SIGMA NOTATION MEAN ABSOLUTE DEVIATION Sigma Summation Notation

SIGMA NOTATION & MEAN ABSOLUTE DEVIATION

Sigma (Summation) Notation Consider the heights of the Jones family members: Mom 65” Dad 72” Bobby 70” Joey 58” Fluffy 22” Spot 28”

Let’s look at those heights as a “set”. � S Is the capital Greek letter “sigma”

Mean (m) in Summation Notation �

Deviation – how far is a certain piece of data from the mean? So here is our family… Here is the mean of 52. 5” that we calculated earlier. Since no single family member is exactly 52. 5” tall, all of them deviate from the mean. Some more than others…

Mean Absolute Deviation & Standard Deviation � These are 2 different statistics to spread (dispersion) of describe the ____ the data. � Mean Absolute Deviation (MAD) – is often preferred because it is less affected by _____. outliers � Standard Deviation (s) - A more traditional way of indicating dispersion.

Calculating Mean Absolute Deviation (MAD) Step 1: Find the mean m of the data. 52. 5” Step 2: Subtract the mean from each data element. 65 -52. 5” 12. 5 72 -52. 5 19. 5 70 -52. 5 17. 5 58 -52. 5 5. 5 22 -52. 5 -30. 5 28 -52. 5 -24. 5

Calculating Mean Absolute Deviation (MAD) 12. 5 19. 5 17. 5 5. 5 -30. 5 -24. 5 Step 3: Take the absolute value of the values found in Step 2 12. 5 19. 5 17. 5 5. 5 30. 5 24. 5 Step 4: Sum those numbers. 12. 5 + 19. 5 + 17. 5 + 5. 5 + 30. 5 + 24. 5 = 110 MAD = 18. 3

Now that we have it, what is it for? � We can use the MAD (18. 3), to determine which of our data (family members) are unusually tall or unusually small. The mean was 52. 5”, so anyone taller than: 52. 5 + 18. 3 70. 8” or smaller than : 52. 5 – 18. 3 34. 2” is “unusual”. So, Dad (72”), Fluffy (22”) and Spot (28”) have unusual heights for the Jones family.