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June 2018 p62 q1
2425
Each of a group of 10 boys estimates the length of a piece of string. The estimates, in centimetres, are as follows.
37, 40, 45, 38, 36, 38, 42, 38, 40, 39
Find the mode.
Find the median and the interquartile range.
Solution
To solve the problem, we first organize the data in ascending order: 36, 37, 38, 38, 38, 39, 40, 40, 42, 45.
Mode: The mode is the number that appears most frequently. Here, 38 appears three times, which is more frequent than any other number. Thus, the mode is 38.
Median: The median is the middle value of the ordered data. Since there are 10 data points, the median is the average of the 5th and 6th values: \(\frac{38 + 39}{2} = 38.5\).
Interquartile Range (IQR): The IQR is the difference between the upper quartile \(Q_3\) and the lower quartile \(Q_1\).
\(Q_1\) is the median of the first half of the data: 36, 37, 38, 38, 38. The median is 38.
\(Q_3\) is the median of the second half of the data: 39, 40, 40, 42, 45. The median is 40.
