Calculators/Outlier Calculator

Descriptive Statistics

Outlier Calculator

Find outliers in a data set with the IQR rule and the z-score method side by side, and see why they sometimes disagree.

Your data

9 values read. Separate with commas, spaces, or new lines. At least 4 values are needed.

IQR multiplier

1.5 = outlier, 3 = extreme

z-score cutoff

Usually 2, 2.5, or 3

IQR method

Q1 = 11.5, Q3 = 15.5, IQR = 4
Fences: 5.5 to 21.5

z-score method (|z| > 3)

no outliers

mean = 18.111, s = 15.823
Range kept: -29.357 to 65.58

Why the z-score method cannot find anything here: with n = 9 values, the largest |z| that any value can reach is (n − 1) ÷ √n = 2.667, which is not above your cutoff of 3. Even an extreme value cannot be flagged, because it inflates the standard deviation used to judge it. The IQR method does not have this weakness.

Value	z-score	IQR flag	z flag
10	-0.513	—	—
11	-0.449	—	—
12	-0.386	—	—
12	-0.386	—	—
13	-0.323	—	—
14	-0.26	—	—
15	-0.197	—	—
16	-0.133	—	—
60	2.647	outlier	—

How to use this tool

Paste your numbers, separated by commas, spaces, or new lines. At least four values are needed.
Keep the IQR multiplier at 1.5 for ordinary outliers, or use 3 to find only extreme ones.
Set the z-score cutoff, commonly 3. The table lists every value with its z-score and both flags.
Read the note under the results if the two methods disagree.

Formula Reference

IQR fences

Q1 − k × IQR and Q3 + k × IQR

z-score

z = (x − x̄) ÷ s

Largest possible |z|

(n − 1) ÷ √n

IQR

Q3 − Q1

ArticleOutlier Detection ArticleLeverage, Outliers & Cook's Distance CalcFive-Number Summary & IQR Calculator ToolBox Plot Generator GlossaryGlossary: Outlier

Frequently Asked Questions

Which method should I use?+

The IQR rule is more robust, because quartiles are barely affected by extreme values. The z-score method assumes roughly normal data and uses the mean and standard deviation, which outliers themselves distort. For small samples, prefer the IQR rule.

Why can the z-score method miss an obvious outlier?+

A single extreme value pulls the mean toward itself and inflates the standard deviation. In a sample of n values no z-score can exceed (n − 1) ÷ √n, so with n = 9 the largest possible |z| is about 2.67, below the usual cutoff of 3.

Should I delete an outlier?+

Not automatically. First check for a data-entry or measurement error. If the value is genuine, deleting it changes the story the data tell. Report results with and without it, or use methods that are robust to outliers.

Which quartile method does this calculator use?+

The median-of-halves method, with the median excluded from both halves when n is odd. Software using interpolation may give slightly different quartiles and fences for small data sets.

Value

z-score

IQR flag

z flag

-0.513

—

-0.449

—

-0.386

—

-0.386

—

-0.323

—

-0.26

—

-0.197

—

-0.133

—

2.647

outlier

—

How to use this tool

Paste your numbers, separated by commas, spaces, or new lines. At least four values are needed.

Keep the IQR multiplier at 1.5 for ordinary outliers, or use 3 to find only extreme ones.

Set the z-score cutoff, commonly 3. The table lists every value with its z-score and both flags.

Read the note under the results if the two methods disagree.