Empirical Rule Demonstration (4)

Recall from the description of the empirical rule, that we can expect to find a certain percentage of the process' outputs within a given number of standard deviations above and below the mean (e.g. 60%-75% within +/- 1 standard deviation). We have just calculated the mean, so now we need to find the standard deviation.

For a stable process, we can estimate the standard deviation using the formula:

Estimated standard deviation = R-bar / d2

Where R-bar is a symbol for the Mean Range, and d2 is a special constant that has a certain value depending on the size of the subgroups used. Because we are using subgroups of size 5, d2 has the value 2.326. Substituting these values into the formula, we get the simple calculation:

Estimated standard deviation = 3.2 / 2.326

Calculate this value now, and enter the result into the box below. Round your answer to 2 decimal places. When you are ready, click the button to check your answer.

Esitmated standard deviation =