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# 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):

**Make a box plot of the data.**

**Step 1:**Order the data from smallest to largest.

Our data is already in order.

**Step 2:**Find the median.

The median is the mean of the middle two numbers:

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

*right*of the median.**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

Recall that ${Q}_{1}=29$ , the median is $32$ , and ${Q}_{3}=35.$

**Step 3:**Draw a whisker from

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 $25\mathrm{\%}$ 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.

*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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