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Nov 2019 p62 q1
2451
Twelve tourists were asked to estimate the height, in metres, of a new building. Their estimates were as follows.
50, 45, 62, 30, 40, 55, 110, 38, 52, 60, 55, 40
Find the median and the interquartile range for the data.
Give a disadvantage of using the mean as a measure of the central tendency in this case.
Solution
To find the median and interquartile range, first arrange the data in ascending order: 30, 38, 40, 40, 45, 50, 52, 55, 55, 60, 62, 110.
Median: The median is the average of the 6th and 7th values: \(\frac{50 + 52}{2} = 51\).
Interquartile Range (IQR): The lower quartile \(Q_1\) is the 3rd value: 40. The upper quartile \(Q_3\) is the 9th value: 57.5. Thus, \(\text{IQR} = Q_3 - Q_1 = 57.5 - 40 = 17.5\).
Disadvantage of using the mean: The mean is disproportionately affected by the extreme value 110, which is an outlier.