What is a Box Plot

A box plot is a visual way of recording a set of data values.

The data from a box plot can show us 5 facts:

• the minimum data value;
• the 1st quartile value (the lower quartile);
• the median value.
• the 3rd quartile value (the upper quartile);
• the maximum data value;

Using these facts, we can also quickly use the box plot work out:

• the range of the data;
• the interquartile range of the data set;
• whether the data is skewed to the left or right.

The median is the midpoint (or middle value) of a set of numbers.

It is found by ordering the set of numbers and then finding the middle value in the set.

The median can also be thought of as the 2nd quartile or Q2.

About ½ (50%) of the data values are lower than the median and ½ (50%) of the data values are higher than the median.

Example 1) Create a box plot of these test scores:

Step 1) Put the scores in order, smallest first.

Step 2) Find the median (middle) score and use the median to split the scores into two halves.

Step 3) Find the 1st and 3rd quartiles by finding the middle of the first half of the data and the middle of the second half of the data.

Step 4) Draw a number line from the minimum to maximum values.

Step 5) Draw a rectangle about the number line from the Q1 (first quartile) value to the Q3 (3rd quartile) value.

Step 6) Draw a vertical line inside the rectangle to show the median value.

Step 7) Draw the whiskers from either side of the rectangle to the minimum and maximum data points.

Example 2) Create a box plot of this data which shows the number of visitors each hour at a museum:

Step 1) Put the scores in order, smallest first.

Step 2) Find the median (middle) score and use the median to split the scores into two halves.

The median value is (55 + 59) ÷ 2 = 57

Step 3) Find the 1st and 3rd quartiles by finding the middle of the first half of the data and the middle of the second half of the data.

The 1st quartile is halfway between 47 and 53 = (47 + 53) ÷ 2 = 50

The 3rd quartile is halfway between 64 and 71 = (64 + 71) ÷ 2 = 67 ½

Step 4) Draw a number line from the minimum to maximum values.

Step 5) Draw a rectangle about the number line from the Q1 (first quartile) value to the Q3 (3rd quartile) value.

Step 6) Draw a vertical line inside the rectangle to show the median value.

Step 7) Draw the whiskers from either side of the rectangle to the minimum and maximum data points.

As well as creating a box plot, another important skill is to be able to interpret a box plot from a given set of data.

We already know that the box plot directly shows us the 5 facts:

• the minimum value
• the maximum value
• the median value (Q2)
• the 1st quartile value (Q1)
• the 3rd quartile value (Q3)

Using this information we can also find the following information:

• the range of data values (by subtracting the minimum value from the maximum value)
• the interquartile range (by subtracting the 1st quartile value (Q1) from the 3rd quartile value (Q3)

We also know that about 25% of the data set is below the 1st quartile (Q1), and about 75% of the data set is above Q1.

We also know that about 75% of the data set is below the 3rd quartile (Q3) and about 25% of the data set is above Q3.

This box plot shows the number of books read by a group of students during a semester.

So what information can this box plot tell us?

• The minimum value is 11 books.
• The 1st quartile (Q1) is 14 books.
• The median value is 16 books.
• The 3rd quartile (Q3) is 21 books.
• The maximum value is 24 books.

The range of books read is maximum value - minimum value = 24 - 11 = 13 bookx

The interquartile range is the 3rd quartile (Q3) - the 1st quartile (Q1) = 21 - 14 = 7 books.

The median is to the left of the center line, and the whisker is slightly shorter on the left hand side, so the data is skewed right (or positively skewed).

About ¼ (25%) of the students read fewer than 14 books and 75% read more than 14 books.

About ¾ (75%) of the students read fewer than 21 books and 25% read more than 21 books.

About half the students read fewer than 16 books, and half read more than 16 books.

If you want some more help identifying the lower and upper quartiles, then take a look at this page.

We also have a selection of box plot worksheets.

The worksheets will help you to practice creating and interpreting box plots.

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.