To find the standard deviation we first find the mean=(∑Xi)/n where n is the size of the dataset and the elements of the dataset are X1, X2, X3, ..., Xn. ∑ means the sum of. So the mean is the sum of all the data divided by the quantity of data.
To find the standard deviation we find the variance first. For each element Xi we need to subtract the mean. This gives the deviation of each element from the mean. Square this value so we end up with n square values. Sum them and divide the result by n to get the variance. The standard deviation is the positive square root of the variance.
There are other ways of finding the variance and hence the standard deviation. In a binomial distribution, for example, we only need n (the number of "trials") and the probability of success p. The mean is np and the variance is np(1-p) making the standard deviation √(np(1-p)).