Let $$M$$ denote the median of the following frequency distribution.

Then $$20M$$ is equal to :

Total frequency N = 28. Median position $$= \frac{N}{2} = 14$$.

The value 14 falls in the class 8 - 12.

• l (lower limit) = 8

• cf (cumulative frequency before) = 12

• f (frequency of class) = 10

• h (width) = 4

Calculate M and 20M

$$M = l + \left( \frac{\frac{N}{2} - cf}{f} \right) \times h = 8 + \left( \frac{14 - 12}{10} \right) \times 4 = 8 + \frac{2}{10} \times 4 = 8 + 0.8 = 10.4$$

• $$20M = 20 \times 10.4 = \mathbf{208}$$ (Option D)