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 definitions of each measure:

• Mean: A measure of central tendency (average), not variability.
• Median: Also a measure of central tendency (middle value), not variability.
• Standard Deviation: A measure of variability that shows how much data values deviate from the mean. However, it is most appropriate for symmetric, unimodal data (like normal distributions).
• Interquartile Range (IQR): A measure of variability that represents the range of the middle 50% of the data. It is robust to outliers and skewed data. Histograms, especially if they are skewed or have outliers, are better analyzed with IQR for variability. Since the problem mentions histograms (which can be skewed), IQR is the best choice for measuring variability among the options.

1. Eliminate the non - variability measures: Mean and median are measures of central tendency, so we can eliminate them.
2. Choose between standard deviation and interquartile range: For data represented in histograms (which may be skewed or have outliers), interquartile range is more appropriate as it is resistant to outliers and skewness, while standard deviation is sensitive to these.

Answer:

D. interquartile range (assuming the options are labeled A - D with A: mean, B: median, C: standard deviation, D: interquartile range)