The Box Plot (or Box-and-Whisker Plot) helps you visualize data distributions by displaying the five-number summary: minimum, first quartile, median, third quartile, and maximum. Combined with outlier detection and group comparisons, it provides comprehensive insights into your data's spread and central tendency. It's particularly useful for comparing distributions across categories, identifying outliers in datasets, and understanding data variability at a glance. Simply upload your data or use our sample datasets to create professional box plots. Not sure where to start? Check out our step-by-step tutorial.
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1. Load Your Data
2. Select Columns & Options
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Learn More About Box Plots
What is a Box Plot?
A box plot (also known as a box and whisker plot) is a standardized way to display data distribution based on five key statistics: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It's particularly useful for comparing distributions across multiple groups and identifying outliers.
The diagram above illustrates all components of a box plot. The box represents the interquartile range (IQR) containing the middle 50% of data, while whiskers extend to show the typical data range.
How to Read a Box Plot
Understanding box plots becomes intuitive once you know what each component represents:
Key Components
- •The Box: Shows where the middle 50% of data falls (from Q1 to Q3)
- •Median Line: Divides the data in half (50th percentile)
- •Whiskers: Extend to the furthest points within 1.5×IQR
- •Outliers: Individual points beyond the whiskers
What to Look For
- →Skewness: Is the median centered in the box?
- →Spread: How tall is the box? How long are the whiskers?
- →Outliers: Are there many points beyond the whiskers?
- →Comparison: How do multiple box plots differ?
How to Make a Box Plot with Our Calculator
- Click Sample Data and select Restaurant Tips
- For Value column, select total_bill
- For Group By column, select day or leave it as None
- For Facet By column, select time or leave it as None
- For Orientation, select horizontal (recommended) or vertical
- For Quartile Method, select linear (default)
- Click Generate Box Plot to visualize the data
How to Create a Box Plot by Hand
Understanding how to create a box plot manually helps you grasp the underlying statistics. Here's a step-by-step guide:
Example Dataset: Test Scores
65, 72, 68, 74, 61, 76, 71, 69, 73, 67, 70, 68, 75, 62, 77
- Step 1: Sort the data
Arrange values from smallest to largest:
61, 62, 65, 67, 68, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77
- Step 2: Find the median (Q2)
With 15 values, the median is the 8th value:
Median = 70
- Step 3: Find Q1 and Q3
Q1 is the median of the lower half (excluding the median):
Lower half: 61, 62, 65, 67, 68, 68, 69
Q1 = 67
Q3 is the median of the upper half:
Upper half: 71, 72, 73, 74, 75, 76, 77
Q3 = 74
- Step 4: Calculate IQR
IQR = Q3 - Q1
IQR = 74 - 67 = 7
- Step 5: Find whisker endpoints
Lower fence = Q1 - 1.5 × IQR = 67 - 10.5 = 56.5
Upper fence = Q3 + 1.5 × IQR = 74 + 10.5 = 84.5
Whiskers extend to the most extreme values within the fences:
Lower whisker ends at: 61 (smallest value ≥ 56.5)
Upper whisker ends at: 77 (largest value ≤ 84.5)
- Step 6: Identify outliers
Any values beyond the fences are outliers.
In this example: No outliers (all values are within fences)
- Step 7: Draw the plot
• Draw a number line with appropriate scale
• Draw a box from Q1 (67) to Q3 (74)
• Draw a line inside the box at the median (70)
• Draw whiskers from the box to 61 and 77
• Mark any outliers as individual points
Pro Tip:
The method shown here uses the "exclusive" approach, which matches Excel and gives whole numbers from the dataset. Modern statistical software often uses "linear" interpolation by default, which can produce fractional values (e.g., Q1 = 67.25 instead of 67).
Advanced Box Plot Concepts
Modified Box Plots
Modified box plots show all outliers as individual points, with whiskers extending only to 1.5×IQR. This provides better visualization of extreme values.
Notched Box Plots
Notched box plots include confidence intervals around the median. Non-overlapping notches suggest statistically significant differences between groups.
Violin Plots
Violin plots combine box plots with kernel density estimation, showing both summary statistics and the full distribution shape.
Grouped Box Plots
Display multiple box plots side-by-side to compare distributions across different categories or time periods effectively.
Box Plot Quick Reference
Key Formulas
IQR = Q3 - Q1
Lower fence = Q1 - 1.5 × IQR
Upper fence = Q3 + 1.5 × IQR
Q1 = 25th percentile
Q2 (Median) = 50th percentile
Q3 = 75th percentile
Frequently Asked Questions
What is the difference between a box plot and a histogram?
Box plots show summary statistics and outliers, while histograms display the frequency distribution of data. Box plots are better for comparing groups, while histograms show data shape more clearly.
When should I use a box plot instead of other charts?
Use box plots when you need to compare distributions between groups, identify outliers, or show data spread and central tendency. They're ideal for displaying multiple datasets side-by-side.
How do I interpret outliers in a box plot?
