1. How can you describe how far apart the responses are from the center in a data set? In this lesson you will learn how to describe the distribution of data by using the mean absolute deviation. MAD

2. 0 2 46 8 10 12 14 16 1820 22 Number of Books First Let’s Review Reading a dot plot How many books did 8 th graders at Lilburn Middle School read this summer?

3. 0 + 0 + 0 + 1 + 1 + 1 + 2 + 2 + 3 + 4 + 5 + 5 = 24 24 ÷ 12 = 2 0 1 23 4 5 Let’s Review The mean of a set of data is the average. How many siblings do you have?

4. Let’s Review Absolute value is the distance any number is from 0. | 3 | = 3 | -5 | = 5

5. Variability: Describes how the spread out or closely clustered the data set is. There are 3 ways to determine the spread: 1.Range 2.Interquartile Range 3.Mean Absolute Deviation

6. A Common Mistake The mean and mean absolute deviation are often confused because they both include the word, “mean.” Mean Mean absolute deviation

7. Mean Absolute Deviation (MAD): MAD- is the average distance between each data value and the mean.

8. 00011122340001112234 5 + 5 24÷12 = 2 Find the mean absolute deviation. How many siblings do you have? 0 1 2 3 4 5 Step 1: Find the mean

9. 222222 012345 Find the mean absolute deviation. How many siblings do you have? 1 2 111111 3333 0000 222111222111 0000 123123 3 Step 2 : Find the distance between the mean and the values | |

10. Stay positive! 3 6 9 12 15 3 2 lllllllllllllll 6 5 MAD= 6+3+2+5 4 =4 Remember:

11. 222222 Find the mean absolute deviation. How many siblings do you have? 0 1 2 3 4 5 3333 1 0 1 2 1 0 1 2221110022211100 123123 +3 18 18 ÷ 12 = 1.5 of Step 3: Find the average the distance.

12. You can also informally compare two populations by using the mean absolute deviation (MAD).

13. NFLTeamPenalties NFC Mean 92 Distance AFC Mean 84 Distance 86 92 – 86=6 8084-80=4 59 92-59=33 6784-67=17 137 137- 92=45 114114- 84=30 68 92-68=24 7684-76=8 113 113- 92=21 9494-84=10 77 92-77=15 7884-78=6 104 104- 92=12 8284-82=2 NFC MAD: 6+33+45+24+21+15+12 7 = 22.2 AFC MAD: 4+17+30+8+10+6+2 7 =11 Comparison The mean absolute deviation for the NFC is greater than the mean absolute deviation for the AFC. That means the data for penalties for the AFC are closer together. The NFC has a farther spread.

14. Guided Practice – Try these two problems Find the range and mean absolute deviation of this data.

15. Find the mean absolute deviation. How many pets do you have? 0, 1, 5, 0, 3, 1, 0, 2, 2, 6

16. 2 4 6 8 1012 Number of CDs owned Race it!!!! Find the range and mean absolute deviation of this data.

17. What is the mean absolute deviation of the data set? How many books did you read this summer? 3, 5, 2, 3, 3, 1, 4, 4, 3, 2

18. What is the mean absolute deviation of the data set and what does it mean? How many pairs of shoes do you own? 3, 7, 2, 8, 3, 19, 5, 9

19. Find the range and mean absolute deviation of this data. How many pairs of shoes do 8 th graders at Lilburn Middle School own?