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