Mini Lesson 2: Showing and describing variability How do I make a dot plot (and scale an axis)?

1. Data Literacy Project Mini Lesson 2: Showing and describing variability How do I make a dot plot (and scale an axis)?

2. 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

3. Making a dot plot is a 2 step process: • Scale the axis • 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.

4. Scale the axis • 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? _____

5. Scale the axis • b. 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)

6. Scale the axis • 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....

7. Scale the axis • Set minor tic marks at equal intervals between the major tic marks • 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 - What value does each minor tic mark represent?

8. ANSWER • Scale the axis • Set minor tic marks at equal intervals between the major tic marks • 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 8.5 6.5 7.5 5.5 - the minor tic marks do not need to be labeled

9. Plot the dots • Plot 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).

10. 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.

11. ANSWER 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.

12. 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

13. ANSWER How 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.