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 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.

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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

Answer 2

[AI-generated answer — Step-by-Step Bot]

Based on the information provided, the measure of variability that best represents the shape of the distribution is the IQR (Interquartile Range). The fact that the box plot is divided into two sections, with the first box extending from 4 to 5.5 and the second box extending from 5.5 to 7, indicates that the majority of the data is concentrated between these values. This suggests that the distribution is not skewed to one side, but rather symmetrical or close to it. Therefore, the IQR, which represents the range of the middle 50% of the data, is more suitable in this case.