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Unit 8

Estimating Population Measures of Center

Probability and Sampling

Lesson 15

Expressions and Equations

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Let’s use samples to estimate measures of center for the population.

Unit 8 ● Lesson 15

Learning

Goal

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Describing the Center

Unit 8 ● Lesson 15 ● Activity 1

Would you use the median or mean to describe the center of each data set? Explain your reasoning.

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Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Three Different TV Shows

Unit 8 ● Lesson 15 ● Activity 2

Here are the ages (in years) of a random sample of 10 viewers for 3 different television shows. The shows are titled, “Science Experiments YOU Can Do,” “Learning to Read,” and “Trivia the Game Show.”

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  1. Calculate the mean for one of the samples. Make sure each person in your group works with a different sample. Record the answers for all three samples.
  2. Which show do you think each sample represents? Explain your reasoning

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Who’s Watching What?

Unit 8 ● Lesson 15 ● Activity 3

Here are three more samples of viewer ages collected for these same 3 television shows.

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  1. Calculate the mean for one of these samples. Record all three answers.
  2. Which show do you think each of these samples represents? Explain your reasoning.
  3. For each show, estimate the mean age for all the show's viewers.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Who’s Watching What?

Unit 8 ● Lesson 15 ● Activity 3

  • Calculate the mean absolute deviation for one of the shows' samples. Make sure each person in your group works with a different sample. Record all three answers.

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  • What do the different values for the MAD tell you about each group?
  • An advertiser has a commercial that appeals to 15- to 16-year-olds. Based on these samples, are any of these shows a good fit for this commercial? Explain or show your reasoning.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Who’s Watching What?

Unit 8 ● Lesson 15 ● Activity 3

  • Why do you think a sample was used in this situation rather than data from the population?
  • How could we improve the estimate of the mean for the populations?
  • If a sample has a large MAD, what does that imply about the population?
  • If a sample has a small MAD, what is the relationship between the data and the mean?
  • Which estimate of the mean for the population do you expect to be more accurate: the mean from a sample with a large MAD or the mean from a sample with a small MAD? Explain or show your reasoning.
  • What do you notice about the different answers for the same show, but the different samples?
  • Why were the answers different for the same show, but different samples?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Who’s Watching What?

Unit 8 ● Lesson 15 ● Activity 3

  • Notice that there is a 56 year old in sample 6. What are some reasons you think they might be watching this show?
  • The questions asked you to consider means, but are there any data sets for which median might be a better measure of center? Explain your reasoning.
  • A lot of families might be watching ‘Learning to Read’ with their children or older people may be using the show to learn English. How might this affect the mean? How could you recognize that there are two main age groups that watch this show?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Movie Reviews

Unit 8 ● Lesson 15 ● Activity 4

A movie rating website has many people rate a new movie on a scale of 0 to 100. Here is a dot plot showing a random sample of 20 of these reviews.

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  1. Would the mean or median be a better measure for the center of this data? Explain your reasoning.
  2. Use the sample to estimate the measure of center that you chose for all the reviews.
  3. For this sample, the mean absolute deviation is 19.6, and the interquartile range is 15. Which of these values is associated with the measure of center that you chose?
  4. Movies must have an average rating of 75 or more from all the reviews on the website to be considered for an award. Do you think this movie will be considered for the award? Use the measure of center and measure of variability that you chose to justify your answer.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Movie Reviews

Unit 8 ● Lesson 15 ● Activity 4

  • Which measure of center did you choose and why?
  • Based on the context, do you think other movie reviews would have non-symmetric distributions as well?
  • A random sample of 20 reviews for another movie has a median of 90 as well, but its IQR is 30. Do you think this movie is more or less likely to be considered for the award?
  • A random sample of 20 reviews for a third movie has a median of 50 and an IQR of 20. Is it possible this third movie will be considered for an award?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Estimating Population Measures of Center

Unit 8 ● Lesson 15

  • How do you determine which measure of center will best describe the data in a sample?
  • When you have the data from a sample, how can you estimate the value of a measure of center for the population?
  • What does the variability of the sample tell you about your estimate for the measure of center of the population?

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Unit 8 ● Lesson 15

  • I can consider the variability of a sample to get an idea for how accurate my estimate is.
  • I can estimate the mean or median of a population based on a sample of the population.

Learning

Targets

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More Accurate Estimate

Unit 8 ● Lesson 15 ● Activity 5

Here are dot plots that represent samples from two different populations.

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  1. Estimate the mean of each population using these samples.
  2. Based on the dot plots, which estimate is more likely to be accurate? Explain your reasoning.

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Lesson Video

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