Mini Lesson 2: Showing and describing variability

How do I make a dot plot (and scale an axis)?

Data Literacy Project

Begin with a question:

How did students in my class do on the quiz?

The following data set represents the grades earned by 23 students on a 10 point quiz.

Grades:9, 7.5, 8, 7, 9, 6, 8, 7, 9, 5, 8.5, 8, 5, 6.5, 8, 9, 6, 7, 8, 7, 5, 6.5, 7.5

Making a dot plot is a 2 step process:

1. Scale the axis2. Plot the dots

Note: For a dot plot, you will only need to scale one axis (usually the horizontal axis) for your data. The other axis will simply be a count or frequency of the number of times each value appears in the data set.

1. Scale the axisa. Find the lowest and highest scores in the data

set (the range).

Scores:9, 7.5, 8, 7, 9, 6, 8, 7, 9, 5, 8.5, 8, 5, 6.5, 8, 9, 6, 7, 8, 7, 5, 6.5, 7.5

What is the lowest score for the quiz data set? _____

What is the highest score for the quiz data set? _____

1. Scale the axisb. Put the highest and lowest grades on the axis so it

will include the full range of your data set.Grades:9, 7.5, 8, 7, 9, 6, 8, 7, 9, 5, 8.5, 8, 5, 6.5, 8, 9, 6, 7, 8, 7, 5, 6.5, 7.5

- the X-axis does not have to start at zero - the Y-axis does not require a label (although “count”

or “frequency” would be appropriate)

1. Scale the axisc. Put tic marks at equal intervals along the

axis.Grades:9, 7.5, 8, 7, 9, 6, 8, 7, 9, 5, 8.5, 8, 5, 6.5, 8, 9, 6, 7, 8, 7, 5, 6.5, 7.5

- The major tic marks are labeled and are at intervals of 1.0.- Note that not all of the quiz scores are whole numbers....

1. Scale the axisd. Set minor tic marks at equal intervals

between the major tic marksGrades:9, 7.5, 8, 7, 9, 6, 8, 7, 9, 5, 8.5, 8, 5, 6.5, 8, 9, 6, 7, 8, 7, 5, 6.5, 7.5

- What value does each minor tic mark represent?

1. Scale the axisd. Set minor tic marks at equal intervals

between the major tic marksGrades:9, 7.5, 8, 7, 9, 6, 8, 7, 9, 5, 8.5, 8, 5, 6.5, 8, 9, 6, 7, 8, 7, 5, 6.5, 7.5

ANSWER

5.5 6.5 7.5 8.5

- the minor tic marks do not need to be labeled

2. Plot the dotsPlot each case using a dot for each student’s grade.

Grades:9, 7.5, 8, 7, 9, 6, 8, 7, 9, 5, 8.5, 8, 5, 6.5, 8, 9, 6, 7, 8, 7, 5, 6.5, 7.5

- There are 3 dots over the grade of 5 because three students got a grade of 5 on the quiz. (5 appears three times in the data set).

What if one of the grades does not fall on a tic mark?

How would you plot a grade of 7.2?Indicate on the graph below where a grade of 7.2 would appear.

What if one of the grades does not fall on a tic mark?

How would you plot a grade of 7.2?Indicate on the graph below where a grade of 7.2 would appear.

ANSWER

How much do wild bears weigh?

Twelve wild bears were caught, anesthetized, and their bodies were measured and weighed.

The data are a sample of data supplied with MiniTab and are attributed to Dr. Gary Alt

Weight (pounds)

14218014212239614011682

18036879

160

Weight (pounds)

14218014212239614011682

18036879

160

ANSWERHow much do wild bears weigh?

The bears in this sample weigh from around 76 pounds to almost 400 pounds. Most of them weigh between 79 and 180 lbs. There were two very big bears.