Outlier Detection Calculator Online – Free | 8gwifi.org

Outlier Detection Calculator

Identify outliers using IQR, Z-score, and Modified Z-score methods with visualization

Data Input
Enter numbers separated by commas, spaces, or newlines
IQR Method (Tukey's Fences):
Most common method. Outliers are values outside [Q1 - k×IQR, Q3 + k×IQR]
Z-Score Method:
Assumes normal distribution. Outliers are values with |Z-score| > threshold
Modified Z-Score (MAD):
Robust to outliers. Uses median absolute deviation instead of standard deviation
Compare All Methods:
See which values are flagged as outliers by each method
Understanding Outliers
What is an Outlier?

An outlier is a data point that differs significantly from other observations. Outliers can occur due to measurement errors, data entry errors, or genuine extreme values in the population.

1. IQR Method (Tukey's Fences)

Formula:

  • Lower fence = Q1 - k × IQR
  • Upper fence = Q3 + k × IQR
  • IQR = Q3 - Q1
  • Typically k = 1.5 (mild) or k = 3.0 (extreme)

Advantages:

  • Distribution-free (no assumptions about normality)
  • Robust to outliers themselves
  • Most widely used method

When to use: General-purpose outlier detection, especially for skewed data

2. Z-Score Method

Formula:

  • Z = (x - μ) / σ
  • Outliers: |Z| > threshold (typically 3)

Advantages:

  • Simple and intuitive
  • Good for normally distributed data
  • Easy to interpret (number of standard deviations)

Disadvantages:

  • Sensitive to outliers (mean and SD affected by outliers)
  • Assumes normal distribution

When to use: Large datasets that are approximately normally distributed

3. Modified Z-Score (MAD)

Formula:

  • M = 0.6745 × (x - median) / MAD
  • MAD = median(|xᵢ - median(x)|)
  • Outliers: |M| > 3.5 (typical threshold)

Advantages:

  • Very robust to outliers (uses median instead of mean)
  • Better for small sample sizes
  • Works well with skewed data

When to use: When you suspect outliers but want a robust method

Which Method to Choose?
Scenario Recommended Method
General purpose IQR (k=1.5)
Normal distribution Z-Score
Skewed data IQR or Modified Z
Small sample Modified Z
Many outliers Modified Z
Conservative (few false positives) IQR (k=3.0)
What to Do with Outliers?
  • Investigate: First, determine if outliers are errors or genuine values
  • Correct: Fix data entry or measurement errors
  • Remove: Exclude if truly erroneous (document why!)
  • Transform: Use log transformation to reduce impact
  • Keep: If genuine, use robust statistical methods
  • Separate Analysis: Analyze with and without outliers
Results

Enter your data and select a method to detect outliers

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Outlier Detection: FAQ

Which method should I use?

Use IQR (Tukey fences) for robust, distribution‑free detection; Z‑score for roughly normal data; Modified Z‑score (MAD) for added robustness against outliers.

What thresholds are common?

IQR: outside [Q1−1.5·IQR, Q3+1.5·IQR]. Z‑score: |Z| ≥ 3 (sometimes 2.5). Modified Z: |Mz| ≥ 3.5 are typical starting points.

Should I remove outliers?

Not automatically. Investigate causes (entry errors, different process). Consider robust summaries or transformations if outliers are genuine.

Do outliers always indicate bad data?

No. They may reflect rare but valid cases. Always use domain knowledge before excluding points.

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