Standard deviation
Standard deviation turns up in 2 fields: statistics, metrology. Here is what it means to the people in each one.
Standard deviation in statistics
Typical distance of individual values from their mean, the basic measure of spread, written as sigma or s.
The sample standard deviation s is the square root of the sum of squared deviations from the mean divided by n minus 1; sigma is the true process value it estimates. Quality work separates short-term sigma, estimated within subgroups from ranges or moving ranges, from long-term or overall sigma computed from all the data, and the gap between them measures between-subgroup variation. Variances add for independent sources; standard deviations do not.
"Within-lot standard deviation is 0.8, overall is 1.9. Most of the spread is between lots."
Standard deviation in metrology
The usual measure of scatter in a set of values, the square root of the average squared deviation from the mean.
A measure of dispersion; for n readings the experimental standard deviation s is the square root of the sum of squared deviations from the mean divided by n minus 1. In uncertainty work it describes the spread of individual readings, which is repeatability, and it is the form every standard uncertainty takes. The standard deviation of the mean, s divided by the square root of n, applies when the reported value is the average of those readings.
"Standard deviation of the ten readings is 0.6 grams, but we report the mean, so that's 0.19 in the budget."