Standard Deviation: The standard deviation commonly denoted by ‘σ’ (Sigma) is the most widely used measure of dispersion. It is the square root of the second moment of dispersion and is calculated from the arithmetic mean. In short, it may be defined as the root-mean-square deviation from the mean.
Merits of Standard Deviation:
1. It is based on each and every item of the data and it is rigidly defined.
2. It is capable of further algebraic treatment. Combined SD of two or more groups can be calculated.
3. It is less affected by fluctuations of sampling than most other measures of dispersion.
4. For comparing variability of two or more series, co-efficient of variation is considered as most appropriate and this is based on SD and Mean.
5. SD is most prominently used in further statistical work.
Demerits of Standard Deviation:
1. It is not easy to calculate and to understand.
2. It gives more weight to extreme items and less to those which are nearer to mean.
Difference Between Mean Deviation and Standard Deviation
1. Algebraic signs are ignored while calculating mean deviations whereas standard deviation takes into account algebraic sign also.
2. Mean deviation can be computed either from median or mean whereas standard deviation is computed always from arithmetic mean.
Coefficient of Variation
It is the ratio of Standard deviation to the mean expressed as percentage. Coefficient of variation can be defined as the coefficient of standard deviation with respect to mean which is generally expressed in terms of percentage. The coefficient of variation is also known as coefficient of variability.
Symbolically, Coefficient of Variation (C.V.) = (S.D / Mean)*100.
Purpose of Coefficient of Variation:
Coefficient of variation is used to compare the variability of two or more series. A series having greater coefficient of variation is said to have more variable, i.e., less uniform, less stable or less consistent. Again a series, having coefficient of variation lesser is said to be less variable, i.e., more uniform, more stable or more consistent.
Difference between Variance and Coefficient of Variation:
Coefficient of variation is the percentage variation in the mean while Variation is the total variation in the mean.