Appendix 2
Standard deviation
Standard deviation is a measure of the spread or scatter in a process and for a sample is given by the equation below:
??where
?? standard deviations?? the sum of the differencexi?the individual value x?the mean value?(x?x)ii?1i?n2n?1
n?the number of values
The spread of a process may be estimated from the range, R . The maximum value minus the minimum. The smaller the range, the less spread in the process.
A more sophisticated way of estimating scatter, which is widely used for statistical process control is standard deviation, ?, which not only provides a measure of the
precision of the process, but also predicts how many parts in a population will be out of tolerance.
For what is known as a normal distribution, 68.3% of the population will lie within one standard deviation above and below the mean, ?1? ; 95.4% lie within ?2?, 99.7% within ?3? and 99.994 within ?4?.
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