The following 10 scores were obtained on a 20-point quiz: 4, 5, 8, 9, 11, 13, 15, 18, 18, and 20. The teacher computed the usual descriptive measures of centre and variability for these data, and then discovered an error was made. One of the 18s should have been a 16. Which pair of the following measures, calculated on the corrected data, would change from the original computation?
A) mean and standard deviation
B) mean and median
C) range and median
D) mean and range

Question

Quizplus · Accepted Answer

The mean and standard deviation are affected by outliers, and changing the 18 to a 16 would change the outlier status of the second 18. The median and range are not affected by outliers, and the corrected data still contain the same minimum and maximum values as the original data. Therefore, B, C, and D are incorrect choices.

The Following 10 Scores Were Obtained on a 20-Point Quiz