# 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:

$25$, $28$, $29$, $29$, $\large{30}$, $\large{34}$, $35$, $35$, $37$, $38$

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.$25$, $28$, $\large{29}$, $29$, $30$

The third quartile is the median of the data points to the

*right*of the median.$34$, $35$, $\large{35}$, $37$, $38$

**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 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 $25\%$ 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 $25\%$ of data is lower than $29$ and about $75\%$ is above is $29$.

About $75\%$ of the boxes of raisins weighed more than $29$ grams.

*Want to learn more about interpreting quartiles? Check out this video.*

*Want to practice more problems like this? Check out this exercise.*