Box Plot Calculator
Generate box plots and calculate five-number summaries for statistical data analysis
Calculate Box Plot Statistics
Or use the individual input fields below
Example Calculation
Student Test Scores Example
Raw Data: 85, 92, 78, 96, 88, 91, 83, 89, 95, 87
Ordered Data: 78, 83, 85, 87, 88, 89, 91, 92, 95, 96
Count (n): 10 students
Five-Number Summary
Minimum: 78 (lowest score)
Q1: 85 (25% of scores below)
Median: 88.5 (middle value)
Q3: 92 (75% of scores below)
Maximum: 96 (highest score)
IQR: 92 - 85 = 7 points
Box Plot Components
Maximum
Highest value in the dataset
Third Quartile (Q3)
75% of data falls below this value
Median (Q2)
Middle value of the dataset
First Quartile (Q1)
25% of data falls below this value
Minimum
Lowest value in the dataset
Quick Tips
Box plots work best with at least 5-10 data points
The box contains the middle 50% of your data (IQR)
Whiskers show the data range (excluding outliers)
Use modified box plot when outliers are present
Understanding Box Plots
What is a Box Plot?
A box plot (box-and-whisker plot) is a graphical representation of data that shows the distribution of a dataset through five key values: minimum, first quartile, median, third quartile, and maximum. It's particularly useful for identifying outliers and comparing distributions between different groups.
Key Benefits
- •Quick visualization of data distribution
- •Easy identification of outliers
- •Shows data spread and symmetry
- •Effective for comparing multiple datasets
Interpreting Box Plots
The Box (IQR)
Contains the middle 50% of data points
Median Line
Shows the center of the data distribution
Whiskers
Extend to the minimum and maximum non-outlier values
Outliers
Points beyond 1.5 × IQR from the quartiles
Modified Box Plot
A modified box plot identifies outliers separately and adjusts the whiskers to extend only to the furthest non-outlier values. Outliers are displayed as individual points beyond the whiskers. This provides a clearer view of the main data distribution when extreme values are present.