Question

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

Keisha’s 10th grade math class measured their arm spans (in cm) to find its relationship to their heights:

152 153 155 158 160 163 165 165 168 170 172 174 175 177 178 184 184

(1 point)
Responses

Range; 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 skewed, and there are 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.
Range; the distribution is symmetrical, or close to it, and there aren’t any 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 in the dataset.

Reason: Median = 168, Q1 = 159, Q3 = 176 (IQR = 17). The outlier fences are 159 − 1.5·17 = 133.5 and 176 + 1.5·17 = 201.5, so all values lie inside — no outliers. The data are roughly symmetric, so the range (184 − 152 = 32) is an appropriate measure of spread.