Outlier calculator
Paste your numbers to see which ones are outliers. The calculator uses the standard 1.5 × IQR rule, shows both fences and marks each outlier on a box plot.
- Outliers
- 48
- Lower fence
- 4.5
- Upper fence
- 40.5
- IQR
- 9
Separate with commas, spaces or new lines, or paste a spreadsheet column. 14 numbers read.
Textbooks and TI calculators take medians of the lower and upper halves. Excel interpolates. Results can differ on small data sets.
| Count (n) | 14 |
|---|---|
| Minimum | 12 |
| First quartile Q1 | 18 |
| Median | 22 |
| Third quartile Q3 | 27 |
| Maximum | 48 |
| Range | 36 |
| Interquartile range (IQR) | 9 |
| Lower fence Q1 − 1.5 × IQR | 4.5 |
| Upper fence Q3 + 1.5 × IQR | 40.5 |
| Outliers | 48 |
| Mean | 23.5714 |
| Standard deviation (sample) | 8.8118 |
Step by step
- Sort the 14 values: 12, 15, 17, 18, 19, 21, 22, 22, 24, 25, 27, 29, 31, 48.
- The median is the middle pair (values 7 and 8), averaged: 22.
- Q1 is the median of the lower half (12, 15, 17, 18, 19, 21, 22): 18. Q3 is the median of the upper half (22, 24, 25, 27, 29, 31, 48): 27.
- IQR = Q3 − Q1 = 27 − 18 = 9.
- Fences: 18 − 1.5 × 9 = 4.5 and 27 + 1.5 × 9 = 40.5. Values outside them are outliers: 48.
How outliers are found
The most common rule, from John Tukey, uses the interquartile range. Work out Q1, Q3 and IQR = Q3 − Q1, then the two fences:
- Lower fence = Q1 − 1.5 × IQR
- Upper fence = Q3 + 1.5 × IQR
Any value outside the fences is an outlier. Values beyond 3 × IQR are sometimes called extreme outliers.
What to do with an outlier
An outlier is a prompt to check, not an automatic delete. It may be a typing error (an extra zero), a measurement problem, or a real and important value. Report it, and if you remove it, say so. The median and IQR are barely affected by outliers; the mean and standard deviation can shift a lot.
To see the rule in motion, drag a value past the fence in the explainer on the box plot maker.
When does a value become an outlier?
Ten delivery times in days. Drag the slowest one further out. It turns into a separate dot once it passes Q3 + 1.5 × IQR.
Q1 5 · median 7 · Q3 9 · IQR 4
Upper fence = Q3 + 1.5 × IQR = 9 + 1.5 × 4 = 15. 12 is inside, so the whisker reaches it.
Questions
What is the 1.5 IQR rule?
A value is an outlier if it is below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR, where IQR = Q3 − Q1.
Can there be no outliers?
Yes. If every value lies between the fences, the data set has no outliers by this rule.
Why does my textbook find a different outlier?
Quartile methods differ. Try both quartile methods above; on small data sets the fences can move enough to change the answer.
Is a z-score better for finding outliers?
Z-scores (|z| > 3) assume roughly normal data and are pulled by the outliers themselves. The IQR rule works for skewed data too, which is why box plots use it.