Definition
The statistic for how widely a set of data spreads around its mean; the wider the spread the larger the standard deviation. It is the common basis for safety stock, process capability and measurement system studies.
In detail
Standard deviation turns how much it varies into a number that can enter a formula. On the inventory side it sizes safety stock: large demand variation forces more stock, so reducing variation beats adding inventory. On the quality side it drives process capability and measurement variation — the specification width divided by the standard deviation is the skeleton of every capability index. Before judging anything, check that the data comes from one process: a standard deviation computed across two shifts or two machines describes neither of them and supports no conclusion.
Example in practice
A part has mean daily demand of 100 pieces with a day-to-day standard deviation of 12, and the team sizes safety stock using Z = 1.64 for a 95% service level. After orders move from weekly to daily batches the standard deviation drops to 4, and the same service level needs two thirds less safety stock.