A Complete Guide to Box Plot Percentages

A box plot is a type of plot that displays the five number summary of a dataset, which includes:

• The minimum value
• The first quartile
• The median value
• The third quartile
• The maximum value

A typical box plot looks like this:

Within a box plot:

• The first quartile represents the 25th percentile of all values in the dataset.
• The median represents the 50th percentile of all values in the dataset.
• The third quartile represents the 75th percentile of all values in the dataset.

The interquartile range tells us the spread of the middle 50% of values in a dataset and can be calculated by subtracting the first quartile from the third quartile in a box plot:

The following example shows how to use a box plot to answer questions related to percentages.

Example: How to Interpret Box Plot Percentages

The following box plot shows the distribution of final exam scores for college students in a certain class:

Use the box plot to answer the following questions.

Question 1: What percentage of students scored below a 70?

From the box plot we can see that 70 lines up with the first quartile, which represents the 25th percentile.

Thus, 25% of students scored below a 70.

Question 2: What percentage of students scored above a 90?

From the box plot we can see that 90 lines up with the third quartile, which represents the 75th percentile.

Thus, 25% of students scored above a 90.

Question 3: What percentage of students scored between a 70 and a 90?

From the box plot we can see that 70 and 90 represent the first and third quartiles of the dataset, which correspond with the 25th and 75th percentiles.

Thus, 75% – 25% = 50% of students scored between a 70 and 90.