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7.
Product and Process Comparisons
7.2. Comparisons based on data from one process 7.2.6. What intervals contain a fixed percentage of the population values?
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| Empirical intervals | A rule of thumb is that where there is no evidence of significant skewness or clustering, two out of every three observations (67 %) should be contained within a distance of one standard deviation of the mean; 90 % to 95 % of the observations should be contained within a distance of two standard deviations of the mean; 99-100 % should be contained within a distance of three standard deviations. This rule can help identify outliers in the data. | ||||||||||||||||||||||||||||
| Intervals that apply to any distribution | The Bienayme-Chebyshev rule states that regardless of how the data are distributed, the percentage of observations that are contained within a distance of \(k\) standard deviations of the mean is at least \(100(1-1/k^2)\) %. | ||||||||||||||||||||||||||||
| Exact intervals for the normal distribution |
The Bienayme-Chebyshev rule is conservative because it applies to
any distribution. For a normal distribution, a higher
percentage of the observations are contained within \(k\)
standard deviations of the mean as
shown in the following table.
Percentage of observations contained between the mean and \(k\) standard deviations
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