Interquartile Range (IQR)

The interquartile range throws away the top and bottom quarters of the data and measures what is left: Q₃ − Q₁, the width of the middle half. If a class's quartile scores are 48 and 72, the IQR is 24 points. Because it depends only on the ranks of the middle observations, it is immune to outliers in a way the range and standard deviation are not — you could replace the single highest value with a million and the IQR would not move at all. That robustness is why it is the spread reported for skewed data like incomes, house prices and reaction times.

The trap is comparing quartiles computed by different software. There are at least nine defensible definitions of a quartile, and Excel, R and most textbooks do not all agree on where Q₁ falls in a small data set — differences that vanish in large samples but can be embarrassing in a homework answer. John Tukey put the IQR at the centre of exploratory data analysis in 1977, using it both for the box in his box plot and for the fences that flag outliers at 1.5 IQR beyond each quartile.