode}=3(30)-2(28)=90-56=34$.

Concept tested: Empirical relation between measures of central tendency

Published 28 September 2026 · How this solution was prepared and checked

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