What is standard deviation?

It is defined as the positive square root of the mean of the squared deviations from mean. The square of S.D is called variance.
The standard deviation is used as a measure of the variance of a measurement within a group of objects. In essence, it is the average difference between the measurement of any one object and the mean measurement for the group.
For example, if the average measured weight of brown bears is 140kg (265lbs) and the standard deviation of weights among brown bears is 5kg (11lbs), then any particular, individual brown bear is likely to weight between 135-145kg (254-276lbs), and very likely to weight between 130-150kg (243-287lbs). It’s impossible to know the weight of an individual bear just by looking at the mean weight for all bears, but the standard deviation tells you what range of weights the weight of an individual bear will fall in.
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