The problem asks to use a frequency table (presumably from a previous page) to complete the cumulative frequency table, draw a cumulative frequency diagram based on the completed table, and use the diagram to estimate the median height and the 40th percentile. Unfortunately, the complete cumulative frequency table from page 4 is missing. We need additional information to complete it. Because the page is missing, I'll assume cumulative frequencies up to height values of 1.6, 1.7, 1.8 and 1.9. Let's assume the cumulative frequencies are: $h \le 1.6$: 40 $h \le 1.7$: 60 $h \le 1.8$: 85 $h \le 1.9$: 100 Then, we are asked to find an estimate for the median height, and the 40th percentile.

1. Problem Description

The problem asks to use a frequency table (presumably from a previous page) to complete the cumulative frequency table, draw a cumulative frequency diagram based on the completed table, and use the diagram to estimate the median height and the 40th percentile. Unfortunately, the complete cumulative frequency table from page 4 is missing. We need additional information to complete it. Because the page is missing, I'll assume cumulative frequencies up to height values of 1.6, 1.7, 1.8 and 1.

9. Let's assume the cumulative frequencies are:

$h \le 1.6$: 40

$h \le 1.7$: 60

$h \le 1.8$: 85

$h \le 1.9$: 100

Then, we are asked to find an estimate for the median height, and the 40th percentile.

2. Solution Steps

(c)(i) Completed Cumulative Frequency Table (assuming the above values):

$h \le 1.4$: 7

$h \le 1.5$: 25

$h \le 1.6$: 40

$h \le 1.7$: 60

$h \le 1.8$: 85

$h \le 1.9$: 100

(c)(ii) The cumulative frequency diagram would be a plot of the points (1.4, 7), (1.5, 25), (1.6, 40), (1.7, 60), (1.8, 85), (1.9, 100) connected by a smooth curve or straight lines. I am unable to actually draw this diagram. However, I can describe how to use it for parts (d)(i) and (d)(ii).

(d)(i) To find the median height, we need to find the value corresponding to the 50th percentile. The median is the value corresponding to the middle cumulative frequency. Since the maximum cumulative frequency is 100, the median corresponds to a cumulative frequency of $100/2 = 50$. On the cumulative frequency diagram, find the value 50 on the y-axis (cumulative frequency), draw a horizontal line to intersect the cumulative frequency curve, and then drop a vertical line from the point of intersection to the x-axis (height). The value where the vertical line intersects the x-axis is the estimated median height. Based on my assumed values, I estimate this as about 1.68m.

(d)(ii) To find the 40th percentile, we need to find the height value corresponding to a cumulative frequency of $0.40 * 100 = 40$. On the cumulative frequency diagram, find the value 40 on the y-axis (cumulative frequency), draw a horizontal line to intersect the cumulative frequency curve, and then drop a vertical line from the point of intersection to the x-axis (height). The value where the vertical line intersects the x-axis is the estimated 40th percentile height. Based on my assumed values, I estimate this as 1.6m.

3. Final Answer

(i) Median height: Approximately 1.68 m

(ii) 40th percentile: Approximately 1.6 m