Question

The median and mode of frequency distribution are 525 and 500, then the mean of same frequency distribution is -
A. 75
B. 107.5
C. 527.5
D. 537.5

Answer 1

Hint: We are given the value of median and mode and we are asked to find the mean. So we need a formula which relates these 3 entities. Mean, median and mode are the three measures of central tendency. The subtraction of 2 times mean from 3 times median gives the value of mode of frequency distribution. Using this relation, find the mean.

Complete step-by-step answer:
We are given that the median and mode of frequency distribution are 525 and 500.
We have to find the mean of the same frequency distribution.
Frequency distribution in statistics is a representation of the number of observations in a given interval. There are many types of frequency distribution. Grouped and ungrouped are the most used ones.
Mean is the average value. It can be obtained by multiplying the midpoint of each interval with its frequency and then dividing the product by the total values of the frequency distribution. Median is the middle value and Mode is the most often appeared value.
The relation between mean, median and mode can be written as $ Mode = 3Median - 2Mean $
The value of the median given is 525 and the mode is 500.
 $ \Rightarrow 500 = 3\left( {525} \right) - 2Mean $
 $ \Rightarrow 2Mean = 1575 - 500 = 1075 $
 $ \therefore Mean = \dfrac{{1075}}{2} = 537.5 $
Therefore, the mean of the same frequency distribution is $ 537.5 $ .
So, the correct answer is “Option D”.

Note: Sometimes, the mean and the median of a frequency distribution are identical. Then such distribution is called a perfectly symmetrical distribution. Mean must be only one value, median and mode can have more than one value. For an odd number of data points, we have one median whereas for an even number of data points, we have two medians.