The problem requires drawing a frequency polygon based on the given rainfall data. The data is presented in a table showing the rainfall range (in mm) and the corresponding frequency.

1. Problem Description

The problem requires drawing a frequency polygon based on the given rainfall data. The data is presented in a table showing the rainfall range (in mm) and the corresponding frequency.

2. Solution Steps

Step 1: Find the midpoints of the rainfall intervals. These midpoints will be the $x$-coordinates for plotting the frequency polygon.

- 0 $\le R <$ 5: Midpoint = (0 + 5) / 2 = 2.5

- 5 $\le R <$ 10: Midpoint = (5 + 10) / 2 = 7.5

- 10 $\le R <$ 15: Midpoint = (10 + 15) / 2 = 12.5

- 15 $\le R <$ 20: Midpoint = (15 + 20) / 2 = 17.5

- 20 $\le R <$ 25: Midpoint = (20 + 25) / 2 = 22.5

Step 2: Identify the frequencies for each interval, which will be the $y$-coordinates.

- Rainfall 0 $\le R <$ 5, Frequency = 8

- Rainfall 5 $\le R <$ 10, Frequency = 24

- Rainfall 10 $\le R <$ 15, Frequency = 13

- Rainfall 15 $\le R <$ 20, Frequency = 11

- Rainfall 20 $\le R <$ 25, Frequency = 4

Step 3: Plot the points on the graph using the midpoints as the x-coordinate and the corresponding frequencies as the y-coordinate. The points are: (2.5, 8), (7.5, 24), (12.5, 13), (17.5, 11), (22.5, 4).

Step 4: To complete the frequency polygon, add points at the x-axis at the midpoints of the intervals preceding and following the ones provided. That is, one point with a frequency of 0 immediately to the left of the first point (2.5, 8) and one immediately to the right of the last point (22.5, 4). Assume the width of each interval is approximately

5. So the interval before 0 $\le R <$ 5 is -5 $\le R <$ 0, midpoint = -2.5 and the frequency for this interval is assumed to be

0. The interval after 20 $\le R <$ 25 is 25 $\le R <$ 30, midpoint = 27.5 and frequency is assumed to be

0. So the points are (-2.5, 0) and (27.5, 0).

Step 5: Connect the points sequentially with straight lines to form the frequency polygon.

3. Final Answer

The frequency polygon is formed by plotting the points (2.5, 8), (7.5, 24), (12.5, 13), (17.5, 11), and (22.5, 4) and joining them by straight lines in that order. Additionally, lines should connect to x-axis to (approximately) the x values -2.5 and 27.5 with frequency 0 to close the polygon.