Question

If in a frequency distribution, the mean and median are 21 and 22 respectively, then the mode of the given data is approximately
a). 22
b). 20.5
c). 25.5
d). 24.0

Answer 1

Hint: To find the mode of the given frequency distribution we will use the relation among the mean, median and mode because we know the value of mean, median and mode. We know that the difference between mean and mode is equal to three times the difference between mean and median. So, the empirical relationship is:
Mean – Mode = 3(Mean - Median)

Complete step by step answer:
Since, we have to find the mode of the given frequency distribution. To find the mode we will use the relationship among mean, median, and mode. We know that for a given frequency distribution the difference between mean and mode is equal to three times the difference between mean and median. So, the empirical relationship is
Mean – Mode = 3(Mean - Median) ……………..(1)
We know from the question that Mean = 21 and Median = 22
Let us assume that mode as x.
So, put the value of Mean = 21 and Median = 22 and Mode =x in equation (1), then we will get:
21 - x = 3(21-22)
So, 21 – x = -3
Hence, x = 21 + 3 = 24
And, we have mode as x. So, mode is equal to 24.

So, the correct answer is “Option D”.

Note: Students are required to memorize the relationship among mean, median and mode for a given frequency distribution. This relation among mean, median and mode is very important and is used many times so students are required to remember it. Another form of the relation is Mode = 3Median - 2Mean.