For each new lot of control materials, new control values must be calculated, and acceptable ranges established. The values necessary for calculating the acceptable ranges are the mean and standard deviation. At least 20 samples are necessary for good statistical data.

The mean is calculated by adding all of the values, and dividing by the number of values. The formula is:

For example, suppose you wanted to find the mean of the values 4, 6, 2, 8, and 5. The mean is:

The standard deviation (abbreviated s or SD) is calculated according to the following formula:

That is, calculate the deviation from the mean for each point, square those results, sum them, divide by the number of points minus one, and finally take the square root. For example, the deviations from the mean in the above example are -1, 1, -3, 3, and 0. The squared deviations are 1, 1, 9, 9, and 0. The standard deviation is therefore:

The standard deviation will be larger if the data are spread out and smaller if the data are closely clustered about the mean.