The standard deviation formula is given by S

The standard deviation formula is given by: S = Standard Deviation xi = each value of dataset UL = + 2 S LL = – 2 S x = with a bar over it is referred to as the mean N = the total number of data points ∑ (xi - mean)2 = The sum of (xi - mean)2 for all data points

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 10 20 30 15 15 10 15 55 20 20 15 10 35 20 25 15 Step 1. Calculate the mean by adding all data points together and divide by the total number of data points: 330/16 = 20. 6 Step 2. Find the individual deviations by taking the differences (the deviations) between the individual data points and the mean and square them -10. 6 -0. 6 9. 4 -5. 6 -10. 6 -5. 6 14. 4 -10. 6 -5. 6 4. 4 34. 4 -5. 6 112. 4. 36 88. 4 31. 4 112. 4 31. 4 207. 4 112. 4. 36 31. 4 19. 4 1, 183. 4 31. 4 Step 3. Add the squares together and divide by the number of data points and then take the square root of that value 1, 994. 2/16 = 124. 6 the square root of which = 11. 2 This is your Std Dev

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 10 20 30 15 15 10 15 55 20 20 15 10 35 20 25 15 11. 2 x 2 = 22. 4 This is two Std Dev or 2 Sigma or a 95% confidence interval that the data is valid Now add this to the mean = 20. 6 + 22. 4 = 43 Now subtract this from the mean = 20. 6 – 22. 4 = -1. 8 95% of the data should fall between -1. 8 and 43 Is it? If not, eliminate the data point and recalculate. Repeat until all data points are within 2 Sigma!