Outlier Calculator
Identify anomalies in your data using Tukey's Method (1.5 Γ IQR) or MAD (Median Absolute Deviation).
π Find Outliers in 3 Steps
Input Data
Select Method
See Anomalies
Supported Data Formats:
- Comma-separated: 1.5, 2.8, 9.1, 16.2
- Space-separated: 1.5 2.8 9.1 16.2
- Newline-separated: one number per line
- Scientific notation: 1.23e-4, 5.67E+8
- Series mode: use "Group Name: value1, value2, value3" per line to compare multiple groups
- Automatically ignores text and special characters
Universal Standard (R, Python, Google Sheets)
Linear interpolation method, default standard for modern data science software
Your calculation results and box plot will appear here instantly
Please enter at least 4 numbers above to start calculating
Calculation Results
Basic Statistics
Quartiles
5 Number Summary
Outliers Detected
The following data points are identified as outliers using the method:
Grouped Series Summary
Enter data to generate box plot
Please enter at least 4 numbers above to start calculating
Box Plot Visualization
This box plot visualizes your data distribution. The box shows the interquartile range (IQR) containing the middle 50% of data. The line inside the box represents the median. Whiskers extend to show the range, and red dots indicate outliers.
Outlier Method: Tukey (1.5ΓIQR)
Box (IQR) / Legend
- Box (IQR)
- Median Line
- Whisker
- Outliers
Combined Summary
π Learn About Outlier Detection
How to Calculate Outliers
An outlier is a data point that differs significantly from other observations. PlotNerd uses two robust statistical methods to detect them:
Method 1: Tukey's Fences (IQR Method)
This is the standard method used in Box Plots.
- Calculate Q1 (25th percentile) and Q3 (75th percentile).
- Calculate the IQR (Interquartile Range) = Q3 - Q1.
- Define the Lower Fence = Q1 - (1.5 Γ IQR).
- Define the Upper Fence = Q3 + (1.5 Γ IQR).
- Any value outside these fences is an outlier.
Method 2: Median Absolute Deviation (MAD)
A more robust method for smaller datasets or non-normal distributions. It uses the median of absolute deviations from the data's median. Values exceeding a threshold (usually 3.5 or 3) are flagged.
π‘ Why Detect Outliers?
- β οΈ Data Quality: Outliers may indicate data entry errors.
- π Statistical Validity: Extreme values can skew the Mean and Standard Deviation.
- π Anomaly Detection: In finance or manufacturing, outliers often signal fraud or defects.
Frequently Asked Questions
Statistical concepts explained in plain language
Mathematical Formulas
View the standard mathematical formulas behind the calculations
Quartile Calculation (Method 2)
First Quartile (Q1):
Median (Q2):
Third Quartile (Q3):
Interquartile Range & Outlier Detection
Interquartile Range (IQR):
Outlier Boundaries:
Algorithm Explanation
PlotNerd uses the statistically standard "Method 2 (Median Quartile Method)" for quartile calculations, consistent with major statistical software (such as R, SPSS). All calculation results are verified against authoritative platforms to ensure accuracy.