What does the interquartile range measure?

What does the interquartile range measure?

• A. The range of the middle 50% of data
• B. The entire data range
• C. The average deviation from the mean
• D. The standard deviation

Answer: (A)

The interquartile range is a measure of how spread out the central portion of the data is. It looks at the middle 50% of observations, from the first quartile (the 25th percentile) to the third quartile (the 75th percentile), and is calculated as the difference between them. So, it tells you how far apart the middle half of the data lie, giving a sense of central variability while being less affected by extreme values outside this middle range. For example, if the first quartile is 10 and the third quartile is 20, the IQR is 10, meaning the central half of values fall within a 10-unit span. This differs from the full range, which is simply max minus min and can be greatly swayed by outliers. It also isn’t the mean absolute deviation, which averages how far each value is from the mean, nor is it the standard deviation, which uses squared deviations from the mean. The IQR provides a robust snapshot of dispersion specifically for the central portion of the data.

The interquartile range is a measure of how spread out the central portion of the data is. It looks at the middle 50% of observations, from the first quartile (the 25th percentile) to the third quartile (the 75th percentile), and is calculated as the difference between them. So, it tells you how far apart the middle half of the data lie, giving a sense of central variability while being less affected by extreme values outside this middle range. For example, if the first quartile is 10 and the third quartile is 20, the IQR is 10, meaning the central half of values fall within a 10-unit span.

This differs from the full range, which is simply max minus min and can be greatly swayed by outliers. It also isn’t the mean absolute deviation, which averages how far each value is from the mean, nor is it the standard deviation, which uses squared deviations from the mean. The IQR provides a robust snapshot of dispersion specifically for the central portion of the data.