How to Find Outliers With the 1.5 IQR Rule

By Dr. Ahmed Mortuza Saleque · Updated November 11, 2026 · How we check our content

The short answer

To find outliers with the IQR rule, find the first quartile (Q1) and third quartile (Q3), subtract to get the interquartile range (IQR = Q3 − Q1), then set fences at Q1 − 1.5 × IQR and Q3 + 1.5 × IQR. Any value outside the fences is an outlier. For data with Q1 = 15 and Q3 = 19.5, the IQR is 4.5 and anything above 26.25 or below 8.25 is an outlier.

Open the Data Plotter →

Box plot of twelve values with Q1 of 15, Q3 of 19.5, fences at 8.25 and 26.25, and one outlier at 45 marked outside the upper fence — Tap the image to enlarge it. Free to share with a link to this page.

Worked example

Sort the data. Twelve delivery times in minutes: 12, 14, 15, 15, 16, 17, 18, 18, 19, 21, 22, 45.
Q1 = 15 and Q3 = 19.5 (the median is 17.5).
IQR = 19.5 − 15 = 4.5.
Lower fence = 15 − 1.5 × 4.5 = 8.25.
Upper fence = 19.5 + 1.5 × 4.5 = 26.25.
45 is above 26.25, so it is an outlier. Nothing is below 8.25.

Why one outlier matters

Statistic	With 45	Without 45
Mean	19.3	17.0
Median	17.5	17
Standard deviation	8.57	3.00

One value nearly triples the standard deviation and pulls the mean up by more than 2 minutes, while the median hardly moves. That is why the median and IQR are preferred for skewed data. Check these with the IQR calculator and the 5-number summary calculator.

Quartile methods give slightly different answers

There are several ways to compute quartiles. Excel's QUARTILE.INC gives Q3 = 19.5 here, while QUARTILE.EXC and some textbooks give 20.5. The fences shift a little, but a clear outlier such as 45 is flagged either way. Use one method consistently and say which one you used.

Find outliers automatically

Paste a column into the Data Plotter. Its insights panel counts outliers with the 1.5 × IQR rule, the box plot draws them as separate points, and the Remove outliers switch redraws every chart without them so you can compare. It also warns when a column is strongly skewed, which often explains apparent outliers.

Should you remove an outlier?

Remove it if it is an error: a typo, a faulty sensor reading, a unit mix-up.
Keep it if it is real. A 45-minute delivery is real information about what customers experience.
If unsure, report results with and without it.
Never remove points just to improve R² or reach significance.
For bell-shaped data, a z-score above 3 is another common test; see the z-score calculator.

Common questions

What is the 1.5 IQR rule?

A value is an outlier if it is more than 1.5 interquartile ranges below the first quartile or above the third quartile.

What is an extreme outlier?

A value more than 3 × IQR beyond the quartiles. In the example, the extreme upper fence is 19.5 + 13.5 = 33, and 45 is an extreme outlier too.

Why 1.5 times the IQR?

John Tukey chose it for box plots. For normally distributed data, it flags about 0.7% of values, so real outliers stand out.

How are outliers shown on a box plot?

As separate dots beyond the whiskers, which end at the most extreme values still inside the fences.