The table shows the number of suitcases possessed... | WAEC SSCE - General Mathematics - 2003 (Essay)

Question 1 Report

The table shows the number of suitcases possessed by a group of travellers.

No. of suitcases	0	1	2	3	4	5
Travellers	2	7	7	2	3	9

(a) Calculate the (i) median (ii) mean, correct to the nearest whole number.

(b) Draw a bar chart to represent the information.

Answer

Given data.

No. of suitcases (x)	0	1	2	3	4	5
Travellers (f)	2	7	7	2	3	9

Total number of travellers: \(\sum f = 2+7+7+2+3+9 = 30\).

(a)(i) Median

With \(N = 30\) values (even), the median is the mean of the 15th and 16th values. Building the cumulative frequencies:

x	0	1	2	3	4	5
Cumulative f	2	9	16	18	21	30

Positions 10 to 16 correspond to \(x = 2\); hence both the 15th and 16th values equal 2.

\[\text{Median} = \frac{2+2}{2} = 2 \text{ suitcases.}\]

(a)(ii) Mean

\[\sum fx = (0)(2)+(1)(7)+(2)(7)+(3)(2)+(4)(3)+(5)(9) = 0+7+14+6+12+45 = 84.\]\[\bar{x} = \frac{\sum fx}{\sum f} = \frac{84}{30} = 2.8 \approx 3 \text{ (nearest whole number).}\]

(b) Bar chart

The number of suitcases (0 to 5) is placed on the horizontal axis and the number of travellers on the vertical axis. Each bar has equal width with equal gaps, and the heights are 2, 7, 7, 2, 3 and 9 respectively.

graph — Bar chart showing the number of travellers against the number of suitcases possessed.

The tallest bar occurs at 5 suitcases, with a height of 9 travellers.

Read lesson note on Percentages (WAEC)

Read lesson note on Surds (radicals) (WAEC)

Read lesson note on Statistics (WAEC)

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