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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 First Let’s Review Reading a dot plot How many books did 8th graders at Lilburn Middle School read this summer? 0 2 4 6 8 10 12 Number of Books 14 16 18 20 22 Let’s Review The mean of a set of data is the average. How many siblings do you have? 0 1 2 3 4 5 0 + 0 + 0 + 1 + 1 + 1 + 2 + 2 + 3 + 4 + 5 + 5 = 24 24 ÷ 12 = 2 Let’s Review Absolute value is the distance any number is from 0. |-5| =5 |3| =3 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 A Common Mistake The mean and mean absolute deviation are often confused because they both include the word, “mean.” Mean Mean absolute deviation Mean Absolute Deviation (MAD): MAD- is the average distance between each data value and the mean. Find the mean absolute deviation. 0 0 How many siblings do you have? 0 1 1 1 2 0 1 2 3 4 5 2 3 Step 1: Find the mean 4 5 +5 24÷12 = 2 2 2 2 1 1 1 0 0 1 2 3 3 Find the mean absolute deviation. How many siblings do you have? 0 1 2 2 2 2 1 1 1 3 0 0 1 2 4 5 3 3 Step 2 : Find the distance between the mean and the values | | Remember: Stay positive! 6 5 3 2 lllllllllllllll 3 6 9 12 15 6+3+2+5 MAD= =4 4 Find the mean absolute deviation. 2 2 How many siblings do you have? 2 1 1 1 0 0 1 2 3 4 5 0 1 3 2 1 0 1 2 3 2 2 1 0 2 1 3 +3 Step 3: Find the average 18 18 ÷ 12 = 1.5 the distance. of You can also informally compare two populations by using the mean absolute deviation (MAD). NFLTeamPenalties NFC Mean 92 NFC MAD: 6+33+45+24+21+15+12 7 Distance AFC Mean 84 Distance 86 92 – 86=6 80 84-80=4 AFC MAD: 59 92-59=33 67 84-67=17 137 13792=45 114 11484=30 4+17+30+8+10+6+2 =11 7 68 92-68=24 76 84-76=8 113 11392=21 94 94-84=10 77 92-77=15 78 84-78=6 104 10492=12 82 84-82=2 = 22.2 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. Guided Practice – Try these two problems Find the range and mean absolute deviation of this data. Find the mean absolute deviation. How many pets do you have? 0, 1, 5, 0, 3, 1, 0, 2, 2, 6 Race it!!!! Find the range and mean absolute deviation of this data. 2 4 6 8 Number of CDs owned 10 12 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 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 Find the range and mean absolute deviation of this data. How many pairs of shoes do 8th graders at Lilburn Middle School own?