Using the returns for Extell for the years 2008– 2012, we can illustrate the deviation of the values from the mean. 

The numerator for the formula for the variance of these Y_t values is Σ(Y_t - Y)², which we will call SS_y, the sum of the squared deviations of the Y_t around the mean. Algebraically, there is a simpler alternative formula:

Using Extell’s annual total returns, we calculate the SS_y both ways.

The variance is the sum of the squared deviations from the mean: 

The standard deviation is the square root of the variance: 

The standard deviation is in the same units of measurement as the original observations, as is the arithmetic mean.  

Transcribed Image Text:

ss, = Σ(x – Y) = Σ n