Question

two histograms showing the number of pets owned by boys and girls in a science class are each skewed left. which measure of variability should be used to describe the data? mean median standard deviation interquartile range

Explanation:

1. First, recall the properties of measures of variability and skewed data:

• The mean and median are measures of central tendency, not variability, so we can eliminate the mean and median options.
• The standard deviation is affected by extreme values (outliers) and skewness. In skewed data, the standard deviation may not be a good measure of variability as it is sensitive to the skewed tail.
• The interquartile range (IQR) is the difference between the third quartile (\(Q_3\)) and the first quartile (\(Q_1\)) (\(IQR = Q_3 - Q_1\)). The IQR measures the spread of the middle 50% of the data and is resistant to skewness and outliers. For skewed data, the IQR is a more appropriate measure of variability than the standard deviation.

Answer:

D. interquartile range