If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Box plot review

## 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 $10$ boxes of raisins has these weights (in grams):
$25$, $28$, $29$, $29$, $30$, $34$, $35$, $35$, $37$, $38$
Make a box plot of the data.
Step 1: Order the data from smallest to largest.
Our data is already in order.
$25$, $28$, $29$, $29$, $30$, $34$, $35$, $35$, $37$, $38$
Step 2: Find the median.
The median is the mean of the middle two numbers:
$25$, $28$, $29$, $29$, $30$, $34$, $35$, $35$, $37$, $38$
$\frac{30+34}{2}=32$
The median is $32$.
Step 3: Find the quartiles.
The first quartile is the median of the data points to the left of the median.
$25$, $28$, $29$, $29$, $30$
${Q}_{1}=29$
The third quartile is the median of the data points to the right of the median.
$34$, $35$, $35$, $37$, $38$
${Q}_{3}=35$
Step 4: Complete the five-number summary by finding the min and the max.
The min is the smallest data point, which is $25$.
The max is the largest data point, which is $38$.
The five-number summary is $25$, $29$, $32$, $35$, $38$.

### 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 ${Q}_{1}$ to ${Q}_{3}$ with a vertical line through the median.
Recall that ${Q}_{1}=29$, the median is $32$, and ${Q}_{3}=35.$
Step 3: Draw a whisker from ${Q}_{1}$ to the min and from ${Q}_{3}$ to the max.
Recall that the min is $25$ and the max is $38$.
We don't need the labels on the final product:
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 $25\mathrm{%}$ of the data in that set.

### Example: Interpreting quartiles

About what percent of the boxes of raisins weighed more than $29$ grams?
Since ${Q}_{1}=29$, about $25\mathrm{%}$ of data is lower than $29$ and about $75\mathrm{%}$ is above is $29$.
About $75\mathrm{%}$ of the boxes of raisins weighed more than $29$ grams.