Question

Which measure of variability—range or IQR—best describes the spread of the dataset?

For a statistics assignment, Shayna randomly surveyed students on how many hours per week they spend playing online games:

1.0 1.0 2.0 6.5 10.0 10.0 10.0 10.0 12.0 12.5 14.0 14.0 14.0 14.0 15.0 15.0 15.5 16.0 17.5 18.0

(1 point)
Responses

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

Range; the distribution is symmetrical, or close to it, and there arent any outliers in the dataset
Range; the distribution is symmetrical, or close to it, and there arent any outliers in the dataset

IQR; the distribution is symmetrical, or close to it, and there arent any outliers in the dataset.

Answer 1

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

Reason: Q1 = 10, Q3 = 15 so IQR = 5 (range = 18 − 1 = 17). Using 1.5·IQR = 7.5 gives a lower fence 10 − 7.5 = 2.5, so 1.0, 1.0 and 2.0 are outliers. The mean (≈11.4) is less than the median (13.25), indicating left (negative) skew — therefore the IQR is the better measure of spread.