UPSC NDA 2 2021 Mathematics Solved Paper

Concept:The median for grouped data is found using the formula:$$\text{Median} = l + \frac{\frac{N}{2} - C}{f} \times h$$where $l$ = lower limit of median class, $N$ = total frequency, $f$ = frequency of median class, $h$ = class width, $C$ = cumulative frequency before median class.Explanation:First, compute cumulative frequencies from the given data.Here $N = 60$, so $\frac{N}{2} = 30$.The cumulative frequency just greater than 30 is 31, which corresponds to the class 35–40. Hence, the median class is 35–40.For this class: $l = 35$, $f = 5$, $h = 5$, and $C$ (cumulative frequency of the preceding class) = 26.Substitute into the formula:$$\text{Median} = 35 + \frac{30 - 26}{5} \times 5 = 35 + \frac{4}{5} \times 5 = 35 + 4 = 39$$Answer:The median is 39.