Question

Find median of the data, using empirical relation when it is given that mode $=12.4$ and mean $=10.5$.

• A. $11.10$
• B. $11.13$
• C. $12$
• D. $13.20$

Answer 1

The correct option is B $11.13$

Given, mode$=12.4$ and mean $=10.5$

Emperical formula is:

$\text{mode}=3\times \text{median}-2\times \text{mean}$

Substituting the values, we get

$12.4=3\times \text{median}$ $-2\left(10.5\right)$

$\Rightarrow 12.4=3\times \text{median}$ $-21$

$\Rightarrow 3\times \text{median}$ $=33.4$

$\Rightarrow \text{Median}$ $=11.13$

The median is $11.13$.