What is the Interquartile Range (IQR)?

What is the Interquartile Range (IQR)?

• A. The spread between the 25th and 75th centile
• B. The difference between the maximum and minimum
• C. The standard deviation
• D. The range of the entire data set

Answer: (A)

Interquartile range measures the spread of the central 50% of the data. It’s computed by subtracting the first quartile (25th percentile) from the third quartile (75th percentile), so IQR = Q3 − Q1. This focuses on the middle portion of the distribution and is less influenced by extreme values than the overall range. Think of what it tells you about dispersion: it shows how widely the middle half of the values differ from each other, without letting outliers at the ends drag the measure up or down. This makes it particularly useful when the data are skewed or contain outliers. In contrast, the full range (max minus min) and the standard deviation either reflect the extremes or average deviation from the mean, respectively, and can be distorted by outliers. The IQR, by honing in on the central portion, provides a robust sense of typical spread.

Interquartile range measures the spread of the central 50% of the data. It’s computed by subtracting the first quartile (25th percentile) from the third quartile (75th percentile), so IQR = Q3 − Q1. This focuses on the middle portion of the distribution and is less influenced by extreme values than the overall range.

Think of what it tells you about dispersion: it shows how widely the middle half of the values differ from each other, without letting outliers at the ends drag the measure up or down. This makes it particularly useful when the data are skewed or contain outliers.

In contrast, the full range (max minus min) and the standard deviation either reflect the extremes or average deviation from the mean, respectively, and can be distorted by outliers. The IQR, by honing in on the central portion, provides a robust sense of typical spread.