Question

Determine whether the range or interquartile range best describes the spread of a dataset.
The times (in seconds) for a high school boys’ 100-meter race:
11.0 11.2 11.7 12.2 12.4 12.6 12.8 12.9 13.1 13.3 13.8 14.2 14.3 14.3 16.5 17.6
18.0
(1 point)
Range; the distribution is skewed, and there are outliers in the dataset.
IQR; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.
IQR; the distribution is skewed, and there are outliers in the dataset.
Range; the distribution is symmetrical, or close to it, and there aren’t any outliers in the dataset.

Answer 1

IQR; the distribution is skewed, and there are outliers in the dataset.

Reason: the data are right-skewed (longer tail of larger times). Q1 = 12.3, Q3 = 14.3, so IQR = 2.0. The upper outlier fence is Q3 + 1.5·IQR = 17.3, so 17.6 and 18.0 are outliers. The range is affected by those outliers, so IQR is the better measure.