Using Measures of Center & Spread To Analyze Data

Using Measures of Center & Spread To Analyze Data

Math Mission

Opening

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

How Long Is 50 Seconds?

Work Time

How Long Is 50 Seconds?

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 Data Sets

Work Time

Compare Data Sets

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

Work Time

Prepare a Presentation

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

Challenge Problem

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

Make Connections

Performance Task

Ways of Thinking: Make Connections

  • 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?

Comparing Different Data Sets

Formative Assessment

Summary of the Math: Comparing Different Data Sets

  • 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?

Estimate the Weight of Water

Formative Assessment

Self Check: Estimate the Weight of Water

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.

  1. 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
  2. Based on this sample, what does a typical seventh grade student at the school think a gallon of water weighs?
  3. How did you reach your conclusion?
  4. Based on the sample, how many seventh grade students at the school think that a gallon of water weighs between 7 and 9 lbs?

Reflect on Your Work

Work Time

Reflection

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…