The table shows the heights in cm of some... | WAEC SSCE - Further Mathematics - 2017 (Essay)

Question 1 Report

The table shows the heights in cm of some seedlings in a certain garden.

Height (cm)	36-40	41-45	46-50	51-55	56-60
Frequency	3	9	21	12	5

(a) Draw the cumulative frequency curve for the distribution.

(b) Using the curve in (a), find thesemi-interquartile range.

Answer

The continuous class boundaries and cumulative frequencies are:

Height (cm)	Class boundaries (cm)	Frequency	Cumulative frequency
36–40	35.5–40.5	3	3
41–45	40.5–45.5	9	12
46–50	45.5–50.5	21	33
51–55	50.5–55.5	12	45
56–60	55.5–60.5	5	50

(a) The cumulative frequency curve is shown below. The point [35.5, 0[0m is included before plotting the upper class boundaries against their cumulative frequencies.

graph — Plot the upper class boundaries against the cumulative frequencies and draw a smooth increasing ogive through the plotted points.

(b) Total frequency, \(N=50\).

On the curve, the lower quartile corresponds to cumulative frequency

\[\frac{N}{4}=\frac{50}{4}=12.5.\]

Reading across from \(12.5\) to the curve and down to the height axis gives

\[Q_1\approx 45.6\text{ cm}.\]

The upper quartile corresponds to cumulative frequency

\[\frac{3N}{4}=\frac{3(50)}{4}=37.5.\]

Reading across from \(37.5\) to the curve and down to the height axis gives

\[Q_3\approx 52.0\text{ cm}.\]

Hence,

\[\text{Semi-interquartile range}=\frac{Q_3-Q_1}{2}=\frac{52.0-45.6}{2}=\boxed{3.2\text{ cm}}.\]

Read lesson note on Statistics (WAEC)

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