Illustrative Mathematics | v.360 Curriculum

15.1

Warm-up

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

heights of 50 basketball players

<p>Histogram from 66 to 80 by 2’s. Height in inches. Beginning at 66 up to but not including 68, height of bar at each interval is 2,3,13,17,7,5,1.</p><br>

ages of 30 people at a family dinner party

<p>Histogram from 5 to 50 by 5’s. Age in years. Beginning at 5 up to but not including 10, height of bar at each interval is 2, 3, 1, 1, 2, 3, 3, 4, 11</p><br>

backpack weights of sixth-grade students

<p>Dot plot from 0 to 16, by 2’s. backpack weight in kilograms. </p><br>

number of books students read over summer break

<p>Box plot from 0 to 16 by 2’s. Number of books. Whisker from 2 to 5. Box from 5 to 10 with vertical line at 8. Whisker from 10 to 15.</p><br>
<br>
<p><br><br>
</p><br>

15.2

Activity

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.

Sample 1

6
6
5
4
8
5
7
8
6
6

Sample 2

15
14
12
13
12
10
12
11
10
8

Sample 3

43
60
50
36
58
50
73
59
69
51

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.
Which show do you think each sample represents? Explain your reasoning.

15.3

Activity

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

Sample 4,
mean: 45.7 years

57
71
5
54
52
13
59
65
10
71

Sample 5,
mean: 7.4 years

15
5
4
5
4
3
25
2
8
3

Sample 6,
mean: 12 years

6
11
9
56
1
3
11
10
11
2

Which show do you think each of these samples represents? Explain your reasoning.
For each show, estimate the mean age for all of the shows’ viewers.
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.

Learning
to Read Science
Experiments
YOU Can Do Trivia the
Game Show

Which sample?

MAD
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.

15.4

Activity

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.

<p>Dot plot from 0 to 100, by 10’s. Movie Rating. Beginning at 0, number of dots above each increment is 0,1,1,1,0,0,1,0,2,3,3,5,3.</p><br>

Would the mean or median be a better measure for the center of this data? Explain your reasoning.
Use the sample to estimate the measure of center that you chose in the previous question.
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?
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.

Student Lesson Summary

Some populations have greater variability than others. For example, we would expect greater variability in the weights of dogs at a dog park than at a beagle meetup.

Dog park:

A picture of 2 small dogs, 2 medium sized dogs, and 3 large dogs.

Mean weight: 12.8 kg MAD: 2.3 kg

Beagle meetup:

A picture of 7 similar sized beagle dogs.

Mean weight: 10.1 kg MAD: 0.8 kg

The lower MAD indicates that there is less variability in the weights of the beagles. We would expect that the mean weight from a sample that is randomly selected from a group of beagles will provide a more accurate estimate of the mean weight of all the beagles than a sample of the same size from the dogs at the dog park.

In general, if samples from a population have similar sizes, a sample with less variability is more likely to have a mean that is close to the population mean.

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Estimating Population Measures of Center

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Lesson 15

Estimating Population Measures of Center

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