## Math Mission

## Opening

Compare data sets from different experiments using a variety of tools.

Compare data sets from different experiments using a variety of tools.

How does your ability to estimate time vary with different time intervals? Once again, you will first need to collect some data.

- Using the 50 Seconds Timer interactive, utilize the Start and Stop buttons to estimate when you think 50 seconds have passed.
- The interactive will record and display your time estimate.
- Repeat the process two more times.

How can you compare the measures of center and spread for the two sets of data?

INTERACTIVE: 50 Seconds Timer

Compare your estimates for 50-second intervals to your estimates for 20-second intervals. Use your data set from the third trial for the 50-second intervals and your data set from the third trial for the 20-second intervals. Do not use graphs to make your comparison. Think about the following questions:

- What tools can you use to analyze the data?
- What evidence can you use to justify your conclusion?
- What is the range for each data set?
- How can you compare the data sets?
- How can you compare the measures of center and spread for the two sets of data?
- How can you compare two data sets when the numbers in each data set are based on different times—that is, 20 seconds versus 50 seconds?

- Prepare a presentation about what how you analyzed your data sets and their results and conclusions.

- Find the mean absolute deviation for the combined data. What does this value tell you about the data sets?

- Take notes about the tools your classmates used to analyze the data sets and their results and conclusions.

As your classmates present, ask questions such as:

- Did you round the numbers to whole numbers? Why or why not?
- How does the range of your 50 second data set compare with the range of your 20 second data set?
- What was your typical time for estimating 50 seconds?
- How did you compare this time to your typical time for estimating 20 seconds?
- How can you compare the middle 50% of the values for each data set?
- Why did you use those measures of center to analyze the data?
- Based on your results, what conclusion can you make about your estimation skills for longer versus shorter intervals of time?
- Can you generalize your conclusion to all seventh grade students? Why or why not?

- Write a summary about comparing different data sets.

Check your summary:

- Do you explain how to compare data sets?
- Do you describe the tools you can use to analyze data and make comparisons?
- Do you explain how to deal with data sets of different sizes or scales?

Complete this Self Check by yourself.

A school has 10 seventh grade classes, each with 30 students. Lucy wants to find out how well the students can estimate the weight of a gallon of water. She realizes that she cannot survey everyone, but she isn’t sure how to proceed.

- How could Lucy go about collecting her data? Lucy decides to start with a random sample of 10 seventh grade students. The students made the following estimates for the weight of a gallon of water (in pounds): 6, 7, 9, 8, 7, 10, 8, 6, 9, 8
- Based on this sample, what does a typical seventh grade student at the school think a gallon of water weighs?
- How did you reach your conclusion?
- Based on the sample, how many seventh grade students at the school think that a gallon of water weighs between 7 and 9 lbs?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**Something that still confuses me about sampling and comparing data sets is…**