Interquartile Range Calculator

The IQR is the spread of the middle 50% of your data. It is the distance between the first quartile (Q1, the 25th percentile) and the third quartile (Q3, the 75th percentile). A small IQR means the middle half of your values is tightly packed; a large IQR means the middle half is spread out. Because it ignores the bottom 25% and top 25%, it tells you about the typical bulk of the data rather than its extremes.

This calculator uses the exclusive (Tukey) method: sort the data, find the median, then for an odd-sized dataset exclude the median from both halves before taking each half's median for Q1 and Q3. The inclusive method (used by Excel's QUARTILE.INC and many textbooks) includes the median in both halves for odd-sized data, which pulls Q1 and Q3 slightly toward the center. For even-sized datasets the two methods agree. Tukey's exclusive method is the original convention from John Tukey's exploratory data analysis work and is what most boxplot tools use.

The IQR only depends on the values near the 25th and 75th percentiles. Changing the largest or smallest value, even pushing it to infinity, does not move Q1 or Q3 at all. Compare that to the range or the standard deviation, both of which respond directly to extreme values. A single typo or a true outlier can multiply your standard deviation while leaving the IQR untouched, which is why analysts reach for the IQR when their data contains anomalies or has a heavy-tailed distribution.

Tukey's fences mark a value as an outlier if it falls below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR. For example, with Q1 = 2, Q3 = 5, and IQR = 3, the lower fence is -2.5 and the upper fence is 9.5; a value like 100 sits well past the upper fence and is flagged. The 1.5 multiplier is a convention, not a probability threshold: in a normal distribution it catches about 0.7% of values on each tail. Some analysts use 3 x IQR for extreme outliers; the calculator uses the standard 1.5 cutoff.

Use the IQR when your data is skewed, has outliers, or comes from an unknown distribution; it gives an honest picture of the middle 50% without being inflated by extreme values. Standard deviation is the right choice when your data is roughly symmetric and outlier-free (often assumed for normal distributions) because it uses every observation and pairs naturally with the mean. Quick rule: if you would report the median as your center, report the IQR as your spread; if you would report the mean, report the standard deviation.