Question

In a moderately asymmetrical distribution, if the mean and the median are 36 and 34 respectively, then find out the value of the empirical mode.
A. 30
B. 32
C. 42
D. 22

Answer 1

Hint: We first try to explain the relation among the measures of central tendencies like mean, median and mode. Then we explain the use of the empirical relation. We use the formula of ${{M}_{0}}=3{{M}_{e}}-2\overline{x}$ to find the empirical mode.

Complete step-by-step answer:
There is no direct relation between the central tendencies like mean, median and mode. We can only use the empirical relation which is found to hold for unimodal distributions that do not deviate much from symmetry.
The relation is if the terminology for mean, median and mode be $\overline{x},{{M}_{e}},{{M}_{0}}$ respectively, then ${{M}_{0}}=3{{M}_{e}}-2\overline{x}$.
We are given that in a moderately asymmetrical distribution, if the mean and the median are 36 and 34 respectively. So, $\overline{x}=36,{{M}_{e}}=34$.
Placing the values, we get ${{M}_{0}}=3\times 34-2\times 36=102-72=30$.
Therefore, the empirical mode is 30. The correct option is A.
So, the correct answer is “Option A”.

Note: This empirical formula is not fully correct to the exact values. But in case of data missing this formula can be applied to get a rough idea about the measurements. Another application of the above formula is in calculating skewness. Since skewness measures the difference between the mean and the mode.