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June 2010 p62 q1
2437
The times in minutes for seven students to become proficient at a new computer game were measured. The results are shown below.
15, 10, 48, 10, 19, 14, 16
Find the mean and standard deviation of these times.
State which of the mean, median or mode you consider would be most appropriate to use as a measure of central tendency to represent the data in this case.
For each of the two measures of average you did not choose in part (ii), give a reason why you consider it inappropriate.
Solution
(i) To find the mean \(\bar{x}\), sum the times and divide by the number of students:
(ii) The median is the most appropriate measure of central tendency because it is not affected by the outlier (48).
(iii) The mode is inappropriate because it is 10, which is the lowest value and not representative of the data. The mean is inappropriate because it is affected by the outlier (48), which skews the average.
