Question

Which measure of variability—range or IQR—best describes the spread of the dataset?
Social studies group project grades (out of 100 points) for Mr. Chang’s first period class
85 88 90 90 92 92 95 96 99
(1 point)
Range; 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 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

Answer 1

Range; the distribution is symmetrical (or close to it) and there aren’t any outliers.

Quick check: median = 92, Q1 = (88+90)/2 = 89, Q3 = (95+96)/2 = 95.5, so IQR = 6.5. Range = 99 − 85 = 14. Using 1.5·IQR = 9.75 gives fences 89 − 9.75 = 79.25 and 95.5 + 9.75 = 105.25, so no outliers. The data are roughly symmetric, so range is an appropriate measure.