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Calculation Machine

Outlier Calculator

IQR fences and z-scores flag unusual points instantly.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Outliers (1.5 × IQR)
42
Lower fence
9.5
Upper fence
23.5
Q1 / median / Q3
14.75 / 15.5 / 18.25
IQR
3.5
Outliers by z-score > 3
None found
Data without outliers
12, 14, 15, 15, 16, 18, 19

Quick answer

A point is a mild outlier when it falls more than 1.5 × IQR below Q1 or above Q3, and an extreme outlier beyond 3 × IQR.

The formula

fences = Q1 − 1.5·IQR and Q3 + 1.5·IQR

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Data values12, 14, 15, 15, 16, 18, 19, 42

Result

  • Outliers (1.5 × IQR)42
  • Lower fence9.5
  • Upper fence23.5
  • Q1 / median / Q314.75 / 15.5 / 18.25
  • IQR3.5
  • Outliers by z-score > 3None found

How to use the Outlier Calculator

  1. 1Paste your dataset separated by commas.
  2. 2Check which points fall outside the fences.
  3. 3Decide whether each outlier is a genuine extreme value or a data-entry error before deleting anything.

Frequently asked questions

Should I always remove outliers?

No. Remove them only when you can show they are errors. Genuine extremes often carry the most interesting information.

IQR rule or z-scores?

IQR is safer for small or skewed samples because the mean and SD are themselves dragged around by outliers.

About this calculator