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Illustrative Math - Algebra 1 - Unit 1- Lesson 15

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16 Questions

Twenty students participated in a psychology experiment which measured their heart rates in two different situations.


What are the appropriate measures of center and variability to use with the data?

Twenty students participated in a psychology experiment which measured their heart rates in two different situations.


Which situation shows a greater typical heart rate?

Twenty students participated in a psychology experiment which measured their heart rates in two different situations.


Which situation shows greater variability?

Invent two situations that you think would result in distributions with similar measures of variability. Explain your reasoning.

Invent two situations that you think would result in distributions with different measures of variability. Explain your reasoning.

The data set and some summary statistics are listed.

11.5, 12.3, 13.5, 15.6, 16.7, 17.2, 18.4, 19, 19.5, 21.5
  • mean: 16.52
  • median: 16.95
  • standard deviation: 3.11
  • IQR: 5.5
How does adding 5 to each of the values in the data set impact the shape of the distribution?

The data set and some summary statistics are listed.

11.5, 12.3, 13.5, 15.6, 16.7, 17.2, 18.4, 19, 19.5, 21.5
  • mean: 16.52
  • median: 16.95
  • standard deviation: 3.11
  • IQR: 5.5
How does adding 5 to each of the values in the data set impact the measures of center?

The data set and some summary statistics are listed.

11.5, 12.3, 13.5, 15.6, 16.7, 17.2, 18.4, 19, 19.5, 21.5
  • mean: 16.52
  • median: 16.95
  • standard deviation: 3.11
  • IQR: 5.5
How does adding 5 to each of the values in the data set impact the measures of variability?

Here are two box plots:
Which box plot has a greater median?

Here are two box plots:
Which box plot has a greater measure of variability?

Here are two box plots:
Which box plot has a greater median?

The depth of two lakes is measured at multiple spots. For the first lake, the mean depth is about 45 feet with a standard deviation of 8 feet. For the second lake, the mean depth is about 60 feet with a standard deviation of 27 feet.

Noah says the second lake is generally deeper than the first lake. Do you agree with Noah?

The dot plots display the height, rounded to the nearest foot, of maple trees from two different tree farms.
Compare the mean and standard deviation of the two data sets.

The dot plots display the height, rounded to the nearest foot, of maple trees from two different tree farms.
What does the standard deviation tell you about the trees at these farms?

Which box plot has an IQR of 10?

What effect does eliminating the lowest value, -6, from the data set have on the mean and median?

-6, 3, 3, 3, 3, 5, 6, 6, 8, 10

This lesson is from Illustrative Mathematics. Algebra 1, Unit 1, Lesson 15. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/1/1/15/index.html ; accessed 26/July/2021.

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