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It is a measure of the values of the variables around its mean or it is the square root of the sum of the squared deviations from the mean divided by the number of observances. The arithmetic mean of the returns may be same for two companies but the returns may vary widely.
Standard deviation (σ) is the square root of the variance, or (6.7833)1/2 = 2.60%. Standard deviation is expressed in the same units as the data, which makes it easier to interpret. It is the most frequently used measure of dispersion.
Our calculations above were done for a population of six mutual funds. In practice, an entire population is either impossible or impractical to observe, and by using sampling techniques, the population variance and standard deviation can be estimated.
The sample variance formula is very similar to the population variance, with one exception: instead of dividing by n observations (where n = population size), it is divided by (n – 1) degrees of freedom, where n = sample size. So in the example, if the problem was described as a sample of a larger database of mid-cap funds, computation of the variance would be done using n – 1, degrees of freedom.
Sample variance (s2)
= (0.16 + 4.0 + 22.09 + 6.76 + 6.25 + 1.44)/(6 – 1)
= 8.14
Sample Standard Deviation (s)
Sample standard deviation is the square root of sample variance:
(8.14)1/2 = 2.85%
In fact, standard deviation is so widely used because, unlike variance, it is expressed in the same units as the original data, so it is easy to interpret, and can be used on distribution graphs (e.g. the normal distribution).
