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Outlier Calculator

Free outlier calculator. IQR, Z-score, Modified Z-score, Grubbs test, Dixon Q test. Data plot with o

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Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

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STATISTICSDescriptive Statistics

IQR, Z-score, Modified Z, Grubbs', Dixon's Q โ€” Outlier Detection

Detect outliers using multiple methods: IQR (Tukey), Z-score, Modified Z-score (MAD), Grubbs' test, Dixon's Q test. Compare methods side by side.

Upper/Lower Fence โ†’IQR Calculator โ†’

Real-World Scenarios โ€” Click to Load

Data โ€” comma or space separated

outlier_results.sh
CALCULATED
$ outlier_detect --method="all" --alpha=0.05 --n=14
IQR
15.7500
Fences
[-15.13, 47.88]
Total Outliers
1
Mean / SD
21.64 / 24.51

Outliers by Method

IQR (mild): None
IQR (extreme): 100
Z-score: 100
Modified Z: 100
Grubbs: 100
Dixon Q: 100
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Outlier Detection Result
n = 14 values
1 Outliers
IQR: 15.75Fences: [-15.1, 47.9]Method: all
numbervibe.com/calculators/statistics/outlier-calculator

Data Plot (outliers in red)

Box Plot with Fences

Lower fence | Q1 | Median | Q3 | Upper fence

|Z-score| by Value (red = |z|>3, amber = |z|>2)

Calculation Breakdown

IQR
Q1, Q3, IQR
Q1=8.50, Q3=24.25, IQR=15.75
ext{IQR} = Q3 - Q1
Inner fences (1.5ร—IQR)
[-15.13, 47.88]
Q1 - 1.5 imes ext{IQR}, Q3 + 1.5 imes ext{IQR}
Outer fences (3ร—IQR)
[-38.75, 71.50]
Q1 - 3 imes ext{IQR}, Q3 + 3 imes ext{IQR}
Z-SCORE
Z-score
z = (x โˆ’ ฮผ)/ฯƒ
ฮผ=21.64, ฯƒ=24.51
MODIFIED Z
Modified Z (MAD)
M = 0.6745(xโˆ’median)/MAD
MAD=7.5000
GRUBBS & DIXON
Grubbs G
G = max|xแตขโˆ’xฬ„|/s
G_crit=2.507
Dixon's Q
Q = gap/range
Q_crit=0.421
Total outliers
1

For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways

  • IQR (Tukey): Outlier if x < Q1 โˆ’ 1.5ร—IQR or x > Q3 + 1.5ร—IQR. Extreme: beyond 3ร—IQR.
  • Z-score: Outlier if |z| > 2 (mild) or |z| > 3 (extreme). z = (x โˆ’ mean)/SD.
  • Modified Z (Iglewicz-Hoaglin): M = 0.6745(x โˆ’ median)/MAD. Outlier if |M| > 3.5.
  • Grubbs' test: G = max|xแตข โˆ’ xฬ„|/s. Compare to critical value for ฮฑ.
  • Dixon's Q: Q = |suspect โˆ’ nearest|/range. Compare to Q_crit(n, ฮฑ).

Did You Know?

๐Ÿ“ŠThe IQR method (Tukey) is robust โ€” it uses quartiles, not the mean, so it is less affected by outliers themselves.Source: Tukey EDA 1977
๐Ÿ“Z-score assumes normality. For non-normal data, the Modified Z-score (MAD) is more robust.Source: Iglewicz-Hoaglin
๐Ÿ”Grubbs' test is designed to detect a single outlier. For multiple outliers, use iterative removal or other methods.Source: NIST Handbook
๐Ÿ“ˆDixon's Q test works best for small samples (n โ‰ค 10). It tests the minimum or maximum as the suspect.Source: Wolfram MathWorld

Method Comparison Table

MethodAssumptionBest ForSample Size
IQR (Tukey)NoneSkewed data, EDAAny
Z-scoreNormalityNormal datan โ‰ฅ 10
Modified ZNoneMany outliers presentAny
Grubbs'Normality, 1 outlierFormal test3โ€“30
Dixon's QNormalitySmall samples3โ€“10

Frequently Asked Questions

Which method should I use?

IQR is a good default. Use Z-score for normal data. Use Modified Z when outliers might inflate SD. Use Grubbs/Dixon for formal hypothesis testing.

Why do methods disagree?

Each method uses different criteria. IQR is robust; Z-score is sensitive to the mean. A point can be an IQR outlier but not a Z-score outlier.

Should I remove outliers?

Not automatically. Investigate first. If they are errors, remove. If genuine, consider robust methods or report both with and without.

Disclaimer: Outlier detection is exploratory. Different methods can yield different results. For formal inference, state your method and significance level. Do not remove data without justification.

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