Interquartile Range Calculator

How it is calculated

This tool does not take raw data; you give it the first quartile Q1 and the third quartile Q3 that you have already found. It computes IQR = Q3 − Q1, then the outlier fences lower fence = Q1 − 1.5 × IQR and upper fence = Q3 + 1.5 × IQR. Results are shown with four decimals, in the same unit as your data. A value outside the two fences is usually flagged as a possible outlier, not automatically as an error. If Q3 is smaller than Q1 the tool returns no result, because quartiles cannot be in that order. Q1 equal to Q3 is accepted and gives an IQR of 0, with both fences at the same value. Only the 1.5 multiplier is used; the tool does not show the stricter 3 × IQR fences.

Common mistakes

• Typing the minimum and maximum of the data instead of Q1 and Q3; that gives the range, not the IQR.
• Entering the median in place of a quartile.
• Swapping the two values so that Q1 is larger than Q3; the tool then returns nothing.
• Assuming every value outside the fences is a mistake. It is only a flag; genuine extreme values can be real and should be checked before removal.
• Comparing quartiles from different software without checking the method. Quartile definitions differ slightly between tools, so Q1 and Q3 may not match your textbook value.