Question

The data set below has an outlier.

2, 10, 10, 11, 11, 12, 12, 12, 13, 14, 14

Which value is changed the most by removing the outlier?

A: the range
B: the median
C: the lower quartile
D: the interquartile range

Answer 1

To answer the problem above, we must define what an outlier is. An outlier is a number in a set of data that is smaller or larger than the rest of the data. In this problem, the outlier is 2. To know which value changed the most we solve each with and without the outlier.
A. range: 12(with), 4(without)
B. median: 12 (with), 12 (without)
C. lower quartile: 10.5(with), 11(without)
D. interquartile range: 2(with), 2(without)

The answer is A. range.

Answer 2

Data set: 2, 10, 10, 11, 11, 12, 12, 12, 13, 14, 14

range: 14 - 2 = 12
median: 12
lower quartile = 10
interquartile range = 4

Data set w/o outlier 2: 10, 10, 11, 11, 12, 12, 12, 13, 14, 14

range: 14 - 10 = 4
median: 12
lower quartile: 10.5
interquartile range = 3.5

The value that change the most by removing the outlier is A.) THE RANGE.