An outlier is a data point that sits far away from the rest of the observations. It may be a typing error, a faulty measurement, a member of a different population – or a genuine but rare event. Spotting outliers before analysing data matters because a single extreme value can shift the mean, inflate the standard deviation and distort a regression line.
The most widely used rule, due to John Tukey, works with quartiles. The interquartile range IQR = Q3 − Q1 measures the width of the middle half of the data; any value more than 1.5 IQRs below Q1 or above Q3 is flagged. Because quartiles hardly move when extreme values are added, the rule is not fooled by the outliers it is trying to detect, unlike rules based on the mean and standard deviation.
Enter your data to see the fences, the low and high outliers, how many there are and the data set without them. Raise the multiplier to 3 to keep only extreme outliers, or switch the quartile method to match your course.
How to use the Outlier Calculator
- Data set
- Fence multiplier (k) — 1.5 is the standard (Tukey) value; use 3 to flag only extreme outliers.
- Quartile method
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How it works
Sort the data and compute Q1 and Q3 with the chosen method. The fences are k × IQR beyond the quartiles; each value outside them is listed as a low or high outlier and plotted as a separate point.
Worked example
Fourteen bench-press results in kilograms: 15, 42, 45, 48, 50, 51, 53, 55, 57, 58, 60, 62, 64, 94. The lower half 15 … 53 has median Q1 = 48 and the upper half 55 … 94 has Q3 = 60, so IQR = 12. The fences are 48 − 18 = 30 and 60 + 18 = 78, so 15 and 94 are outliers. With k = 3 the fences widen to 12 and 96 and neither value is flagged – both are mild, not extreme, outliers.
What to do after finding outliers
- Check the source: typos, unit mix-ups (kg vs lb) and sensor glitches are common causes.
- Ask whether the point belongs to the population you are studying.
- If it is genuine, keep it and prefer the median and IQR, or run the analysis with and without it.
- Never remove outliers just to obtain a significant result.
Formula
Outlier if x < Q1 − k·IQR or x > Q3 + k·IQR · IQR = Q3 − Q1 · k = 1.5 (mild) or 3 (extreme)
Worked example
Inputs — Data set: 15, 42, 45, 48, 50, 51, 53, 55, 57, 58, 60, 62, 64, 94; Fence multiplier (k): 1.5; Quartile method: Median of halves, median excluded (TI-84, most textbooks).
Results — Outliers = 15, 94; Number of outliers = 2; Low outliers (below the lower fence) = 15; High outliers (above the upper fence) = 94; Lower fence (Q1 − k × IQR) = 30; Upper fence (Q3 + k × IQR) = 78.
Key terms
- Outlier
- An observation far from the bulk of the data.
- Mild outlier
- Between the inner (1.5·IQR) and outer (3·IQR) fences.
- Extreme outlier
- Beyond the outer fences.
- Masking
- When several outliers inflate a spread measure so that none of them looks unusual.
Frequently asked questions
How do you find outliers?
Compute Q1, Q3 and IQR. Any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is an outlier.
Which values are outliers in 15, 42, 45, 48, 50, 51, 53, 55, 57, 58, 60, 62, 64, 94?
Q1 = 48, Q3 = 60, IQR = 12 and the fences are 30 and 78, so 15 and 94 are outliers.
What is the difference between mild and extreme outliers?
Mild outliers lie between 1.5 and 3 IQRs beyond the quartiles; extreme outliers lie more than 3 IQRs beyond them.
Can I use z-scores instead?
Yes, |z| > 3 is common for roughly normal data, but outliers inflate the standard deviation and can mask each other. The IQR rule is more robust.
Should outliers be removed?
Only if they are errors or clearly not part of the population studied. Otherwise keep them and use robust statistics, or report results both ways.
How many outliers are normal?
For normal data about 0.7% of values fall outside the 1.5 × IQR fences – roughly 1 in 140.
What is the smallest data set for outlier detection?
The rule works from about 5 values, but with fewer than 10 the quartiles are unstable and conclusions should be cautious.