mean absolute deviation (mad) swbat use mean absolute deviation to analyze variability in data

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

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Page 1: Mean Absolute Deviation (MAD) SWBAT use mean absolute deviation to analyze variability in data

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

Page 2: Mean Absolute Deviation (MAD) SWBAT use mean absolute deviation to analyze variability in data

Do Now1.Make a box and whisker plot using the following

data set: 2, 2, 3, 5, 6, 7, 7, 7, 9

2.Ariel got the following test scores: 79, 84, 80, 89. What is her test average?

A)332 B) 83 C) 82 D) 10

3. What is an outlier? Provide an example.

Page 3: Mean Absolute Deviation (MAD) SWBAT use mean absolute deviation to analyze variability in data

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.

Page 4: Mean Absolute Deviation (MAD) SWBAT use mean absolute deviation to analyze variability in data

Visual Representation

12 13

14 15 16 17 18 19 20 21 22 23 24

25 26

X XX XX XX

MEAN

X

Page 5: Mean Absolute Deviation (MAD) SWBAT use mean absolute deviation to analyze variability in data

Finding MAD1. Find the mean

2. 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.1.This means we are going to subtract

3. Find the average of those differences.

Page 6: Mean Absolute Deviation (MAD) SWBAT use mean absolute deviation to analyze variability in data

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

Page 7: Mean Absolute Deviation (MAD) SWBAT use mean absolute deviation to analyze variability in data

12 13 14 15 16 17 18 19 20 21 22 23 24

25 26

X XX XXX X

MEAN

19 – 12 = 719 – 17 = 2

19 - 18 = 1

19 - 19 = 0

19 - |20| = 1

19 - | 22| = 3

X

19 - |24| = 5

19 - |26| = 7

Page 8: Mean Absolute Deviation (MAD) SWBAT use mean absolute deviation to analyze variability in data

7 + 2 + 1 + 0 + 1 +

3 + 5 +

7 =

8

26

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.

Page 9: Mean Absolute Deviation (MAD) SWBAT use mean absolute deviation to analyze variability in data

Your turn….

Page 10: Mean Absolute Deviation (MAD) SWBAT use mean absolute deviation to analyze variability in data

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

Page 11: Mean Absolute Deviation (MAD) SWBAT use mean absolute deviation to analyze variability in data

Exit Ticket1. 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

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