Unit 8, Lesson 11

Comparing Groups

Grade 7

11.1

Warm-up

What do you notice? What do you wonder?

A dot plot, gymnastics team, is labeled “height in inches”. — gymnastics team

A dot plot, volleyball team, is labeled “height in inches”. — volleyball team

11.2

Activity

How much taller is the volleyball team than the gymnastics team?
- Gymnastics team’s heights (in inches): 56, 59, 60, 62, 62, 63, 63, 63, 64, 64, 68, 69
- Volleyball team’s heights (in inches): 72, 75, 76, 76, 78, 79, 79, 80, 80, 81, 81, 81
Make dot plots to compare the heights of the tennis and badminton teams.
- Tennis team’s heights (in inches): 66, 67, 69, 70, 71, 73, 73, 74, 75, 75, 76
- 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 are taller than the badminton team. Lin disagrees. Do you agree with either of them? Explain or show your reasoning.

11.3

Activity

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

11.4

Activity

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

A dot plot labeled “A.” The numbers 0 through 7, in increments of 0 point 5, are indicated. — A

A dot plot labeled “B.” The numbers 0 through 7, in increments of 0 point 5, are indicated. The data are as follows: 0 point 5, 1 dot. 0 point 7 5, 1 dot. 1 point 5, 2 dots. 2, 1 dot. 3 point 7 5, 1 dot. 4 point 2 5, 1 dot. 5, 1 dot. — B

A dot plot labeled “C.” The numbers 0 through 7, in increments of 0 point 5, are indicated. The data are as follows: 3 point 5, 3 dots. 4, 3 dots. 4 point 25, 1 dot. 4 point 5, 1 dot. — C

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.
One of these data sets has a mean absolute deviation (MAD) 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.
Do you think the three groups are very different or not? Be prepared to explain your reasoning.
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?

Student Lesson Summary

Comparing two individuals is fairly straightforward. The question, “Which dog is taller?” can be answered by measuring the heights of two dogs and comparing them directly. Comparing two groups can be more challenging. What does it mean for beagle dogs to generally be taller than pug dogs?

To compare two groups, we use the distribution of values for the two groups. Most importantly, a measure of center (usually mean or median) and its associated measure of variability (usually mean absolute deviation or interquartile range) can help determine the differences between groups.

For example, if the average height of pugs in a dog show is 11 inches, and the average height of the beagles in the dog show is 15 inches, it seems that the beagles are generally taller. On the other hand, if the mean absolute deviation (MAD) is 3 inches, it would not be unreasonable to find a beagle that is 11 inches tall or a pug that is 14 inches tall. Therefore the heights of the two dog breeds may not be very different from one another.

The mean is one way to measure the center of a data set. It can be thought of as a balance point. To find the mean, add all the numbers in the data set. Then divide by how many numbers there are.

Data set: 7, 9, 12, 13, 14
Add values:
Divide by number of values:

The mean is 11. So, the typical travel time is 11 minutes.

The mean absolute deviation (MAD) is one way to measure how spread out a data set is. To find the MAD, find the distance between each data value and the mean. Add all the distances. Then divide by how many distances there are.

Data set: 7, 9, 12, 13, 14
Add distances:
Divide by number of distances:

The MAD is 2.4. So, these travel times are typically 2.4 minutes away from the mean of 11 minutes.

<p>data set for travel time in minutes with a mean of 11 minutes</p>

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 of value.

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 2 numbers in the middle. The median is the average of these 2 numbers. , and . The median is 7.

Navigation

Gradeband

Course

Unit

Lesson

Settings

Language

Audience

Assessment Access

Lesson | Loading...

Settings

Language

Audience

Assessment Access

Comparing Groups

Warm-up

Activity

Activity

Activity

Student Lesson Summary