Mean Absolute Deviation (MAD) SWBAT use mean absolute deviation to analyze variability in data.

Do Now Make a box and whisker plot using the following data set: 2, 2, 3, 5, 6, 7, 7, 7, 9 Ariel got the following test scores: 79, 84, 80, 89. What is her test average? 332 B) 83 C) 82 D) 10 3. What is an outlier? Provide an example.

Mean Absolute Deviation The mean absolute deviation describes variability in the data. Specifically, it is the average distance from each data value and the mean.

Visual Representation MEAN X X X X X X X X 13 15 17 19 21 22 23 24 25 26

Finding MAD Find the mean Find the distance between each data value and the mean. That is, find the absolute value of the difference between each data value and the mean. This means we are going to subtract Find the average of those differences.

Example The following table shows the amount of pairs of shoes owned by 8 sixth graders. Step one: Find the mean the mean of this data is 19 12 24 18 17 22 19 20 26

MEAN X X X X X X X X 13 15 17 19 21 22 23 24 25 26 19 – 12 = 7 19 - |20| = 1 19 – 17 = 2 19 - | 22| = 3 19 - 18 = 1 19 - |24| = 5 19 - 19 = 0 19 - |26| = 7

The mean absolute deviation of this data set is 3.25 26 7 + 2 + 1 + 0 + 1 + 3 + 5 + 7 = 8 8 The mean absolute deviation of this data set is 3.25 Since our mean absolute deviation is a smaller number, we can assume that our data is consistent (or closer together in value). The closer the mean absolute deviation is to 0, the more consistent the data is.

Your turn….

Did you find…. Speeds of Top Ten Fastest Birds (mph) Mean of data = 78.6 Distances from the data = 9.4, 1.6, 13.6, 8.6, 27.4, 13.6, 6.6, 16.4, 1.4, 10.6 Mean of distances from the data = 10.92 Describe what it represents = Data has variability or it is inconsistent. Large spread

Exit Ticket 1. Explain in words the steps to find the mean absolute deviation of a data set. 2. How does the mean absolute deviation describe a data set? 3. Find the mean absolute deviation of this data set and tell how it describes the data