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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):
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
30+342=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
Q1=29
The third quartile is the median of the data points to the right of the median.
34, 35, 35, 37, 38
Q3=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 Q1 to Q3 with a vertical line through the median.
Recall that Q1=29, the median is 32, and Q3=35.
Step 3: Draw a whisker from Q1 to the min and from Q3 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 Q1=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.