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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 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 .
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 .
The max is the largest data point, which is .
The five-number summary is , , , , .
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 to with a vertical line through the median.
Recall that , the median is , and
Step 3: Draw a whisker from to the min and from to the max.
Recall that the min is and the max is .
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 of the data in that set.
Example: Interpreting quartiles
About what percent of the boxes of raisins weighed more than grams?
Since , about of data is lower than and about is above is .
About of the boxes of raisins weighed more than 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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