Standard Deviation is the most scientific and most popular measure of dispersion. It was first used by Karl Pearson in 1893.
“Standard deviation is the square root of the arithmetic mean of the squares of deviations of items from their arithmetic mean.”
It can also be defined as the positive square root of variance.
Standard deviation is an ideal measure of dispersion because of the following reasons
- Based on all items of the series.
- Deviations are always taken from arithmetic mean, which is rigidly defined measure of dispersion.
- Algebraic signs + and – are considered.
- SD is fully capable of further algebraic treatment.
Comparison with other measures
- Range is based on two extreme values and ignore all other values. SD do not ignore any value.
- Quartile deviation only take the middle 50% of the items and other remaining items are left out. SD takes all values.
- Mean deviation does not consider the + and – signs and its values is not certain because it can be calculated from any average. SD does consider the + or minus sign.
The following are properties of Standard Deviation
Following are the properties of standard deviation
- It is the Minimum sum of the square of deviations.
- Combined standard deviation can be calculated.
- If a constant number is added or subtracted from all values of the series, there would be no effect on SD or variance. This is why we call SD is independent of origin.
- If all the values of a series are multiplied by a constant number, SD can also be calculated by multiplying SD of original data by the constant number. Similar for the divide. This is why we say that SD is not independent of origin.
- Square of value can be summed If Arithmetic mean, standard deviation and number of items of two are more groups are known.
MERITS AND DEMERITS OF STANDARD DEVIATION
Merits of Standard Deviation
- It is based on all values.
- Used in higher algebraic analysis like kurtosis, correlation, regression etc.
- It is rigidly defined.
- It is less influence by fluctuations in sampling in comparison to other measures of dispersion.
- It is specifically related to the area of normal curve.
Limitations of Standard Deviations
- It is relatively difficult to calculate.
- It gives more weightage to extreme values.