Five Number Summary

Box Plot Generator

Generate a Box Plot from Five Numbers



The Complete Guide to Box Plots: What They Are, How They Work, and When to Use Them

What is a Box Plot?

A box plot (also called a box-and-whisker plot) is a powerful data visualization tool that displays the distribution of numerical data, highlighting central tendency, spread, and outliers. It is built from the five number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

  • Box: Shows Q1 (25th percentile), median (Q2, 50th percentile), and Q3 (75th percentile).
  • Whiskers: Extend to Q1 - 1.5×IQR and Q3 + 1.5×IQR, or to the dataset’s minimum and maximum.
  • Outliers: Data points beyond the whiskers, often marked with dots or asterisks.

Why Use a Box Plot?

  • Visualize data distribution: See the spread and center of your data at a glance.
  • Identify outliers: Instantly spot unusual values for further analysis.
  • Compare groups: Place multiple box plots side by side to compare different datasets (e.g., A/B testing).
Best for:
  • Statistical analysis: Quickly understand central tendency and spread.
  • Data cleaning: Detect outliers (e.g., extreme income values).
  • Academic research: Compare experimental and control groups.
  • Business analysis: Compare sales distributions across products or regions.

When to Use a Box Plot?

ScenarioExampleBox Plot’s Role
Data distribution analysisStudent test scoresSee score ranges and gaps
Outlier detectionWebsite session durationsSpot unusually short/long visits
Comparing groupsCity home pricesCompare medians and spread
Skewness checkEmployee salariesSee if data is right-skewed
Not recommended for: Very small datasets (fewer than 5 values), categorical data, or when you need detailed distribution shapes (use a histogram or density plot instead).

Box Plot Result Examples

Below are several example box plots generated from different five-number summaries. These visuals help you understand how the five-number summary translates into a box plot, highlighting the minimum, quartiles, median, and maximum values in various data distributions.

Box plot example 1: symmetric distributionSymmetric distribution
Box plot example 2: right-skewed distributionRight-skewed distribution
Box plot example 3: left-skewed distributionLeft-skewed distribution

Box Plot vs. Other Charts

Chart TypeBest UseHow It Differs from Box Plot
HistogramShow distribution shapeBox plot focuses on summary stats (quartiles, outliers)
Scatter plotShow relationship between two variablesBox plot shows only one variable’s distribution
Line chartTrend analysis (e.g., over time)Box plot does not show time trends