Question

can someone tell me the formula to work out 'total standard deviation'.

Answer 1

The total standard deviation is the square root of the mean of the square of the deviation of numbers from the mean of those numbers. In mathematical form:\[\sigma=\sqrt{\frac{\sum_{1}^i(x_i - \bar{x})^2}{n}}\]

\(x_i\) corresponds to each of the numbers in the set, \(\bar{x}\) is the mean of those numbers, and n is the number of numbers.

Take the set {1, 3, 5, 7, 9} for example. The mean is 5. The squares of the deviations are:
(1 - 5)^2 = 16
(3 - 5)^2 = 4
(5 - 5)^2 = 0
(7 - 5)^2 = 4
(9 - 5)^2 = 16

The sum of those is 40.

The mean of those is 40 / 5 (because there are 5 numbers) = 8.

The square root of that is \(\sqrt{8}\)

The standard deviation is thus \(\sqrt{8}\)