1 of 23

Unit 8

Comparing Groups

Probability and Sampling

Lesson 11

Expressions and Equations

​

​

7

2 of 23

Let’s compare two groups.

Unit 8 ● Lesson 11

Learning

Goal

7

3 of 23

Comparing Heights

Unit 8 ● Lesson 11 ● Activity 1

What do you notice? What do you wonder?

7

Warm-up: Notice and Wonder

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

4 of 23

MAD - Mean Absolute Deviation

Unit 8 ● Lesson 11

Which data set will have a larger MAD? How can you tell?

MAD- MEAN ABSOLUTE DEVIATION �The Mean Absolute Deviation (MAD) tells you, �on average, how far away each number in a set of data is from the average (mean) of that set.

​

7

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

5 of 23

MAD - Mean Absolute Deviation

7

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

6 of 23

MAD - Mean Absolute Deviation

7

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

7 of 23

More Team Heights

Unit 8 ● Lesson 11 ● Activity 2

  1. How much taller is the volleyball team than the gymnastics team?
  2. Gymnastics team’s heights (in inches) : 56, 59, 60, 62, 62, 63, 63, 63, 64, 64, 68, 69
  3. Volleyball team’s heights (in inches): 72, 75, 76, 76, 78, 79, 79, 80, 80, 81, 81, 81
  4. Make dot plots to compare the heights of the tennis and badminton teams.
  5. Tennis team’s heights (in inches): 66, 67, 69, 70, 71, 73, 73, 74, 75, 75, 76
  6. Badminton team’s heights (in inches): 62, 62, 65, 66, 68, 71, 73

What do you notice about your dot plots?

  • Elena says the members of the tennis team were taller than the badminton team. Lin disagrees. Do you agree with either of them? Explain or show your reasoning.

​

​

7

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

8 of 23

More Team Heights

Unit 8 ● Lesson 11 ● Activity 2

  • Think about the distribution of the data shown in the dot plots. What would you say about the:
    • shape of the data?
    • center of the data?
    • spread of the data?
  • How might the following measures from your previous course students of data and distributions help you to compare the data sets of two groups?
    • mean
    • mean absolute deviation (MAD)
    • median
    • interquartile range (IQR)
  • How might data distributions and data measures help us compare groups of things?

​

​

7

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

9 of 23

Family Heights

Unit 8 ● Lesson 11 ● Activity 3

  • Two groups of adults have mean weights that are different by 10 pounds. Are the two groups very different in weight?
  • Two groups of 8 year olds have weights that are different by 10 pounds. Are the two groups very different in weight?
  • Two groups of birds have weights that are different by 3.2 ounces (0.2 pounds). Are the two groups very different in weight?

7

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

10 of 23

Family Heights

Unit 8 ● Lesson 11 ● Activity 3

Compare the heights of these two families. Explain or show your reasoning.

  • The heights (in inches) of Noah’s family members: �28, 39, 41, 52, 63, 66, 71
  • The heights (in inches) of Jada’s family members: �49, 60, 68, 70, 71, 73, 77

​

​

7

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

11 of 23

Family Heights

Unit 8 ● Lesson 11 ● Activity 3

  • How can we use the differences of the means and mean absolute deviation (MAD) to compare groups?
  • If the MAD is different for each data set, which one do you use?

7

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

12 of 23

Track Length

Unit 8 ● Lesson 11 ● Activity 4

Here are three dot plots that represent the lengths, in minutes, of songs on different albums.

​

​

​

​

​

​

​

​

​

​

  1. One of these data sets has a mean of 5.57 minutes and another has a mean of 3.91 minutes.
    1. Which dot plot shows each of these data sets?
    2. Calculate the mean for the data set on the other dot plot.

​

​

​

7

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

13 of 23

Track Length

Unit 8 ● Lesson 11 ● Activity 4

  1. One of these data sets has a mean absolute deviation of 0.30 and another has a MAD of 0.44.
    1. Which dot plot shows each of these data sets?
    2. Calculate the MAD for the other data set.
  2. Do you think the three groups are very different or not? Be prepared to explain your reasoning.
  3. A fourth album has a mean length of 8 minutes with a mean absolute deviation of 1.2. Is this data set very different from each of the others?

7

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

14 of 23

Track Length

Unit 8 ● Lesson 11 ● Activity 4

7

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

15 of 23

Comparing Groups

Unit 8 ● Lesson 11

  • What does a dot plot tell you?
  • What are some measures of center, and how are they calculated?
  • Why is a measure of center useful for comparing two groups?
  • Why is a measure of variability also needed when comparing two groups?
  • What is the general rule we will use to determine whether two groups have a large difference or not?

7

Lesson Synthesis

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

16 of 23

Unit 8 ● Lesson 11

  • I can calculate the difference between two means as a multiple of the mean absolute deviation.
  • When looking at a pair of dot plots, I can determine whether the distributions are very different or have a lot of overlap.

Learning

Targets

7

17 of 23

Prices of Homes

Unit 8 ● Lesson 11 ● Activity 4

Noah's parents are interested in moving to another part of town. They look up all the prices of the homes for sale and record them in thousands of dollars.

neighborhood 1

80 55 80 120 60 90 60 80 55 70

neighborhood 2

110 120 160 110 100 110 140 150 120 120

​

​

​

​

​

​

Find the mean and MAD for each of the neighborhoods. Then decide whether the two groups are very different or not.

​

7

Cool-down

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

18 of 23

Word:

Mean

​

Definition:

The mean is one way to measure the center of a data set. It is commonly known as the average.

Example:

​

To find the mean, add up all the numbers in the data set. Then, divide by how many numbers there are.

​

For example, for the data set �7, 9, 12, 13, 14:

​

​

​

19 of 23

Word:

Median

​

Definition:

The median is one way to measure the center of a data set. It is the middle number when the data set is listed in order.

Example:

​

For the data set 7, 9, 12, 13, 14, the median is 12.�

​

For the data set 3, 5, 6, 8, 11, 12, there are two numbers in the middle. The median is the average of these two numbers. The median is 7.

20 of 23

Word:

Mode

​

Definition:

The mode is the value that occurs the most in a data set.

Example:

​

For example, for the data set

5, 7, 8, 10, 10, 11:

​

The mode is 10.

21 of 23

Word:

Range

​

Definition:

The difference between the largest and smallest values in a data set is called the range.

Example:

​

Example: In the data set

2, 3, 9, 5, 8:

​

the lowest value is 2, and the highest is 9.

9 - 2 = (7)

​

The range is 7.

22 of 23

Word:

Mean Absolute Deviation (MAD)�

Definition:

The mean absolute deviation is one way to measure how spread out a data set is.

Example:

​

For example, for the data set 7, 9, 12, 13, 14, the MAD is 2.4.

​

​

​

​

​

To find the MAD, add up the distance between each data point and the mean. Then, divide by how many numbers there are.�

4 + 2 + 1 + 2 + 3 = 12

​

23 of 23

Lesson Video

SLIDESMANIA.COM