Interpret the IQR in a dataset.

Interpret the IQR in a dataset.

• A. The IQR measures the spread of the full data set.
• B. The IQR is the same as the variance.
• C. The IQR measures the spread of the middle 50% of observations.
• D. The IQR expands with sample size.

Answer: (C)

The interquartile range measures the spread of the middle 50% of observations. It’s the distance between the 75th percentile and the 25th percentile, so it focuses on the central portion of the data rather than the tails. This makes it a robust measure of spread, since extreme values outside the middle half have little effect. That’s why describing the IQR as the spread of the middle 50% is the best interpretation. It doesn’t describe the full spread of the data set (that would be the range), it isn’t the same as the variance, and it doesn’t inherently expand just because you collect more observations—the IQR reflects the central dispersion in the data.

The interquartile range measures the spread of the middle 50% of observations. It’s the distance between the 75th percentile and the 25th percentile, so it focuses on the central portion of the data rather than the tails. This makes it a robust measure of spread, since extreme values outside the middle half have little effect. That’s why describing the IQR as the spread of the middle 50% is the best interpretation. It doesn’t describe the full spread of the data set (that would be the range), it isn’t the same as the variance, and it doesn’t inherently expand just because you collect more observations—the IQR reflects the central dispersion in the data.