Question

Use the image to answer the question.

A number line ranges from 2 to 9.5 in increments of 0.5. A boxplot is placed above the number line. The box is divided into two sections. The first box extends from 4 to 5.5. The second box extends from 5.5 to 7. A line extends from each end of the box, terminating at 2 on the left and terminating at 9.5 on the right.

For the given box plot, which measure of variability—range or IQR—best represents the shape of the distribution?

(1 point)
Responses

Range; the shape of the distribution is symmetrical, or close to it.
Range; the shape of the distribution is symmetrical, or close to it.

IQR, the shape of the distribution is symmetrical, or close to it.
IQR, the shape of the distribution is symmetrical, or close to it.

Range, the shape of the distribution is skewed to the right.
Range, the shape of the distribution is skewed to the right.

IQR, the shape of the distribution is skewed to the right.
IQR, the shape of the distribution is skewed to the right.
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Answer 1

IQR, the shape of the distribution is skewed to the right.

Explanation: the box (IQR) is symmetric around the median but the right whisker is slightly longer than the left, indicating a mild right skew; IQR is the better measure of spread for skewed distributions because it is not affected by extreme values.