# Variance and Standard Deviation

Variance and standard deviations are measures of dispersion. In statistics, variance is the average of the squared differences from the mean. Variance is the measurement of deflection of values from its mean. It is denoted by square of a Greek letter sigma ($\sigma ^{2}$). Variance is one of the moments of a distribution and is always non-negative as the squares are positive.

Standard deviation is the root of the sum of the squares of the deviations divided by
their number. Also known as root mean square deviation. It is a second
moment of a dispersion. Since the sum of the squares of the deviations
from the mean is minimum, the deviations are taken only from mean.It is by far the most important and widely used
measure of dispersion. It is rigidly defined and based on all the
observations. The squaring of the deviations (x - $\bar{x}$) removes the
drawback of ignoring the signs of deviations in computing the mean
deviation. This step renders it suitable for further mathematical
treatment. Moreover, of all the measures of dispersion, standard
deviation is affected least by fluctuations of sampling.

Standard deviation gives greater weight to extreme values and as such
has not found favor with economists or businessmen who are more
interested in the results of the modal class. Standard deviation is
considered as the best and the most powerful measure of dispersion.