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

#1
#2
#3
#4
#5

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

1

Maximum

Highest value in the dataset

2

Third Quartile (Q3)

75% of data falls below this value

3

Median (Q2)

Middle value of the dataset

4

First Quartile (Q1)

25% of data falls below this value

5

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.