Question

The data set below has a lower quartile of 13 and an upper quartile of 37.

1, 12, 13, 15, 18, 20, 35, 37, 40, 78

Which statement is true about any outliers of the data set?

The data set does not have any outliers.
The lowest value, 1, is the only outlier.
The greatest value, 78, is the only outlier.
Both 1 and 78 are outliers.

Answer 1

IQR = 37 − 13 = 24.
Lower fence = 13 − 1.5(24) = 13 − 36 = −23.
Upper fence = 37 + 1.5(24) = 37 + 36 = 73.

1 > −23 so 1 is not an outlier. 78 > 73 so 78 is an outlier.

Answer: The greatest value, 78, is the only outlier.