1. Core Focus on Ratios, Rates & Statistics
Lesson 4.7
Core Focus on Ratios, Rates & Statistics
Mean Absolute Deviation

2. Warm-Up
Use the following data set: 20, 13, 9, 15, 34, 17, What are the mean, median and mode of the data set? 2. Is there an outlier in the data set? Explain. 3. Which measure of center best describes the data set? Why?
Mean = 17; median = 15; no mode
Yes, 34 is far higher than the other values.
Median; there is an outlier and no mode, so the median would best describe the data.

3. Mean Absolute Deviation
Lesson 4.7
Mean Absolute Deviation
Find and use the mean absolute deviation to describe the spread of data.

4. Vocabulary
Mean Absolute Deviation The average distance from the mean for all numbers in a data set. Good to Know!  The smaller the mean absolute deviation, the less spread there is in the data set. It means the numbers are all close to the mean.  When the mean absolute deviation is larger, the numbers are more spread out from the mean and there is greater variability in the numbers in the data set.

5. Explore! Mercury’s Rising
Jeron and Gary are pen pals living across the United States from each other; Jeron lives in San Francisco, CA and Gary lives in Boston, MA. Gary wondered how the temperatures in the two cities compared to each other, so he looked up the average monthly high temperatures for each city. These temperatures are listed below:
San Francisco: 57, 57, 60, 62, 63, 63, 64, 67, 67, 68, 69, 70
Boston: 36, 39, 41, 45, 52, 56, 61, 66, 72, 76, 80, 82
Source: weather.com
Step 1 How do the highest and lowest average monthly temperatures in each city compare to each other?
Step 2 Find the mean temperatures for each city. Round to the nearest whole degree. Your rounded mean for San Francisco should match the value in the table in Step 3.

6. Explore! Mercury’s Rising
Step 3 Copy the Boston table below and write the mean value from Step 2 in the blank.

7. Explore! Mercury’s Rising
Step 4 Find the “Deviations from the Mean” for Boston. Subtract the mean for Boston from each value in the Boston table (Data Value – Mean). Some of these values should be negative. Record these numbers in the “Deviation from Mean” column for Boston. See the San Francisco table as an example.
Step 5 Find the “Absolute Deviation” for each value in the Boston table. The absolute deviation is the absolute value of the deviation in the second column. Absolute deviations are always positive.
Step 6 Find the sum of all the “Absolute Deviations” in the Boston table. Finally, divide this sum by the number of data values (12) to find the Mean Absolute Deviation. Round to two decimal places.
Step 7 How does the mean absolute deviation of San Francisco’s temperatures compare to that of Boston? What does this tell you about the variations in the temperatures of the two cities?

8. How to Find the Mean Absolute Deviation of a Data Set
1. Find the mean of the data set. 2. Find the deviation from the mean for each data value. Data Value − Mean 3. Find the absolute deviation for each data value. These are always positive. 4. Find the mean of the absolute deviations.

9. Example 1
Bonnie surveyed six classmates about the number of hours of TV they watched each week. 6, 7.5, 4, 10, 13.5, 7 a. What is the mean absolute deviation of the data set? Find the mean of the data set. Organize the work in a table. Write the data values from Bonnie’s survey in order to keep the information more organized. For each value, find the deviation from the mean and the absolute deviation.
Avg. Hours TV Watching
Deviation from Mean
Absolute Deviation 4
4 – 8 = –4 6
6 – 8 = –2 7
7 – 8 = –1
7.5
7.5 – 8 = –0.5 10
10 – 8 = 2
13.5
13.5 – 8 = 5.5 4 2 1
0.5 2
5.5

10. Example 1 Continued…
Bonnie surveyed six classmates about the number of hours of TV they watched each week. 6, 7.5, 4, 10, 13.5, 7 a. What is the mean absolute deviation of the data set? Find the mean of the absolute deviations. The mean absolute deviation is 2.5.

11. Example 1 Continued…
Bonnie surveyed six classmates about the number of hours of TV they watched each week. 6, 7.5, 4, 10, 13.5, 7 b. What does the mean absolute deviation value mean in terms of the data set? On average, the number of hours students watch TV per week is within about 2.5 hours of the mean (8 hours).

12. Communication Prompt
Explain in your own words how to find the mean absolute deviation of a data set.

13. Exit Problem
Rachel’s average javelin throw is 165 feet with a mean absolute deviation of 8.5 feet. Hannah’s average javelin throw is 161 feet with a mean absolute deviation of 5 feet. Write two sentences explaining the meaning of these statistics.
Rachel usually throws within 8.5 of her average of 165 feet. Hannah usually throws within 5 feet of her average of 161 feet.