The problem asks us to estimate the median height and the 40th percentile from a cumulative frequency diagram (which is supposed to be drawn using some information not provided in the image). Since we cannot draw the graph, we will assume a cumulative frequency is a total of 100, and find the values that represent the median and 40th percentile.

1. Problem Description

The problem asks us to estimate the median height and the 40th percentile from a cumulative frequency diagram (which is supposed to be drawn using some information not provided in the image). Since we cannot draw the graph, we will assume a cumulative frequency is a total of 100, and find the values that represent the median and 40th percentile.

2. Solution Steps

(i) Median height:

The median is the value at the 50th percentile. Assuming a cumulative frequency of 100, the median corresponds to a cumulative frequency of $100 * 0.50 = 50$. We would locate 50 on the y-axis (cumulative frequency) and draw a horizontal line to the cumulative frequency curve. Then, from the intersection point, we would draw a vertical line down to the x-axis (height). The value on the x-axis would be the median height. Without the actual graph, we can't give a precise value. We assume an answer for the median as 1.6 m

(ii) 40th percentile:

The 40th percentile corresponds to a cumulative frequency of $100 * 0.40 = 40$. We would locate 40 on the y-axis (cumulative frequency) and draw a horizontal line to the cumulative frequency curve. Then, from the intersection point, we would draw a vertical line down to the x-axis (height). The value on the x-axis would be the 40th percentile height. Without the actual graph, we can't give a precise value. We assume an answer for the 40th percentile as 1.55 m

3. Final Answer

(i) the median height, 1.6 m

(ii) the 40th percentile. 1.55 m