Variance and Standard Deviation

For example, we have three number: 1,2 and 3. The mean is 1/3*(1+2+3)=2. The variance is calculated by dividing the sum of squaring the absolute value of the difference between the number and the mean by the total number of numbers. Thus, variance for our example: 1/3 * [( 1-2)^2 + (2-2)^2 + (3-2)^2] = 2/3. Standard deviation equals square roof of variance, hence in our example it equals square roof of 2/3 = 0.8165

Hope my explanation can help you.

Variance of a random variable, probability distribution, or sample is one measure of statistical dispersion, averaging the squared distance of its possible values from the expected value (mean).

Standard deviation of a continuous random variable
Continuous distributions usually give a formula for calculating the standard deviation as a function of the parameters of the distribution. In general, the standard deviation of a continuous real-valued random variable X with probability density function p(x) is