Calculating Sigma

• 1). Take a sample of the population being studied for SPC purposes. If a pop bottling plant is being monitored, for example, to ensure proper filling of bottles, 50 bottles might be taken off the filling line at random and their contents measured. For illustration purposes, find the standard deviation of a much smaller group of measurements. Measure 4 bottles and find contents of 20, 22, 18 and 25 ounces.
  
  
• 2). Calculate the average of the sample measurements by adding together all the individual measurements and dividing by the total quantity of measurements. The equation to find the average is (20 + 22 + 18 + 25)/4 = 85/4 = 21.25.
  
  
• 3). Subtract this average from each individual measurement. Perform the calculations as such, 20 - 21.25 = -1.25, 22 - 21.25 = 0.75, 18 - 21.25 = -3.25 and 25 - 21.25 = 3.75.
  
  
• 4). Square each of the differences just calculated. Multiply each difference by itself. Note that squaring a negative number produces a positive one. Keeping with the same example, the numbers are -1.25^2 = 1.5625, 0.75^2 = 0.5625, -3.25^2 = 10.5625 and 3.75^2 = 14.0625.
  
  
• 5). Add all the above squared values together and divide by the total number of values minus 1. In this example, calculate as (1.5625 + 0.5625 + 10.5625 + 14.0625)/(4 - 1) = 8.917.
  
  
• 6). Find the square root of the number just calculated. Use square root function on a calculator. The square root of 8.917 is 2.99. This is the standard deviation, sigma, of the sample.