UPSC NDA 2 2022 Mathematics Solved Paper

Concept:The median for grouped data is given by:${\displaystyle \text{Median} = L + \frac{\frac{N}{2} - CF}{f} \times h}$where $L$ = lower limit of median class, $N$ = total frequency, $CF$ = cumulative frequency before median class, $f$ = frequency of median class, $h$ = class width.Explanation:First, compute cumulative frequencies from the given distribution:Total $N = 20$, so $\frac{N}{2} = 10$.The cumulative frequency just greater than 10 is 13, which belongs to class 30-40.Thus median class is 30-40.Here $L = 30$, $CF = 7$, $f = 6$, $h = 10$.Substitute into the formula:${\displaystyle \text{Median} = 30 + \frac{10 - 7}{6} \times 10 = 30 + \frac{3}{6} \times 10 = 30 + 5 = 35}$Answer:$35$ (Option C).