Box Plot Generator – Create Box and Whisker Plots Online

Generate box plots (box-and-whisker plots) from any dataset with our free online box plot generator. Visualize quartiles, median, and outliers with a clear and accurate diagram.

Data Values

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Understanding Box Plots

A box plot, also called a box-and-whisker plot, is a visual way to show how data is distributed. Instead of listing every single number, it summarizes your dataset using five key values: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. This five-number summary gives you an instant picture of where most of your data clusters and whether there are any unusual values.

The "box" in the middle contains the middle 50% of your data – everything between Q1 and Q3. The line inside the box marks the median, which is the middle value when all numbers are sorted. The "whiskers" extend to show the range of typical values, and any points beyond the whiskers are flagged as outliers – values that are unusually high or low compared to the rest of the data.

How Box Plots Work: The Five-Number Summary

The Five Numbers

Minimum

The smallest value in your dataset

Q1 (First Quartile)

The 25th percentile – 25% of data falls below this value

Median (Q2)

The 50th percentile – the middle value

Q3 (Third Quartile)

The 75th percentile – 75% of data falls below this value

Maximum

The largest value in your dataset

Finding Quartiles

Step 1: Sort the data

Arrange all values from smallest to largest

Step 2: Find the median

For odd n, take the middle value. For even n, average the two middle values

Step 3: Find Q1

Find the median of the lower half (values below the overall median)

Step 4: Find Q3

Find the median of the upper half (values above the overall median)

Identifying Outliers

Outliers are values that fall far outside the typical range of your data. Box plots use the interquartile range (IQR) to determine what counts as an outlier. The IQR is simply Q3 minus Q1 – it measures the spread of the middle 50% of your data.

The 1.5 × IQR Rule

IQR = Q3 - Q1

Lower Fence = Q1 - 1.5 × IQR

Upper Fence = Q3 + 1.5 × IQR

Any value below the lower fence or above the upper fence is an outlier

The whiskers extend to the most extreme values that are still within the fences. Values beyond the fences are plotted as individual points – these are your outliers. This method, developed by statistician John Tukey, catches values that are genuinely unusual without flagging normal variation.

Worked Examples

Example 1: Test Scores

Find the five-number summary for these 11 test scores:

65, 70, 72, 75, 78, 80, 82, 84, 86, 89, 92

Step 1: Data is already sorted (n = 11)

Step 2: Minimum = 65, Maximum = 92

Step 3: Median = 80 (the 6th value, middle of 11)

Step 4: Lower half: 65, 70, 72, 75, 78 → Q1 = 72 (middle value)

Step 5: Upper half: 82, 84, 86, 89, 92 → Q3 = 86 (middle value)

Five-number summary: Min = 65, Q1 = 72, Median = 80, Q3 = 86, Max = 92

IQR: 86 - 72 = 14

Fences: Lower = 72 - 1.5(14) = 51, Upper = 86 + 1.5(14) = 107

Outliers: None (all values are between 51 and 107)

Example 2: Salaries with Outliers

Analyze this salary dataset (in thousands):

35, 38, 40, 42, 45, 47, 48, 50, 52, 54, 55, 57, 58, 60, 62, 65, 68, 72, 95, 150

Step 1: Data is sorted (n = 20, even)

Step 2: Min = 35, Max = 150

Step 3: Median = (54 + 55) / 2 = 54.5 (average of 10th and 11th values)

Step 4: Lower half (10 values): 35, 38, 40, 42, 45, 47, 48, 50, 52, 54

Q1 = (45 + 47) / 2 = 46

Step 5: Upper half (10 values): 55, 57, 58, 60, 62, 65, 68, 72, 95, 150

Q3 = (62 + 65) / 2 = 63.5

IQR: 63.5 - 46 = 17.5

Fences: Lower = 46 - 1.5(17.5) = 19.75, Upper = 63.5 + 1.5(17.5) = 89.75

Outliers: 95 and 150 (both exceed 89.75)

Whiskers: Lower = 35, Upper = 72 (highest non-outlier)

Example 3: Small Dataset

Calculate for this small dataset:

12, 15, 18, 20, 25, 28, 30, 35

Step 1: Sorted data (n = 8, even)

Step 2: Min = 12, Max = 35

Step 3: Median = (20 + 25) / 2 = 22.5

Step 4: Lower half: 12, 15, 18, 20 → Q1 = (15 + 18) / 2 = 16.5

Step 5: Upper half: 25, 28, 30, 35 → Q3 = (28 + 30) / 2 = 29

IQR: 29 - 16.5 = 12.5

Fences: Lower = 16.5 - 1.5(12.5) = -2.25, Upper = 29 + 1.5(12.5) = 47.75

Outliers: None

Quick Fact

John Tukey introduced the box plot in 1970 as part of his work on exploratory data analysis. He called it the "box-and-whisker plot" and designed it to be drawn by hand quickly while still revealing the essential features of a dataset. Tukey also coined terms like "bit" (binary digit) and "software." His book "Exploratory Data Analysis" remains influential today, and the box plot is one of the most widely used statistical graphics in the world.

Frequently Asked Questions

What does the box in a box plot represent?

The box spans from Q1 to Q3, containing the middle 50% of your data. The line inside the box marks the median. A narrow box means data is tightly clustered; a wide box means more spread. If the median line is off-center, the data is skewed in that direction.

How do you interpret the whiskers?

The whiskers extend from the box to the most extreme values that are not outliers. They show the range of "typical" data. The lower whisker goes down to the smallest value above the lower fence; the upper whisker goes up to the largest value below the upper fence.

What if there are no outliers?

That's perfectly normal! Many datasets don't have outliers. The whiskers will simply extend all the way to the minimum and maximum values. The absence of outliers suggests your data is fairly consistent without extreme values.

Can a box plot show the mean?

Traditional box plots show the median, not the mean. Some variations add a symbol (like a dot or triangle) to mark the mean. Comparing the mean and median tells you about skewness – if the mean is higher than the median, the data likely has a right skew.

When should I use a box plot instead of a histogram?

Box plots are better for comparing multiple groups side by side and for quickly spotting outliers. Histograms show more detail about the shape of the distribution but take up more space. Use box plots when you need a compact summary or want to compare several datasets at once.

What does it mean if the median is closer to Q1 than Q3?

This indicates right skew (positive skew) – the data has a longer tail on the high end. Most values cluster toward the lower end, with a few high values pulling the distribution right. Salary data often shows this pattern: many people earn modest amounts, but a few earn very high salaries.

How many data points do I need for a meaningful box plot?

You can technically make a box plot with as few as 5 values, but it's most useful with at least 15-20 data points. With very small datasets, the quartile calculations become less stable. For large datasets (100+ points), box plots excel at summarizing the distribution without overwhelming detail.

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