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7.
Product and Process Comparisons
7.2. Comparisons based on data from one process 7.2.5. 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 tandard deviations of the mean is at least (1 - 1/k2)100%. | ||||||||||||||||||||||||||||
| 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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