Learning Focus

Compare sets of data using center, spread, and shape.

How do I use measures of center and spread together to make decisions about data?

How do I compare two or more data sets that are represented by different plots?

Open Up the Math: Launch, Explore, Discuss

Principal Scanner wants to make his school the best ever. He has offered to buy pizza for the class that shows the best results on the department final at the end of the semester. He tells all the teachers in the department to submit their student test-score data so that he can determine which class did the best. Unfortunately, Principal Scanner underestimated the job he was going to have in determining the best class. To make matters worse, teachers used different representations for the data they submitted for him to evaluate.

So, Principal Scanner has turned the job over to you. You are to compare the two data sets in each problem and give the principal a report, using the sentence frames provided for this purpose. Give each comparison some thoughtful analysis, and use your best statistical language to describe your findings. Somebody’s pizza is depending on you!

Data Set I: Williams’ Class

Data Set II: Lemon’s Class

Data Set III: Croft’s Class

Data Set IV: Anderson’s Class

Data Set V: Hurlea’s Class

Data Set VI: Jones’ Class

1.

Compare data distributions between Anderson’s and Williams’ classes.

a.

Complete the sentence frames with your findings:

The data from has a greater than because .

The data from has less than because .

The data from is skewed left/right (choose one) while the data from is not because .

b.

Which of these two classes do you think did the best? Why?

2.

Compare data distributions between Croft’s and Hurlea’s classes.

a.

Complete the sentence frames with your findings:

The data from has a greater than because .

The data from has less than because .

The data from contains an outlier while the data from . I know this because .

b.

Which of these two classes do you think did the best? Why?

3.

Compare data distributions between Jones’ and Williams’ classes.

a.

Complete the sentence frames with your findings.

The data from has a greater than because .

The data from has less than because .

The data from is skewed left/right (choose one) while the data from is not because .

b.

Which of these two classes do you think did the best? Why?

4.

Compare data distributions between Lemon’s class and that of a teacher of your choice.

a.

Complete the sentence frames with your findings.

The data from has a greater than because .

The data from has less than because .

b.

Which of these two classes do you think did the best? Why?

You now get to make your final recommendation to Principal Scanner. Which class do you choose, and why?

Box plot:

Histogram:

Dot plot:

Lesson Summary

In this lesson, we compared data distributions using shape, center, and spread. We learned to consider the interquartile range and the median when using a box plot and to consider the mean and the standard deviation when using a histogram. We also discussed the effect of outliers on the median, mean, and standard deviation.

Retrieval

Sketch a graph for each of the functions.