Outlier Calculator

Paste a dataset and find its outliers using the 1.5×IQR (Tukey) fence method, with Q1, Q3, the interquartile range, lower/upper fences, and Z-scores.

Quick Facts

Method
Tukey fences: outlier if x < Q1 − k·IQR or x > Q3 + k·IQR (k = 1.5)
IQR = Q3 − Q1. Quartiles use linear interpolation on the sorted data.

Your Results

Calculated
Outliers found
-
Values outside the fences
Lower fence
-
Q1 − k·IQR
Upper fence
-
Q3 + k·IQR
Q1 / Median / Q3
-
IQR = -

Ready

Enter a dataset and click Calculate.

What this outlier calculator does

An outlier is a data point that sits far away from the rest of a dataset. This calculator finds outliers using the two most widely taught rules: the 1.5×IQR (Tukey) fence method and the Z-score method. Paste your numbers, and it sorts them, computes the quartiles, and reports which values fall outside the "typical" range.

The 1.5×IQR (Tukey) rule

The interquartile range method is based on three quartiles of the sorted data:

  • Q1 — the first quartile (25th percentile): a quarter of the data lies below it.
  • Q3 — the third quartile (75th percentile): a quarter of the data lies above it.
  • IQR = Q3 − Q1 — the interquartile range, the spread of the middle 50% of the data.

The fences (cutoffs) are then:

  • Lower fence = Q1 − 1.5 × IQR
  • Upper fence = Q3 + 1.5 × IQR

Any value below the lower fence or above the upper fence is flagged as an outlier. This is exactly the rule that draws the "whiskers" and plotted dots on a box-and-whisker plot. Using a multiplier of 3.0 instead of 1.5 identifies "extreme" or "far" outliers only. This calculator lets you change the multiplier k if you want a stricter or looser cutoff.

A worked example

Take the dataset 10, 11, 12, 13, 14, 15, 16, 17, 18, 100 (n = 10, already sorted). Using linear interpolation for quartiles: Q1 = 12.25, Q3 = 16.75, so IQR = 4.5. The fences are 12.25 − 1.5×4.5 = 5.5 and 16.75 + 1.5×4.5 = 23.5. The value 100 is above 23.5, so it is the single outlier — which matches intuition, since every other value is between 10 and 18.

The Z-score rule

The Z-score of a value measures how many standard deviations it sits from the mean: Z = (x − mean) / σ. A common convention flags any point with |Z| > 3 as an outlier. This calculator reports the Z-score flags alongside the IQR result. The Z-score rule assumes the data is roughly normal (bell-shaped) and symmetric; it can miss outliers in small or skewed samples because the outlier itself inflates both the mean and the standard deviation.

Why the quartile numbers can differ between tools

There is no single universal definition of a quartile. This calculator uses the common linear interpolation method (equivalent to the default in NumPy's percentile and many statistics courses). Spreadsheet functions and different textbooks may use slightly different rules (for example, Excel's QUARTILE.INC vs. QUARTILE.EXC, or the Tukey "hinge" method), which can shift Q1 and Q3 by a small amount on the same data. The outliers flagged are usually identical, but the exact fence values may differ by a little.

Frequently Asked Questions

What counts as an outlier with the 1.5×IQR rule?
A value is an outlier if it falls below Q1 − 1.5×IQR or above Q3 + 1.5×IQR, where IQR = Q3 − Q1. Values beyond Q1 − 3×IQR or Q3 + 3×IQR are often labeled "extreme" or "far" outliers. This is the same rule that produces the dots beyond the whiskers on a box plot.
When should I use the Z-score method instead of IQR?
Use the Z-score method (|Z| > 3) when the data is roughly normal and symmetric. Prefer the IQR method for skewed data or small samples: the median and quartiles are resistant to extreme values, whereas the mean and standard deviation used in Z-scores are pulled toward the very outliers you are trying to detect.
Should I always delete outliers?
No. An outlier is a signal to investigate, not an instruction to delete. It may be a genuine extreme observation, a data-entry error, or a value from a different population. Understand why the point is unusual before you decide to keep, correct, or exclude it — and report any exclusions you make.
How many data points do I need?
You need at least a handful of values for quartiles to be meaningful; the IQR rule is typically used with 8 or more points. With very small samples (fewer than about 5 values) the fences are unstable and a single point can dominate the quartiles, so treat the result as a rough guide.

Related calculators