For a certain frequency distribution the values of Mean and Mode are $54.6$ and $54$ respectively. Find the value of median.
Given: $\text{Mean} = 54.6$, $\text{Mode} = 54$
We know that,
$$\text{Mean} - \text{Mode} = 3(\text{Mean} - \text{Median})$$
$$\therefore 54.6 - 54 = 3(54.6 - \text{Median})$$
$$\therefore 0.6 = 3(54.6 - \text{Median})$$
$$\therefore \frac{0.6}{3} = 54.6 - \text{Median}$$
$$\therefore 0.2 = 54.6 - \text{Median}$$
$$\therefore \text{Median} = 54.6 - 0.2$$
$$\therefore \text{Median} = 54.4$$