Elementary Statstics

7.1.6 Standard Deviation and Root Mean Square Deviation

Standard deviation usually denoted by the Greek letter small sigma ($$\sigma$$) is the positive square root of the arithmetic mean of the squares of the deviations of the given values from their arithmetic mean. For the frequency distribution x_i/f_i – 1,2, …..n,

Where is the arithmetic mean of the distribution and

The step of squaring the deviations (x_i – ) overcomes the drawback of ignoring the signs in mean deviation. Standard deviation is also suitable for further mathematical treatment. Moreover of all the measures, standard deviation is affected least by fluctuations of sampling.