Copy - Variability, MAD, and Mean to Make Comparisons

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Variability, MAD, and Mean to Make Comparisons

Data Sets

• Elena
• 4 5 1 6 9 7 2 8 3 3 5 7

• Jada
• 2 4 5 4 6 6 4 7 3 4 8 7

• Lin
• 3 6 6 4 5 5 3 5 4 6 6 7

Scenario: Elena, Jada, and Lin like to play basketball near their homes. They practice shooting free throws. Each day, they take 10 shots and count how many baskets they make. They do this for 12 days. Their results are shown in data sets on the left.

Answer these questions:

• Did all three players shoot about the same overall?
• Did all three players shoot about the same every day, or was one more consistent?
• If you had to pick one player for your team based on these results, who would you choose?

Elena, Jada, and Lin are practicing basketball free throws. Each day, they take 10 shots and record how many baskets they make. They do this for 12 days. Their results are shown in the dot plots.

Mean Absolute Deviation (MAD)

One way to tell how spread out a data set is, is to see how far each number is from the mean (average). This distance is called the deviation. Distance is always a positive number. Look at the dot plot to see how far each data point is from the mean. Example: If the mean is 5 and a data point is 3, the distance is 2. So, the deviation is 2. The mean absolute deviation (MAD) tells us, on average, how far the data is from the mean. Steps to find MAD:

1. Find the distance from the mean for each data point.
2. Add all the distances together.
3. Divide by the total number of data points.

A larger MAD means the data is more spread out. A smaller MAD means the data is closer together.

Mean Absolute Deviation (MAD) is the average distance of the data values from the mean. Look at the table. The second row shows how far each number is from the mean of 5. To find the MAD: 1. Add all the distances from the mean. 2. Divide by the total number of data values (12). This means that, on average, the values are 2 baskets away from the mean.

MAD=

MAD=

1+0+4+1+4+2+3+3+2+2+0+2

12

24

12

=2

Below are the number of free throws out of 10 that Jada made over 12 days. The deviations from the mean has been found for you and entered into the table below.

Complete the table.

Andre and Noah joined the other players in tracking their basketball scores. Each player recorded how many baskets they made out of 10 shots for 12 days. Andre’s mean was 5.25, and his MAD was 2.6. Noah’s mean was also 5.25, but his MAD was 1. This shows that both players scored the same on average. The difference is how spread out their scores are. Andre’s scores changed more from day to day, while Noah’s scores stayed closer to the mean.

Complete the table.

Ten sixth-grade students in five different countries were asked about their travel times to their extracurricular activities. Their responses were organized into five data sets. The mean and MAD of each data set is shown in the table below.

Han recorded the number of pages that he read each day for five days. The number for each day is 25, 28, 32, 36, and 42. The mean number of pages he read per day was 32.6 pages.

In an archery competition, scores for each round are calculated by averaging the distances of 3 arrows from the center of the target. An archer has a mean distance of 1.6 inches and a MAD distance of 1.3 inches in the first round. In the second round, the archer's arrows are farther from the center but are more consistent.

The dot plots show the amounts of time that ten U.S. students and ten Australian students took to get to soccer practice.

Drag the correct number to the box.

Steps to find MAD:

1. Find the distance from the mean for each data point.
2. Add all the distances together.
3. Divide by the total number of data points.

Learners can:

• calculate the mean absolute deviation (MAD) for a data set and interpret what it tells you about the situation
• analyze by comparing and contrasting the means and mean absolute deviations of different distributions
• apply the understanding that “mean absolute deviation (MAD)” is a measure of variability, i.e., a single number summarizing how spread out the data set is

Steps to find MAD:

1. Find the distance from the mean for each data point.
2. Add all the distances together.
3. Divide by the total number of data points.

Steps to find MAD:

1. Find the distance from the mean for each data point.
2. Add all the distances together.
3. Divide by the total number of data points.

Steps to find MAD:

1. Find the distance from the mean for each data point.
2. Add all the distances together.
3. Divide by the total number of data points.

Drag the correct number to the box.