For a certain frequency distribution the values of Median and Mode is $95.75$ and $95.5$ respectively, find the mean.
Solution:
Given: $\text{Median} = 95.75$, $\text{Mode} = 95.5$
We know that,
$$\text{Mean} - \text{Mode} = 3(\text{Mean} - \text{Median})$$
$$\therefore \text{Mean} - 95.5 = 3(\text{Mean} - 95.75)$$
$$\therefore \text{Mean} - 95.5 = 3\text{Mean} - 287.25$$
$$\therefore 287.25 - 95.5 = 3\text{Mean} - \text{Mean}$$
$$\therefore 191.75 = 2\text{Mean}$$
$$\therefore \text{Mean} = \frac{191.75}{2}$$
$$\therefore \text{Mean} = 95.875$$