Since \(x + y = 100,\ \therefore y = 100 - x\) Now, the frequency distribution table is as follows: | Class Interval | Frequency | Cumulative Frequency (less than type) | |----------------|-----------|----------------------------------------| | 0–10 | 10 | 10 | | 10–20 | \(x\) | \(10 + x\) | | 20–30 | 25 | \(35 + x\) | | 30–40 | 30 | \(65 + x\) | | 40–50 | \(100 - x\) | \(65 + x + 100 - x = 165\) | | 50–60 | 10 | 175 = \(n\) | Here, total frequency \(n = 175\) And given: \(x + y = 100\) — (i) Also, since the median is 32, The median class is (30–40) So, median is calculated as: \[ \text{Median} = l + \left( \frac{\frac{n}{2} - cf}{f} \right) \times h \] Where \(l = 30,\ n = 175,\ cf = 35 + x,\ f = 30,\ h = 10\) \[ = 30 + \left( \frac{87.5 - (35 + x)}{30} \right) \times 10 = 30 + \frac{52.5 - x}{30} \times 10 = 30 + \frac{52.5 - x}{3} \] Given: \[ 30 + \frac{52.5 - x}{3} = 32 \Rightarrow \frac{52.5 - x}{3} = 2 \Rightarrow 52.5 - x = 6 \Rightarrow x = 46.5 \] Substituting in (i): \[ 46.5 + y = 100 \Rightarrow y = 100 - 46.5 = 53.5 \] Final values: \(x = 46.5,\ y = 53.5\)