Statistics Tool

Box Plot Maker

Create a Box and Whisker plot from data.

Σ The Formula

IQR = Q3 - Q1 | Lower Whisker = Q1 - 1.5×IQR | Upper Whisker = Q3 + 1.5×IQR

Real World Examples

Test Scores
Dataset: 65, 70, 75, 80, 85, 90, 95 → Min=65, Q1=72.5, Median=80, Q3=87.5, Max=95
Sales Data
Dataset: 100, 120, 150, 180, 200 → Min=100, Q1=120, Median=150, Q3=180, Max=200
Height (cm)
160, 162, 165, 170, 175, 180 → Median=167.5, IQR spread visualized
Outlier Example
1, 2, 3, 4, 100 → 100 appears as a distant separate point

# About This Calculator

A Box and Whisker Plot (or Box Plot) is a standardized way of displaying the distribution of data based on a five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

The central "box" represents the middle 50% of the data (Interquartile Range or IQR), while the "whiskers" extend to show the rest of the distribution. Points beyond the whiskers are often considered outliers. This plot is superior to a simple mean/average because it shows the spread and skewness of the data.

Box plots are widely used in statistics, scientific research, and quality control to compare distributions between different groups (e.g., comparing test scores of Class A vs Class B) without making assumptions about the underlying statistical distribution.

This tool calculates all the quartiles automatically from your dataset and generates a visual representation, helping you instantly see the center, spread, and symmetry of your data.

How To Use

  1. Enter a list of numbers separated by commas (e.g., 10, 20, 5, 40).
  2. Click Generate Plot.
  3. View the five-number summary and the visual plot.

Frequently Asked Questions

What is the 'Five Number Summary'?+

It consists of: 1) Minimum (smallest value), 2) Q1 (25th percentile), 3) Median (middle value), 4) Q3 (75th percentile), and 5) Maximum (largest value).

What is the Interquartile Range (IQR)?+

IQR = Q3 - Q1. It represents the range of the middle 50% of the data. A larger IQR means the data is more spread out in the middle.

How are outliers determined?+

A common rule is that any value more than 1.5 × IQR below Q1 or above Q3 is an outlier. Box plots often display these as individual dots.

What does the line inside the box mean?+

That line represents the Median (the middle value of the dataset, dividing it into two equal halves). It's distinct from the Mean (average).

Why use a box plot instead of a histogram?+

Box plots are better for comparing multiple datasets side-by-side and spotting outliers efficiently. Histograms give a better detailed view of the distribution shape.

Is Box Plot Maker free to use?+

Yes, Box Plot Maker on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

A Box and Whisker Plot (or Box Plot) is a standardized way of displaying the distribution of data based on a five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

The central "box" represents the middle 50% of the data (Interquartile Range or IQR), while the "whiskers" extend to show the rest of the distribution. Points beyond the whiskers are often considered outliers. This plot is superior to a simple mean/average because it shows the spread and skewness of the data.

Box plots are widely used in statistics, scientific research, and quality control to compare distributions between different groups (e.g., comparing test scores of Class A vs Class B) without making assumptions about the underlying statistical distribution.

This tool calculates all the quartiles automatically from your dataset and generates a visual representation, helping you instantly see the center, spread, and symmetry of your data.

Related Tools

Mean, Median, Mode

Average Calculator

Standard Deviation

Histogram Maker