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.
The following tutorials provide additional information about box plots: