Question

If the value of mean and mode of a grouped data are 50.25 and 22.5 respectively, then by using the empirical relation, find the median for the grouped data.

• A. 41
• B. 40
• C. 51
• D. 31

Answer 1

Answer:

A. 41

Solution:

Given:

The value of the mean of a grouped data = 50.25

The value of mode of a grouped data = 22.5

Formula used:

$3\times{Median}=Mode+2\times{Mean}$

Calculation:

According to the question,

⇒ $3\times{Median}=22.5+(2\times{50.25})$

⇒ $3\times{Median} = 22.5 +100.5$

⇒ $3\times{Median} = 123$

⇒ Median = $\frac{123}{3}$= 41

∴ The value of Median for the required grouped data is 41.