What is a Box and Whisker Plot?
A box and whisker plot is a representation of a set of data that shows a 5-number summary of the data. The five numbers used are minimum, maximum, first quartile, median, and third quartile. The box is from the first quartile to the third quartile. There is a vertical line drawn between the first and third quartile where the median is. The whiskers go to the minimum and maximum.
How to use the Box and Whisker Plot:
Assume the following data set:
25, 28, 29, 30, 30, 34, 35, 35, 37, 38
First make sure that the data is in order. In this case, our data set already is.
Then, find the median. (The median is the average of the middle two numbers):
(30+34)/2 = 64/2 = 32
The median is 32
The first quartile is the median of data that is found to the left of the median.
25, 28, 29, 30, 30
The third quartile is the median of data that is found to the right of the median
34, 35, 35, 37, 38
The minimum is 25
The maximum is 38
Our five number summary is:
Minimum: 25
First quartile: 29
Median: 32
Third quartile: 35
Maximum: 38
To draw the box and whisker plot: The box is from the first quartile to the third quartile. There is a vertical line drawn between the first and third quartile where the median is. The whiskers go to the minimum and maximum.
Sample Math Problems
Question
Assume that the following number line represents the number of tomatoes in John’s basket at each weight in ounces. What percentage of tomatoes in John’s basket are less than 10 ounces?
a) 0%
b) 25%
c) 50%
d) 75%
e) 100%
Answer
Option C – 50%. At 10 ounces we see a vertical line in the box of the box and whisker plot. As the vertical line is the median of the data set - this means that 50% of the tomatoes found in John’s basket were less than 10 ounces.
Question
The following is the five-number summary for the number of years Edison High School’s swim teammates have been swimming. What percent of the swim team has more than 2 years of swimming experience?
Minimum – 1
Q1 – 2
Median – 2.5
Q3 – 4
Max – 6
a) 0%
b) 25%
c) 50%
d) 75%
e) 100%
Answer
Option D – 75%. The question is asking how many team members have more than 2 years of swimming experience, or the percent of team members that are to the right of Q1 on the number line. As the minimum to Q1 consists of 25% of the team, Q1 to the maximum will consist of 75% of the team.
Question
The following is the five-number summary for the number of years Edison High School’s swim teammates have been swimming. The summary suggests that 50% of Edison High School’s swim teammates have fewer than how many years of experience of swimming?
Minimum – 1
Q1 – 2
Median – 2.5
Q3 – 4
Max – 6
a) 1
b) 2
c) 2.5
d) 4
e) 6
Answer
Option C – 2.5 years. Percentiles show the percent of the distribution of data that are below a certain value. 2 years of experience is the first quartile, meaning that 25% of the team has less than 2 years of experience. 2.5 years of experience is the median, meaning that 50% of the team has less than 2.5 years of experience swimming.
Question
Assume that the following number line represents the number of tomatoes in John’s basket at each weight in ounces. The box plot suggests that about 75% of tomatoes were less than how many ounces?
a) 4
b) 7
c) 10
d) 14
e) 18
Answer
Option D – 14. Each quartile contains 25% of the data. The box plot suggests that 75% of tomatoes are less than 14 ounces in weight
