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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.
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 symmetrical, or close to it.
IQR, the shape of the distribution is symmetrical, or close to it.
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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IQR, the shape of the distribution is symmetrical, or close to it.
The IQR (Interquartile Range) is a measure of variability that is more robust to outliers compared to the range. Since the boxplot has evenly distributed data points within each section of the box, it suggests that the distribution is symmetrical or close to it. Therefore, the IQR would best represent the shape of the distribution in this case.