Box Plots

Warmup

Here are the birth weights, in ounces, of all the puppies born at a kennel in the past month.

What is your observation about the distribution of the puppy weights?

Activity #1

Representing Box Plots.

Twenty people participated in a study about blinking. The number of times each person blinked while watching a video for one minute was recorded. The data values are shown here, in order from smallest to largest.

• Use the grid and axis to make a dot plot of this data set.
• Click on “List” to generate data.​
• Click on “List” to generate data.
• Find the first quartile (Q1) and the third quartile (Q3). Mark their locations on the dot plot.

A box plot can be used to represent the five-number summary graphically. Let’s draw a box plot for the number-of-blinks data.

• On the grid in the applet above use the red handles to draw a box that extends from the first quartile (Q1) to the third quartile (Q3). Remember that you have to find these values first. Drag the labels to the diagram.
• Use the red handles to locate the minimum and the maximum values.

You have now created a box plot to represent the number of blinks data. What fraction of the data values are represented by each of these elements of the box plot;

(1.) The left whisker?

(2.) The box?

(3.) The right whisker?

(4.) Suppose there were some errors in the data set: the smallest value should have been 6 instead of 3, and the largest value should have been 41 instead of 51. Determine if any part of the five-number summary would change. If you think so, describe how it would change. If not, explain how you know.

Activity #2

Box Plots Practice.

• Enter new values in the column on the right and locate Minimum, Lower Quartile, Median, Upper Quartile, and Maximum values.

Activity #3

Practice Questions.

Each student in a class recorded how many books they read during the summer. Here is a box plot that summarizes their data in the summer. Here is a box plot that summarizes their data.

• Use the data to answer the following questions;

(1.) What is the greatest number of books read by a student in this group?

(2.) What is the median number of books read by the students?

(3.) What is the interquartile range (IQR)?

Use this five-number summary to draw a box plot. All values are in seconds. Minimum: 40, First quartile (Q1): 45, Median: 48, Third quartile (Q3): 50, Maximum: 60.

The data shows the number of hours per week that each of 13 seventh-grade students spent doing homework. 3, 10, 12, 4, 7, 9, 5, 5, 11, 11, 5, 12, 11.

• Create a box plot to summarize the data.

Challenge #1

Here is a dot plot that represents a data set. Explain why the mean of the data set is greater than its median.

Challenge #2

The box plot displays the data on the response times of 100 mice to seeing a flash of light. How many mice are represented by the rectangle between 0.5 and 1 second?