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June 2006 p6 q1
2441
The salaries, in thousands of dollars, of 11 people, chosen at random in a certain office, were found to be:
40, 42, 45, 41, 352, 40, 50, 48, 51, 49, 47.
Choose and calculate an appropriate measure of central tendency (mean, mode or median) to summarise these salaries. Explain briefly why the other measures are not suitable.
Solution
To find the median, first arrange the data in ascending order: 40, 40, 41, 42, 45, 47, 48, 49, 50, 51, 352.
The median is the middle value, which is the 6th value in this ordered list: 47.
The median is $47,000.
The mean is not suitable because the data contains an outlier (352), which skews the mean. The mode is not suitable because it does not represent the central tendency effectively in this context.