Discussion
If mean and median of a frequency distribution are 20 and 22 respectively, then the mode of the distribution will be :
Answer: C
The mode is 26.
For a moderately skewed distribution, Karl Pearson's empirical relation links the three averages:
\[ \begin{aligned} \text{Mode} &= 3\,\text{Median} - 2\,\text{Mean} \\ &= 3(22) - 2(20) \\ &= 66 - 40 = 26 \end{aligned} \]
21 is the average of the mean and median, and 16 comes from reversing the roles (3 x 20 - 2 x 22). 11 does not come from the formula at all.
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