1. MEAN ABSOLUTE DEVIATION

2. Vocabulary  Deviation: The distance that two points are separated from each other.  Deviation from the mean : How far the data point is from the mean. To find this distance, subtract the two values (the data point and the mean).  Mean absolute deviation (MAD) : the average distance of all the data points from their mean. This will tell you how spread out your data is around the mean.

3. Larger MAD- more spread out. Smaller MAD- less spread out.

4. Example 1: You and your friends have just measured the heights of your dogs (in millimeters): The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm You want to know how far from the mean each dog is, on average …so you need to find the Mean Absolute Deviation

5. Meanxx - Mean 394600206 39447076 394170-224 39443036 394300-94 Mean = 600 + 470 + 170 + 430 + 300 = 1970 = 394 55 Step 4: Find the Mean Absolute Deviation = = 127.2 Step 1: Find the Mean Step 2: Find the Deviations Step 3: Find the Absolute Deviations Meanxx - Mean|x-Mean| 394600206 | 206 | 39447076 |76||76| 394170-224 | -224 | 39443036 | 36 | 394300-94 | -94 | 636

6. Example 2: Calculate the Mean Absolute Deviation (MAD) of the following test scores 87, 94, 72, 65, 97, 77 Column 1Column 2Column 3Column 4 DataMeanDifferenceAbsolute Value Sum Count MAD 87 94 72 65 97 77

7. 87, 94, 72, 65, 97, 77 Column 1Column 2Column 3Column 4 DataMeanDifferenceAbsolute Value Sum Count MAD 87 94 72 65 97 77 87 94 72 65 97 + 77 492 492 ÷ 6 = 82 Step 1: Calculate the mean of the data and write that in each cell of column 2. 82

8. 87, 94, 72, 65, 97, 77 Step 2: Subtract column 1 from column 2 and write the difference in column 3. Column 1Column 2Column 3Column 4 DataMeanDifferenceAbsolute Value Sum Count MAD 87 94 72 65 97 77 82 82 – 87 = -5 82 – 94 = -12 82 – 72 = 10 82 – 65 = 17 82– 97 = -15 82 – 77 = 5 -5 -12 10 17 -15 5

9. 87, 94, 72, 65, 97, 77 Step 5: Rewrite all the numbers from column 3 as positive numbers in column 4 (Absolute Value). Column 1Column 2Column 3Column 4 DataMeanDifferenceAbsolute Value Sum Count MAD 87 94 72 65 97 77 82 -5 -12 10 17 -15 5 12 10 17 15 5

10. 87, 94, 72, 65, 97, 77 Step 4: Calculate the mean of the data in column 4, and you’re done! This is the MAD. Column 1Column 2Column 3Column 4 DataMeanDifferenceAbsolute Value Sum Count MAD 87 94 72 65 97 77 82 -5 -12 10 17 -15 5 12 10 17 15 5 64÷ 6 = 10.7 64 6 10.7

11. Using MAD to Compare Data Sets

12. Basketball team … and the basketball team

13. Field Hockey MAD: Basketball MAD: 64.76 3.58 Field Hockey Mean: 1.75 Basketball Mean: 72.5

14. 4 /

15. Field Hockey player because they have three athlete that are 65 inches and basketball only has one athlete that is 65 inches.

16. PRACTICE