(i) Plot the cumulative frequency points at the upper class boundaries: (20, 52), (30, 94), (40, 142), (50, 172), (70, 222), (100, 250). Draw a smooth curve or straight lines connecting these points.

(ii) To find \(k\), locate the cumulative frequency of 150 on the graph and read the corresponding rainfall value. From the graph, \(k \approx 42\) mm.

(iii) Calculate the frequencies for each class interval: \(52, 42, 48, 30, 50, 28\).

Find the midpoints of each class: \(10, 25, 35, 45, 60, 85\).

Calculate the mean: \(\bar{x} = \frac{(10 \times 52) + (25 \times 42) + (35 \times 48) + (45 \times 30) + (60 \times 50) + (85 \times 28)}{250} = \frac{9980}{250} = 39.9 \text{ mm}\)

Calculate the variance: \(s^2 = \frac{(10^2 \times 52) + (25^2 \times 42) + (35^2 \times 48) + (45^2 \times 30) + (60^2 \times 50) + (85^2 \times 28)}{250} - \bar{x}^2 = 539.59\)

Standard deviation: \(s = \sqrt{539.59} = 23.2 \text{ mm}\)