Quartiles & IQR Calculator

Worked example

Inputs: 1, 2, 3, 4, 5, 6, 7, 8. There are 8 values, so the median 4.5 splits them into 1, 2, 3, 4 and 5, 6, 7, 8. The median of the lower half is 2.5 and of the upper half is 6.5. Result: Q1 = 2.5, median = 4.5, Q3 = 6.5, and IQR = 6.5 − 2.5 = 4.

With an odd count the method matters. For 1, 2, 3, 4, 5, 6, 7 the median 4 is left out of both halves, which are 1, 2, 3 and 5, 6, 7, so Q1 = 2 and Q3 = 6 and the IQR is 4. A method that keeps the median in both halves gives Q1 = 2.5, Q3 = 5.5 and an IQR of 3 for the same data.

How it works

This tool splits your sorted numbers into four equal parts using the "median of halves" method: find the overall median, then the median of the lower half (Q1) and of the upper half (Q3), leaving the middle value out of both halves when there is an odd number of values. The interquartile range (IQR) is Q3 minus Q1, the spread of the middle half of the data. Quartile conventions genuinely differ: methods that keep the median in both halves, and the interpolation-based functions in spreadsheet software, can give different Q1 and Q3 for the same data. That is a difference between methods, not an error, so compare results only with a source that uses the same method. At least 2 numbers are needed, since a single number has no upper or lower half.