Outlier Detector (1.5 IQR)

How it is calculated

The numbers, separated by spaces or commas, are sorted and split into a lower and an upper half. With an odd count the middle value is left out of both halves. Q1 is the median of the lower half and Q3 the median of the upper half, so this is the median-of-halves method, not an interpolated percentile, and other software can give slightly different quartiles. Then IQR = Q3 − Q1, lower fence = Q1 − 1.5 × IQR and upper fence = Q3 + 1.5 × IQR. Any value strictly below the lower fence or above the upper fence is listed as an outlier, together with a count; if nothing falls outside, the list reads None. At least four numbers are needed, and an entry that is not a number gives no result. Fences and IQR are shown to two decimals.

Common mistakes

• Entering fewer than four numbers. Quartiles need enough points, and the tool gives no result below four.
• Assuming a value flagged here is an error. The rule marks values that are unusual compared with the middle half of the data, and they may be real.
• Comparing the answer with a spreadsheet's QUARTILE function. This tool uses medians of the two halves, so Q1 and Q3 can differ from other methods, especially with small samples.
• Being surprised when a single different value is flagged in a nearly constant list. With the values 5 5 5 5 5 5 9 the IQR is 0, so the fences sit on the quartiles and the 9 is reported as an outlier.
• Typing a decimal comma such as 2,5. A comma separates numbers here, so 2,5 is read as the two numbers 2 and 5; use a point for decimals.