Table of Contents
A box plot is a graphical representation of a dataset that displays five key measures of the data: the median, the upper and lower quartiles, and the minimum and maximum values. The percentages in a box plot show the relative frequency of values in the data, with the median showing the 50th percentile and the quartiles showing the 25th and 75th percentiles. The minimum and maximum values represent the 0th and 100th percentiles, respectively.
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.
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: