Outlier Calculator: Find Outliers with IQR & Z-Scores

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Formula at a glance

Outlier Calculator: IQR fences — lower = Q1 − 1.5·IQR, upper = Q3 + 1.5·IQR. Example: One high value → Outliers (1.5 × IQR rule): 45 — How the Outlier Calculator works: IQR fences — lower = Q1 − 1.5·IQR, upper = Q3 + 1.5·IQR

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📘 About the Outlier Calculator

An outlier is a value far from the rest of the data — a typing error, a measuring fault or a genuinely unusual case. Outliers can drag the mean and inflate the standard deviation, so it pays to find them first.

Tukey’s rule (used for box-plot whiskers) flags values below Q1 − 1.5·IQR or above Q3 + 1.5·IQR, and extreme outliers beyond 3·IQR. The z-score method flags values more than 3 standard deviations from the mean. The calculator lists both, with each value’s z-score.

🧮 Formula

IQR fences

lower = Q1 − 1.5·IQR, upper = Q3 + 1.5·IQR

z-score

z = (x − x̄)/s, outlier if |z| > 3

✏️ Worked examples

One high value

You enter
Data	12, 14, 14, 15, 16, 17, 18, 19, 21, 22, 45
Fence multiplier	1.5

You get
Outliers (1.5 × IQR rule)	45
Fences	lower 3.5 · upper 31.5
Extreme outliers (3 × IQR)	45
Q1 · median · Q3 · IQR	14 · 17 · 21 · 7
Z-score method (\|z\| > 3)	None
Data without the outliers	12, 14, 14, 15, 16, 17, 18, 19, 21, 22

Outliers: 45.

Low and high outliers

You enter
Data	2, 31, 33, 34, 35, 35, 36, 38, 40, 75
Fence multiplier	1.5

You get
Outliers (1.5 × IQR rule)	2, 75
Fences	lower 25.5 · upper 45.5
Extreme outliers (3 × IQR)	2, 75
Q1 · median · Q3 · IQR	33 · 35 · 38 · 5
Z-score method (\|z\| > 3)	None
Data without the outliers	31, 33, 34, 35, 35, 36, 38, 40

Outliers: 2, 75.

🧭 How to use this calculator

What you enter

DataSeparate numbers with commas, spaces or new lines.
Fence multiplier1.5 is standard; 3 finds only extreme outliers.

What you get

Outliers (1.5 × IQR rule)
Fences
Extreme outliers (3 × IQR)
Q1 · median · Q3 · IQR
Z-score method (|z| > 3)
Data without the outliers

❓ Frequently asked questions

How do you determine an outlier?

Find Q1, Q3 and IQR = Q3 − Q1; anything below Q1 − 1.5·IQR or above Q3 + 1.5·IQR is an outlier.

Should I remove outliers?

Only if they are errors. Genuine outliers can be the most important data; consider reporting results with and without them.

Why might the z-score method miss outliers?

In small samples a big outlier inflates the standard deviation, hiding itself. The IQR method is more robust.

⚠️ Outlier Calculator (IQR & Z-Score Methods)