5 Number Summary Calculator
Instantly calculate the Minimum, Q1, Median, Q3, and Maximum. The essential summary statistics for any dataset.
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See 5 Numbers
A 5 number summary gives the minimum, Q1, median, Q3, and maximum. It is the fastest way to describe where your data starts, where the middle sits, and how far the upper values extend.
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 Deep Dive into Statistics
What is the 5-Number Summary?
The Five-Number Summary is a set of descriptive statistics that provides a concise snapshot of a dataset's distribution. It was introduced by mathematician John Tukey as part of his Exploratory Data Analysis (EDA) toolkit.
The Five Components
- Minimum: The smallest value in the dataset. This represents the lower bound of the range (excluding outliers).
- First Quartile (Q1): The 25th percentile. 25% of the data falls below this value. It marks the beginning of the "middle 50%" of the data.
- Median (Q2): The 50th percentile. The exact middle value that separates the higher half from the lower half of the data.
- Third Quartile (Q3): The 75th percentile. 75% of the data falls below this value. It marks the end of the "middle 50%".
- Maximum: The largest value in the dataset. This represents the upper bound of the range.
Visualizing with Box Plots
The 5-number summary is the raw data used to construct a Box and Whisker Plot:
- The Box is drawn from Q1 to Q3.
- The Line inside the box represents the Median.
- The Whiskers extend from the box to the Minimum and Maximum values.
Why use the 5-Number Summary?
It is superior to using just the Mean (Average) because it gives you information about the skewness and dispersion of the data.
- If the Median is closer to Q1 than Q3, the data is positively skewed (right-skewed).
- If the Median is closer to Q3 than Q1, the data is negatively skewed (left-skewed).
- If the Min and Max are very far from the quartiles, it suggests the presence of outliers.
PlotNerd's 5 Number Summary Calculator instantly generates all five key statistics for quick exploratory data analysis.
When to Use This Tool
Quick Exploratory Data Analysis (EDA)
Get a 5-second snapshot of data distribution before deeper analysis.
Creating Box Plots by Hand
The 5-number summary provides all data needed to draw a box plot.
Detecting Skewness at a Glance
If Q2 is closer to Q1 or Q3, your data is skewed left or right.
Not for: Detailed Distribution Analysis
For fine-grained shape analysis, use a histogram or density plot instead.
Related Tools & Resources
Tukey Hinges Calculator
Box plots were invented by John Tukey using the 5-number summary
β Use Tukey methodIQR Calculator
Calculate IQR (Q3 - Q1) from your 5-number summary
β Calculate IQRExcel Quartile Calculator
Generate 5-number summary using Excel's QUARTILE.INC method
β Use Excel methodHow to Read a Box Plot
Learn how the 5-number summary maps to box plot elements
β Read guideAlgorithm Comparison
See how different algorithms calculate the same dataset's 5-number summary
β View comparisonUniversal Calculator
Compare 4 different 5-number summaries simultaneously
β Try all methodsFrequently 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.