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

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

Cumulative frequency table (cf plotted against upper class boundaries). \(N = 50\).

Height (cm)	Freq	Upper boundary	Cumulative freq
36 - 40	3	40.5	3
41 - 45	9	45.5	12
46 - 50	21	50.5	33
51 - 55	12	55.5	45
56 - 60	5	60.5	50

(a) Plot (40.5, 3), (45.5, 12), (50.5, 33), (55.5, 45), (60.5, 50) and join with a smooth ogive.

(b) Semi-interquartile range.

\(Q_1\) at position \( \tfrac{50}{4} = 12.5\), in class 46 - 50 (\(L=45.5, \text{cf}=12, f=21\)):

\[ Q_1 = 45.5 + \frac{12.5 - 12}{21}\times 5 = 45.5 + 0.12 = 45.62 \]

\(Q_3\) at position \( \tfrac{3\times 50}{4} = 37.5\), in class 51 - 55 (\(L=50.5, \text{cf}=33, f=12\)):

\[ Q_3 = 50.5 + \frac{37.5 - 33}{12}\times 5 = 50.5 + 1.88 = 52.38 \] \[ \text{Semi-interquartile range} = \frac{Q_3 - Q_1}{2} = \frac{52.38 - 45.62}{2} \approx \mathbf{3.4 \text{ cm}} \]

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Answer Details

Cumulative frequency table (cf plotted against upper class boundaries). \(N = 50\).

Height (cm)	Freq	Upper boundary	Cumulative freq
36 - 40	3	40.5	3
41 - 45	9	45.5	12
46 - 50	21	50.5	33
51 - 55	12	55.5	45
56 - 60	5	60.5	50

(a) Plot (40.5, 3), (45.5, 12), (50.5, 33), (55.5, 45), (60.5, 50) and join with a smooth ogive.

(b) Semi-interquartile range.

\(Q_1\) at position \( \tfrac{50}{4} = 12.5\), in class 46 - 50 (\(L=45.5, \text{cf}=12, f=21\)):

\[ Q_1 = 45.5 + \frac{12.5 - 12}{21}\times 5 = 45.5 + 0.12 = 45.62 \]

\(Q_3\) at position \( \tfrac{3\times 50}{4} = 37.5\), in class 51 - 55 (\(L=50.5, \text{cf}=33, f=12\)):

\[ Q_3 = 50.5 + \frac{37.5 - 33}{12}\times 5 = 50.5 + 1.88 = 52.38 \] \[ \text{Semi-interquartile range} = \frac{Q_3 - Q_1}{2} = \frac{52.38 - 45.62}{2} \approx \mathbf{3.4 \text{ cm}} \]

Read lesson note on Statistics (WAEC)

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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 cumula...

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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 cumula...

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