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June 2016 p63 q2
2490
A group of children played a computer game which measured their time in seconds to perform a certain task. A summary of the times taken by girls and boys in the group is shown below.
Minimum
Lower quartile
Median
Upper quartile
Maximum
Girls
5
5.5
7
9
13
Boys
4
6
8.5
11
16
On graph paper, draw two box-and-whisker plots in a single diagram to illustrate the times taken by girls and boys to perform this task.
State two comparisons of the times taken by girls and boys.
Solution
(i) To draw the box-and-whisker plots:
For girls: Minimum = 5, Lower quartile = 5.5, Median = 7, Upper quartile = 9, Maximum = 13.
For boys: Minimum = 4, Lower quartile = 6, Median = 8.5, Upper quartile = 11, Maximum = 16.
Draw the plots on the same scale, labeling the axes with 'Time in seconds'.
(ii) Comparisons:
The range for girls (13 - 5 = 8) is smaller than for boys (16 - 4 = 12).
The interquartile range for girls (9 - 5.5 = 3.5) is smaller than for boys (11 - 6 = 5).
The median time for girls (7) is less than the median time for boys (8.5), indicating girls are generally quicker.
The distribution for boys is almost symmetrical, while for girls it is positively skewed.