Question

21. A college professor recorded the speed with which students ran out the door after class after taking the final exam (using a radar gun) for each of the last 4 semesters. The histogram below shows the distribution of speed for 168 students. The maximum value is 18 mph.

The value, 18 mph, was actually supposed to be 8 mph and this error is corrected. Which of the following is true?

(A) The mean will change the same amount as than the median, and the range will change the same amount as the SD.
(B) The mean will change more than the median, and the range will change more than the SD.
(C) The median will change more than the mean, and the range will change more than the SD.
(D) The mean will change more than the median, and the SD will change more than the range.
(E) The median will change more than the mean, and the SD will change more than the range.

Answer 1

B

Explanation:

Removing an outlier will have a larger impact on the mean than the median because the mean is nonresistant to outliers, while the median is resistant. Decreasing the maximum value will decrease the range by around 5 mph, while the SD will change by much less.

Answer 2

b

Explanation:

The correct answer is (B). The correction will decrease the mean because 8 is less than 18 and will decrease the standard deviation because the value, 8, is closer to the mean than the value 18.