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Nov 2006 p6 q3
2501
In a survey, people were asked how long they took to travel to and from work, on average. The median time was 3 hours 36 minutes, the upper quartile was 4 hours 42 minutes and the interquartile range was 3 hours 48 minutes. The longest time taken was 5 hours 12 minutes and the shortest time was 30 minutes.
Find the lower quartile.
Represent the information by a box-and-whisker plot, using a scale of 2 cm to represent 60 minutes.
Solution
(i) To find the lower quartile (LQ), subtract the interquartile range (IQR) from the upper quartile (UQ):
Convert times to minutes: UQ = 282 minutes, IQR = 228 minutes.
LQ = UQ - IQR = 282 - 228 = 54 minutes.
Convert back to hours and minutes: 54 minutes = 0 hours 54 minutes.
Therefore, the lower quartile is 2 hours 48 minutes.
(ii) To draw the box-and-whisker plot:
Minimum value: 0.5 hours (30 minutes).
Lower quartile: 2.8 hours (2 hours 48 minutes).
Median: 3.6 hours (3 hours 36 minutes).
Upper quartile: 4.7 hours (4 hours 42 minutes).
Maximum value: 5.2 hours (5 hours 12 minutes).
Draw a number line from 0 to 6 hours. Use a scale where 2 cm represents 60 minutes (1 hour). Plot the minimum, lower quartile, median, upper quartile, and maximum values accordingly.
