Mean Absolute Deviation (MAD) Statistics 7.SP.3, 7.SP.4
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1 Mean Absolute Deviation (MAD) Statistics 7.SP.3, 7.SP.4
2 Review
3 Let s Begin The Mean Absolute Deviation (MAD) of a set of data. is the average distance between each data value and the mean. 1. Find the mean. 2. Find the distance between data and the mean. 3. Find the average of the differences
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5 Lesson
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8 Mean Absolute Deviation CELL PHONES The table shows the number of contacts eight friends have stored in each of their cell phones. 1. Find the mean of the data. 2. What is the difference between the data value 52 and the mean? 3. Which value is farthest from the mean? 4. Overall, are the data values close to the mean or far away from the mean? Explain. Another way to describe the variability of a set of data is to use its mean absolute deviation. The mean absolute deviation of a set of data is the average distance between each data value and the mean.
9 Key Concept
10 The mean number of contacts stored and the distance each data value is from the mean is shown below. Each data value is represented by an. The average of the distances is _ _ _ , or So, the mean absolute deviation is The average distance between each data value and the mean is 3.75 contacts.
11 Real-World Example
12 Step 2 Find the absolute value of the differences between each value in the data set and the mean.
13 Step 3 Find the average of the absolute values of the differences between each value in the data set and the mean. What do we add together? The mean absolute deviation is This means that the average distance each data value is from the mean is 12.5 miles per hour
14 Check Your Progress! a. BIRDS The table shows the maximum flying speeds of the ten fastest birds worldwide. Find the mean absolute deviation of the set of data. Round to the nearest hundredth. Describe what the mean absolute deviation represents. You can compare the mean absolute deviations for two data sets. A data set with a smaller mean absolute deviation has data values that are closer to the mean than a data set with a greater mean absolute deviation.
15 Real-World Example Compare Variation BASEBALL The top five salaries and the bottom five salaries for the 2010 New York Yankees are shown in the table below. Salaries are in millions of dollars and are rounded to the nearest hundredth.
16 a. Find the mean absolute deviation for each set of data. Round to the nearest hundredth. What are we going to do? Top Five Salaries Find the mean. The mean is about $23.40 million
17 Find the mean absolute deviation by finding the absolute values of the differences between each data value and the mean. Then average the differences. The mean absolute deviation is about $4.19 million.
18 Bottom Five Salaries Find the mean. The mean is about $0.43 million.
19 Find the mean absolute deviation by finding the absolute values of the differences between each data value and the mean. Then average the differences. How do we do that? The mean absolute deviation is about $0.01 million.
20 Math Literacy b. Write a few sentences comparing their variation. What can we say? The mean absolute deviation for the bottom five salaries is much less than that for the top five salaries. The data for the bottom five salaries are closer together than the data for the top five salaries.
21 Check Your Progress! b. MOVIES The table shows the running time in minutes for two kinds of movies. Find the mean absolute deviation for each set of data. Round to the nearest hundredth. Then write a few sentences comparing their variation.
22 Check Your Understanding Example 1 Find the mean absolute deviation for each set of data. Round to the nearest hundredth if necessary. Then describe what the mean absolute deviation represents WATER PARKS The table shows the height of waterslides at two different water parks. Find the mean absolute deviation for each set of data. Round to the nearest hundredth. Then write a few sentences comparing their variation.
23 Example 2. BASKETBALL The table shows the number of points scored each game for two different basketball teams. Find the mean absolute deviation for each set of data. Round to the nearest hundredth if necessary. Then write a few sentences comparing their variation.
24 Vocabulary What does the word deviate mean? How can it help you remember what the mean absolute deviation refers to? How does the word absolute help you to remember how to calculate the mean absolute deviation?
25 Test Practice The table shows the prices for parking at various beaches along the same coastline. Which of the following is the mean absolute deviation for the set of data? A. $0.25 B. $0.66 C. $2.50 D. $2.55
26 Test Practice Which of the following is true concerning the mean absolute deviation of a set of data? F. It describes the variation of the data values around the median. G. It describes the absolute value of the mean. H. It describes the average distance between each data value and the mean. I. It describes the variation of the data values around the mode.
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