How do you compute the interquartile range (IQR) and what does it indicate?

How do you compute the interquartile range (IQR) and what does it indicate?

• A. IQR = Q1 − Q3; indicates the spread of the data.
• B. IQR = Q3 − Q1; indicates the spread of the middle 50%.
• C. IQR = (Q3 + Q1)/2; indicates the central tendency.
• D. IQR equals the standard deviation of the middle half.

Answer: (D)

Interquartile range measures the spread of the central portion of the data. To compute it, order the data, find the first quartile (the median of the lower half) and the third quartile (the median of the upper half), then subtract Q1 from Q3. The result tells you how far apart the middle 50% of observations are, giving a sense of variability that's less sensitive to outliers than the overall range or the standard deviation. A larger IQR means more variability within the central half; a smaller IQR means the central values are closer together. It isn’t Q1 minus Q3, which would not represent a spread, nor the average of Q1 and Q3, which is a central value. It also isn’t the standard deviation, a different dispersion measure that uses all data points and deviations from the mean.

Interquartile range measures the spread of the central portion of the data. To compute it, order the data, find the first quartile (the median of the lower half) and the third quartile (the median of the upper half), then subtract Q1 from Q3. The result tells you how far apart the middle 50% of observations are, giving a sense of variability that's less sensitive to outliers than the overall range or the standard deviation. A larger IQR means more variability within the central half; a smaller IQR means the central values are closer together. It isn’t Q1 minus Q3, which would not represent a spread, nor the average of Q1 and Q3, which is a central value. It also isn’t the standard deviation, a different dispersion measure that uses all data points and deviations from the mean.