Which measure of variability would you use to find the middle fifty percent of data points?

The interquartile range is the measure of variability that is specifically used to find the middle fifty percent of data points in a data set. It does this by calculating the difference between the first quartile (Q1) and the third quartile (Q3). Quartiles divide the data into four equal parts, so the first quartile represents the value below which 25% of the data fall, and the third quartile represents the value below which 75% of the data fall. By taking the difference between Q3 and Q1 (Q3 - Q1), the interquartile range captures the spread of the middle half of the data, effectively isolating the central 50% and providing a measure that is resistant to outliers, which could distort other measures of variability.

In contrast, the range calculates the difference between the maximum and minimum values, the standard deviation measures the average distance of data points from the mean, and variance is the square of the standard deviation. None of these measures specifically target the central half of the data in the same way as the interquartile range does.