Question

In a frequency distribution. $\text{Mode}-\text{Median}=......\times \left( \text{Median}-\text{Mean} \right)$
A. $1$
B. $2$
C. $3$
D. $4$

Answer 1

Hint: In this problem we need to calculate the missing value in the given expression according to the given data. In the problem they have mentioned the distribution as frequency distribution. We know that the relation between the Mean, Mode and Median in a frequency distribution is given by $\text{Mode}=3\text{Median}-2\text{Mean}$ . For this equation we will subtract a Median term from both sides and simplify the equation to convert it into required format. Now we will compare both the equations to get the required value.

Complete step by step answer:
Given distribution is Frequency distribution.
We know that in frequency distribution the relation between the Mean, Mode and Median is given by $\text{Mode}=3\text{Median}-2\text{Mean}$.
From the above equation subtracting a Median term from both sides, then we will get
$\text{Mode}-\text{Median}=3\text{Median}-2\text{Mean}-\text{Median}$
Simplifying the above equation by performing basic mathematical operation, then we will have
$\text{Mode}-\text{Median}=2\text{Median}-2\text{Mean}$
Now taking $2$ as common from the left side of the above equation, then we will get
$\text{Mode}-\text{Median}=2\left( \text{Median}-\text{Mean} \right)$
We can observe that the above equation is in the given format which is $\text{Mode}-\text{Median}=......\times \left( \text{Median}-\text{Mean} \right)$.
Now comparing both the equations, we will get the missing value as $2$ .

So, the correct answer is “Option B”.

Note: The relation between mean, median and mode for the frequency distribution is taken as $\text{Mode}=3\text{Median}-2\text{Mean}$. This formula holds good when the distribution is uniform. However it is an approximate relation but not the exact one. If the distribution is symmetric, then this relation holds exactly because $\text{mean}=\text{median}=\text{mode}$ in this case.