Boxplots

Learn how to use boxplots to summarize distributions and compare groups.

Skill Level: Beginner
Prerequisites: Histograms
Estimated Time: 25 minutes

Story Time

In the previous lesson, you used histograms to study the distribution of one numerical variable.

Now you will learn another powerful chart for understanding distribution: the boxplot.

A boxplot gives a compact summary of the data and helps you quickly see the center, spread, and possible outliers. It is especially useful when you want to compare distributions across different groups.

In this lesson, you will learn how to create boxplots in Matplotlib and how to interpret what each part of the plot means.

Learning Objectives

By the end of this lesson, you will be able to:

• explain when a boxplot should be used
• create a boxplot with Matplotlib
• identify the median, quartiles, and whiskers
• interpret spread using the box and whiskers
• recognize possible outliers
• compare distributions across groups

Why This Topic Matters

In real data analysis, it is not enough to know only the average value.

Analysts also need to understand:

• how spread out the data is
• where the middle values lie
• whether the distribution is balanced or uneven
• whether unusual values appear

A boxplot helps answer these questions in a compact visual form. It is based on the five-number summary and is widely used in exploratory data analysis.

What Is a Boxplot?

A boxplot, also called a box-and-whisker plot, is a chart that summarizes the distribution of a numerical variable.

A boxplot usually shows:

• the median
• the first quartile (Q1)
• the third quartile (Q3)
• whiskers extending toward the lower and upper values
• possible outliers shown as individual points

This makes it easier to understand the overall distribution without showing every individual observation.

Understanding the Main Parts

Median

The line inside the box represents the median, which is the middle value of the data when sorted.

Quartiles

The bottom and top edges of the box represent:

• Q1: the 25th percentile
• Q3: the 75th percentile

This means the box contains the middle 50% of the data.

Interquartile Range

The distance from Q1 to Q3 is called the interquartile range (IQR).

It tells you how spread out the middle 50% of the data is. A wider box means greater spread in the middle portion of the distribution.

Whiskers

The whiskers extend beyond the box toward lower and higher values that are not considered outliers.

Outliers

Points that fall far outside the typical range may be shown individually as outliers. Boxplots often use the 1.5 × IQR rule to determine which points count as outliers.

When Should You Use a Boxplot?

Use a boxplot when:

• you want to summarize the distribution of a numerical variable
• you want to compare spread across groups
• you want to inspect median and quartiles
• you want to detect possible outliers

For example:

• compare math scores across gender groups
• compare reading scores across lunch categories
• compare salaries across departments

Boxplots are especially helpful when comparing several groups side by side.

Your First Boxplot

You can create a basic boxplot in Matplotlib with plt.boxplot().

import matplotlib.pyplot as plt

math_scores =[2][3][4][5][6][7][8][9][10][11]

plt.boxplot(math_scores)
plt.show()

This creates a single boxplot summarizing the distribution of mathematics scores.

Adding a Title and Axis Labels

import matplotlib.pyplot as plt;

math_scores =[3][4][5][6][7][8][9][10][11][2]

plt.boxplot(math_scores)
plt.title("Boxplot of Mathematics Scores")
plt.ylabel("Math Score")
plt.show()

Loading interactive boxplot…

The title and axis label make the plot easier to interpret.

Reading a Single Boxplot

When interpreting a single boxplot, ask:

1. Where is the median?
2. Is the box wide or narrow?
3. Are the whiskers long or short?
4. Are there any outliers?
5. Is the median centered in the box or closer to one side?

For example, if the median is near the center of the box and the whiskers are fairly balanced, the distribution may be reasonably symmetric. If one whisker is much longer, the distribution may be skewed.

Example: Detecting an Outlier

import matplotlib.pyplot as plt

scores =[12][13][4][7][8][9][10][11][14][15][2]

plt.boxplot(scores)
plt.title("Boxplot with a Possible Outlier")
plt.ylabel("Score")
plt.show()

In this example, the value 98 may appear as a separate point beyond the whisker.

A strong interpretation would be:

• most scores are grouped in a lower range
• one value appears much higher than the rest
• that value may be a possible outlier

Comparing Groups with Boxplots

One of the biggest strengths of boxplots is side-by-side comparison.

import matplotlib.pyplot as plt

female_scores =[13][7][8][9][11][15][2][12]
male_scores =[16][4][5][8][10][11][17][3]

plt.boxplot([female_scores, male_scores], labels=["Female", "Male"])
plt.title("Math Scores by Gender")
plt.ylabel("Math Score")
plt.show()

This chart lets you compare:

• median score
• spread of the middle 50%
• overall range
• possible outliers

between the two groups.

Interpreting Group Comparison

Suppose the Male boxplot has a higher median line than the Female boxplot.

That suggests the median math score is higher for male students.

If one box is taller, that means the middle 50% of values are more spread out in that group. If one group has more outliers, that may indicate greater variability or unusual cases.

Boxplot vs Histogram

Both boxplots and histograms are used to study distributions, but they do so differently.

A histogram helps you see:

• shape
• peaks
• clustering
• approximate distribution form

A boxplot helps you see:

• median
• quartiles
• spread
• possible outliers
• group comparisons

Google Colab Activity

Using the Students Performance dataset, create a boxplot for mathematics score.

Then create side-by-side boxplots comparing mathematics score by gender.

Write 2–3 sentences that describe:

• which group has the higher median
• which group has greater spread
• whether any possible outliers appear

Practice in Colab

Notebook

Open in Google Colab

Practice boxplots with short runnable examples and exercises.

After completing the activity in Google Colab, mark it as complete below.

Practice Exercise

Create side-by-side boxplots for reading score by lunch type.

Then answer:

• Which group has the higher median?
• Which group has the wider box?
• Are there any possible outliers?

Check Your Understanding

1. What does the line inside the box of a boxplot represent?

The maximum valueThe meanThe medianThe mode

2. What does the box itself usually represent?

The full range of the dataThe middle 50% of the dataOnly the outliersThe mean and standard deviation

3. What is the interquartile range (IQR)?

The distance from the minimum to the maximumThe distance from the median to the maximumThe distance between Q1 and Q3The number of outliers

4. Why are boxplots especially useful?

They show exact frequencies for every valueThey are useful for comparing distributions across groupsThey only work for categorical dataThey replace all other chart types

5. What might a point beyond the whiskers represent?

A category labelA plotting errorA possible outlierThe mean

Challenge Exercise

Choose a numerical variable and a grouping variable from your dataset.

Create side-by-side boxplots that help compare the groups clearly.

Your chart should include:

• a clear title
• readable group labels
• a y-axis label
• a short written interpretation

Your interpretation should mention median, spread, and any unusual points.

Common Mistakes

Thinking the Box Shows All Data

The box only shows the middle 50% of the data, not the entire dataset.

Ignoring the Median

The median is one of the most important parts of the boxplot. It often provides the clearest comparison between groups.

Forgetting What Outliers Mean

An outlier is a possible unusual value, not automatic proof of an error. It should be investigated, not blindly removed.

Using a Boxplot Without Interpretation

Do not stop at identifying the box and whiskers. Explain what they suggest about center, spread, and group differences.

Key Takeaways

In this lesson, you learned how to:

• create boxplots with Matplotlib
• interpret the median, quartiles, whiskers, and possible outliers
• compare distributions across groups
• understand how boxplots differ from histograms
• use boxplots as a compact tool for exploratory analysis

Continue Your Journey

Next, you will learn Heatmaps, which help you visualize values across a grid and identify patterns more quickly.