Outliers appear as individual points beyond the whiskers. They represent unusual values that may indicate data errors, special cases, or important insights requiring further investigation.
Can box plots show mean values?
Standard box plots show medians, not means. However, some variations include a point or symbol to indicate the mean value alongside the median for additional context.
Creating Box Plot in R
Here's a simple example of creating and customizing a box plot in R using theggplot2 package.
library(tidyverse)
tips <- read.csv("https://raw.githubusercontent.com/plotly/datasets/master/tips.csv")
# basic box plot of total bills
ggplot(tips, aes(y = total_bill)) +
geom_boxplot(fill = "steelblue", color = "darkblue") +
labs(title = "Distribution of Total Bills",
y = "Total Bill Amount") +
theme_minimal()
# box plot grouped by day
ggplot(tips, aes(x = day, y = total_bill)) +
geom_boxplot(fill = "steelblue", color = "darkblue") +
labs(title = "Restaurant Bills by Day of Week",
x = "Day",
y = "Total Bill Amount") +
theme_minimal()
# box plot with individual points
ggplot(tips, aes(x = day, y = total_bill)) +
geom_boxplot(fill = "steelblue", color = "darkblue", alpha = 0.7) +
geom_jitter(width = 0.2, alpha = 0.3, color = "darkred") +
labs(title = "Restaurant Bills by Day with Individual Points",
x = "Day",
y = "Total Bill Amount") +
theme_minimal()
# faceted box plot by time (figure below)
ggplot(tips, aes(x = day, y = total_bill, fill = time)) +
geom_boxplot(alpha = 0.7) +
facet_wrap(~time) +
scale_fill_manual(values = c("Lunch" = "lightblue", "Dinner" = "steelblue")) +
labs(title = "Restaurant Bills by Day and Time",
x = "Day",
y = "Total Bill Amount") +
theme_minimal() +
theme(legend.position = "none")
This code creates faceted box plots showing the distribution of total bills by day of the week, separated into lunch and dinner times. The box plots reveal differences in spending patterns across different days and meal times.
For publication-quality box plots with statistical comparisons, theggpubr package provides additional features.
library(ggpubr)
tips <- read.csv("https://raw.githubusercontent.com/plotly/datasets/master/tips.csv")
# publication-ready box plot with p-values
ggboxplot(tips, x = "day", y = "total_bill",
color = "day", palette = "jco",
add = "jitter", shape = "day",
title = "Restaurant Bills by Day",
xlab = "Day of Week",
ylab = "Total Bill ($)") +
stat_compare_means(method = "anova", label.y = 55) +
stat_compare_means(comparisons = list(c("Thur", "Fri"),
c("Sat", "Sun")),
method = "t.test", label.y = c(45, 50))
# box plot comparing lunch vs dinner with statistics
ggboxplot(tips, x = "time", y = "total_bill",
color = "time", palette = "npg",
add = "jitter",
add.params = list(size = 0.1, alpha = 0.5),
title = "Total Bills: Lunch vs Dinner",
xlab = "Meal Time",
ylab = "Total Bill ($)") +
stat_compare_means(method = "t.test",
label = "p.format",
label.y = 52)
Creating Box Plot in Python
Here's how to create box plots in Python using popular visualization libraries like matplotlib and seaborn.
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
# Load the data
tips = pd.read_csv("https://raw.githubusercontent.com/plotly/datasets/master/tips.csv")
# Set style for better-looking plots
plt.style.use('seaborn-v0_8')
sns.set_palette("husl")
# Define the order for categorical variables
day_order = ['Thur', 'Fri', 'Sat', 'Sun']
time_order = ['Lunch', 'Dinner']
# Basic box plot with matplotlib
plt.figure(figsize=(8, 6))
plt.boxplot(tips['total_bill'])
plt.ylabel('Total Bill Amount')
plt.title('Distribution of Total Bills')
plt.show()
# Box plot by day with seaborn
plt.figure(figsize=(10, 6))
sns.boxplot(data=tips, x='day', y='total_bill', order=day_order, color='steelblue')
plt.title('Restaurant Bills by Day of Week')
plt.xlabel('Day')
plt.ylabel('Total Bill Amount')
plt.show()
# Box plot with individual points
plt.figure(figsize=(10, 6))
sns.boxplot(data=tips, x='day', y='total_bill', order=day_order, color='lightblue')
sns.stripplot(data=tips, x='day', y='total_bill', order=day_order,
color='darkred', alpha=0.5, size=4)
plt.title('Restaurant Bills by Day with Individual Points')
plt.xlabel('Day')
plt.ylabel('Total Bill Amount')
plt.show()
# Box plot by time and day (figure below)
plt.figure(figsize=(12, 6))
sns.boxplot(data=tips, x='day', y='total_bill', hue='time',
order=day_order, hue_order=time_order,
palette={'Lunch': 'lightblue', 'Dinner': 'steelblue'})
plt.title('Restaurant Bills by Day and Time')
plt.xlabel('Day')
plt.ylabel('Total Bill Amount')
plt.legend(title='Time')
plt.show()