Quartile IQR Calculator

Quartiles and the IQR

The interquartile range (IQR) measures how spread out the middle 50% of your data is. A small IQR means the data clusters tightly around the median; a large IQR indicates more variability. Because it uses only the middle values, the IQR is resistant to outliers — unlike the range (max − min) or the standard deviation, which are heavily influenced by extreme values.

The IQR is the foundation of box-and-whisker plots. The box spans Q1 to Q3, the line inside the box marks Q2 (median), and the whiskers extend to the Tukey fences.

Tukey fences and outlier detection

The Tukey method defines outlier fences as: lower fence = Q1 − 1.5 × IQR, upper fence = Q3 + 1.5 × IQR. Any value below the lower fence or above the upper fence is flagged as an outlier. For more extreme outliers, some analysts use inner fences (1.5 × IQR) and outer fences (3 × IQR).

The 1.5 × IQR rule is not a strict statistical test; it is a heuristic for identifying values that deserve closer inspection. Whether a flagged value is truly erroneous depends on domain knowledge.

Interpolation method

This calculator uses linear interpolation (Excel QUARTILE.INC method): Q1 = value at the 25th percentile by linear interpolation, Q2 = median (50th percentile), Q3 = value at the 75th percentile. For a dataset of n values sorted in ascending order, the index for the kth quartile is k/4 × (n − 1).