Interquartile range, Q1, Q3 and outliers — with worked steps
Enter your numbers to calculate the interquartile range (IQR), the first and third quartiles, and any outliers — with a full step-by-step solution.
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The interquartile range (IQR) is the distance between the third quartile and the first quartile: IQR = Q3 − Q1. It describes the spread of the middle 50% of the data. Because it ignores the smallest and largest quarter of the values, the IQR is far less sensitive to outliers than the full range or the standard deviation, which makes it a reliable measure of spread for skewed data.
Sort the data, split it at the median into a lower half and an upper half, then take Q1 as the median of the lower half and Q3 as the median of the upper half. Subtract: Q3 − Q1. Textbooks disagree on whether the median itself is included when the count is odd, so this calculator lets you switch between Tukey (exclude), Moore & McCabe (include) and Excel-style interpolation to match your course.
The IQR defines the standard outlier "fences". A value is a potential outlier if it falls more than 1.5 × IQR below Q1 or above Q3 (the inner fences), and an extreme outlier if it is beyond 3 × IQR (the outer fences). The box plot above marks any such points automatically.
Find the first quartile (Q1) and third quartile (Q3), then subtract: IQR = Q3 − Q1.
The full range depends on the two most extreme values, so a single outlier can distort it. The IQR uses only the middle 50% of the data, making it a more robust measure of spread.
Values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are flagged as potential outliers; values beyond 3 × IQR are considered extreme.