# 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:
$25$, $28$, $29$, $29$, $\large{30}$, $\large{34}$, $35$, $35$, $37$, $38$
$\dfrac{30+34}{2}=32$
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.
$25$, $28$, $\large{29}$, $29$, $30$
$Q_1=29$
The third quartile is the median of the data points to the right of the median.
$34$, $35$, $\large{35}$, $37$, $38$
$Q_3=35$
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:
The five-number summary divides the data into sections that each contain approximately $25\%$ of the data in that set.
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.