What is a box and whisker plot?

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum.
In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median. The whiskers go from each quartile to the minimum or maximum.

Example: Finding the five-number summary

A sample of 1010 boxes of raisins has these weights (in grams):
2525, 2828, 2929, 2929, 3030, 3434, 3535, 3535, 3737, 3838
Make a box plot of the data.
Step 1: Order the data from smallest to largest.
Our data is already in order.
2525, 2828, 2929, 2929, 3030, 3434, 3535, 3535, 3737, 3838
Step 2: Find the median.
The median is the mean of the middle two numbers:
2525, 2828, 2929, 2929, 30\large{30}, 34\large{34}, 3535, 3535, 3737, 3838
30+342=32\dfrac{30+34}{2}=32
The median is 3232.
Step 3: Find the quartiles.
The first quartile is the median of the data points to the left of the median.
2525, 2828, 29\large{29}, 2929, 3030
Q1=29Q_1=29
The third quartile is the median of the data points to the right of the median.
3434, 3535, 35\large{35}, 3737, 3838
Q3=35Q_3=35
Step 4: Complete the five-number summary by finding the min and the max.
The min is the smallest data point, which is 2525.
The max is the largest data point, which is 3838.
The five-number summary is 2525, 2929, 3232, 3535, 3838.

Example (continued): Making a box plot

Let's make a box plot for the same dataset from above.
Step 1: Scale and label an axis that fits the five-number summary.
Step 2: Draw a box from Q1Q_1 to Q3Q_3 with a vertical line through the median.
Recall that Q1=29Q_1=29, the median is 3232, and Q3=35.Q_3=35.
Step 3: Draw a whisker from Q1Q_1 to the min and from Q3Q_3 to the max.
Recall that the min is 2525 and the max is 3838.
We don't need the labels on the final product:
Want to learn more about making box and whisker plots? Check out this video.
Want to practice making box plots? Check out this exercise.

Interpreting quartiles

The five-number summary divides the data into sections that each contain approximately 25%25\% of the data in that set.

Example: Interpreting quartiles

About what percent of the boxes of raisins weighed more than 2929 grams?
Since Q1=29Q_1=29, about 25%25\% of data is lower than 2929 and about 75%75\% is above is 2929.
About 75%75\% of the boxes of raisins weighed more than 2929 grams.
Want to learn more about interpreting quartiles? Check out this video.
Want to practice more problems like this? Check out this exercise.
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