IQR Calculator (Interquartile Range)

The interquartile range is the spread of the middle 50% of a dataset. Compute Q1 (25th percentile) and Q3 (75th percentile), then subtract: IQR = Q3 - Q1. Unlike the full range (max - min), IQR ignores the extremes, so a single rogue value cannot inflate it. That makes it the go-to spread measure for skewed data, income distributions, test scores, and anything where outliers are expected.

The quartile method used here is the exclusive one, also called Tukey’s hinges: split the sorted data at the median position and leave the median itself out of both halves when n is odd. It is what Moore and McCabe’s textbook teaches and what a TI-83 returns.

It is worth being precise about what it does not match, because quartiles are one of the few places where reputable software openly disagrees. Excel’s QUARTILE.EXC uses a different rule, interpolating at position k(n+1)/4, and the two agree only sometimes. On the data 1, 2, 3, 4 this page gives Q1 = 1.5 and Q3 = 3.5, while QUARTILE.EXC gives 1.25 and 3.75. On 1, 2, 3, 4, 5 both give 1.5 and 4.5. R alone ships nine different quartile definitions and defaults to a tenth thing again. None of them is wrong; they are answering slightly different questions about what a quartile of a finite sample means. If your answer differs from a textbook or a spreadsheet by a little, check which convention it used before assuming an error.

Once you have the IQR, outlier fences follow automatically. A mild outlier falls below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. An extreme outlier is beyond Q1 − 3 × IQR or Q3 + 3 × IQR. Both thresholds come from Tukey’s 1977 book on exploratory data analysis and are built into every major stats package, though they are a rule of thumb rather than a law. The 1.5 was chosen because on normally distributed data it flags roughly 0.7% of points, which is rare enough to be interesting and common enough to be worth looking at.

A fence is a prompt to investigate, never a licence to delete. A flagged point is sometimes a typo and sometimes the most important observation in the set.

The IQR only measures spread, not shape. A dataset with IQR = 10 could be symmetric, left-skewed, or bimodal. Always pair it with a quick look at the median and the actual sorted values before drawing conclusions about the distribution.

How to use: enter your values in any order (blanks are skipped). At least 4 values are needed to compute meaningful quartiles. The result shows Q1, Q3, IQR, both Tukey fences, and any detected outliers.