If the mean and the mode of a particular data set are 36 and 63 , respectively, then, using an empirical relation, find the value of the median of the same data set.

Correct option is C

Given:

Mean= 36

Mode= 63

Formula Used:

The empirical relation between the mean, mode, and median of a data set is:

​$$\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}$$

Substitute these values into the formula:

​Solution:​

​$$63 = 3 \times \text{Median} - 2 \times 36 \\$$ 

$$63 = 3 \times \text{Median} - 72 \\$$ 

$$3 \times \text{Median} = 63 + 72 \\$$ 

$$3 \times \text{Median} = 135 \\$$ 

$$\text{Median} = \frac{135}{3} = 45 \\$$

Thus the correct answer is (C)