Unit 8, Lesson 12
Using Mean and MAD to Make Comparisons
Grade 6
12.2
Activity
-
Andre and Noah joined Elena, Jada, and Lin in recording their basketball scores. They all record their scores in the same way: the number of baskets made out of 10 attempts. Each person collects 12 data points.
- Andre’s mean number of baskets is 5.25, and his MAD is 2.6.
- Noah’s mean number of baskets is also 5.25, but his MAD is 1.
Here are two dot plots that represent the two data sets. The triangle indicates the location of the mean.
Data set A A dot plot, data set A, number of baskets made, 0 to 10 by ones. Beginning at 3, number of dots above each increment is 1, 2, 5, 2, 1, 1, triangle approximately 5 point 2.Data set B A dot plot, data set B, number of baskets made, 0 to 10 by ones. Beginning at 1, number of dots above each increment is 1, 2, 1, 2, 0, 1, 1, 2, 2, triangle approximately 5 point 2- Without calculating, decide which dot plot represents Andre’s data and which represents Noah’s. Explain how you know.
- If you are the captain of a basketball team and can use 1 more player on your team, do you choose Andre or Noah? Explain your reasoning.
- An eighth-grade student decides to join Andre and Noah and keeps track of his scores. His data set is shown here. The mean number of baskets he makes is 6.
eighth‐grade
student6 5 4 7 6 5 7 8 5 6 5 8 distance
from 6- Calculate the MAD. Show your reasoning.
-
Draw a dot plot to represent his data and mark the location of the mean with a triangle.
- Compare the eighth-grade student’s mean and MAD to Noah’s mean and MAD. What do you notice?
- Compare their dot plots. What do you notice about the distributions?
- What can you say about the two players’ shooting accuracy and consistency?
12.3
Activity
The mean age of swimmers on a 1984 national swim team is 18.2 years and the MAD is 2.2 years. The mean age of the swimmers on the 2016 team is 22.8 years, and the MAD is 3 years.
- How has the average age of the swimmers on the national team changed from 1984 to 2016? Explain your reasoning.
- Are the swimmers on the 1984 team closer in age to one another than the swimmers on the 2016 team are to one another? Explain your reasoning.
-
Here are dot plots showing the ages of the swimmers on the national swim teams in 1984 and in 2016. Use them to make two other comments about how the team has changed over the years.
A dot plot, 1984, age of swimmers in years, 14 to 32 by twos. Beginning with 15 in increments of 1, the number of dots above each increment is 2, 2, 1, 2, 4, 1, 1, 0, 1.
A dot plot, 2016, age of swimmers in years, 14 to 32 by twos. Beginning with 19 increments of 1, the number of dots above each increment is 3, 3, 3, 3, 1, 2, 4, 1, 0, 0, 1, 1.
Student Lesson Summary
A measure of center, such as the mean, gives a sense of what is typical for a set of data. A measure of variability, such as the MAD, gives a sense of how consistent the data are. Together, these values can be used to compare data sets.
Sometimes two distributions have different means but the same MAD.
Pugs and beagles are two different dog breeds. The dot plot shows two sets of weight data—one for pugs and the other for beagles.
A dot plot for two sets of data: "pug weights in kilograms" and "beagle weights in kilograms". The numbers 6 through 11 are indicated and there are tick marks midway between each indicated number. There are also two triangles indicated. The first triangle is at 7 kilograms with a horizontal line drawn below the triangle that begins at 6.5 and ends at 7.5 kilograms. The second triangle is indicated at 10 kilograms with a horizontal line drawn below the triangle that begins at 9.5 and ends at 10.5 kilograms. The data for "pug weights in kilograms" are as follows: 6 kilograms, 1 dot. 6.2 kilograms, 2 dots. 6.4 kilograms, 2 dots. 6.6 kilograms, 2 dots. 6.8 kilograms, 2 dots. 7 kilograms, 3 dots. 7.2 kilograms, 3 dots. 7.4 kilograms, 1 dot. 7.6 kilograms, 2 dots. 7.8 kilograms, 1 dot. 8 kilograms, 1 dot. The data for "beagle weights in kilograms" are as follows: 9 kilograms, 1 x. 9.2 kilograms, 2 x's. 9.4 kilograms, 1 x. 9.6 kilograms, 3 x's. 9.8 kilograms, 1 x. 10 kilograms, 3 x's. 10.2 kilograms, 3 x's. 10.4 kilograms, 1 x. 10.6 kilograms, 2 x's. 10.8 kilograms, 2 x's. 11 kilograms, 1 x.
- The mean weight for pugs is 7 kilograms, and the MAD is 0.5 kilogram.
- The mean weight for beagles is 10 kilograms, and the MAD is 0.5 kilogram.
We can say that, in general, the beagles are heavier than the pugs. A typical weight for the beagles in this group is about 3 kilograms heavier than a typical weight for the pugs.
The variability of pug weights, however, is about the same as the variability of beagle weights. In other words, the weights of pugs and the weights of beagles are equally spread out.
None