What is Standard Deviation?
The idea of Standard Deviation was first presented by Karl Pearson in 1893. This measure is widely used for studying dispersion. Standard deviation does not suffer from those defects from which range, quartile range, and mean deviation suffer. Standard Deviation is also called the Root-Mean Square Deviation, as it is the square root of the mean of the squared deviations from the actual mean.
Standard deviation is superior to other measures because of its merits showing the variability which is important for statistical data. The standard deviation enjoys many qualities of a good measure of dispersion.
In mean deviation we take the sum of deviations from actual mean after ignoring +- signs. In standard deviation, we get the same results without ignoring signs. In this case deviation from actual mean are squared, so every term is positive.
What are the merits and demerits of Standard Deviation?
- This is the most rigidly defined measure of dispersion and therefore is dependable.
- It is further capable of Algebraic Treatment; Coefficient of S.D., Variance and Coefficient of Variation are used to test the variability and consistency by using S.D.
- Unlike Mean Deviation, Combined S.D. for given two or more series can be computed if Xs and S.D. are given.
- It is based on all the terms or observations hence is more reliable.
- As sum of squares of deviations from X is minimum, so it is the best measure.
- Standard Error of the different methods are also based on S.D.
- To Compare Variability or Consistency co-efficient of S.D., C.V. is most dependable as compared to Coefficient of Mean Deviation or Q.D.
- As it is based on A.M.; It has vast good qualities of A.M.
- We can also find sum of terms as well as sum of squares of terms if X and S.D. are given.
Demerits or Limitations
- As compared with other measures of dispersion it is more difficult to compute and not so easy to understand.
- In the case of open end intervals we have to make the assumption of lower limit of first interval and upper limit of last interval.
- As far as S.D. is concerned it does not compare two series itself. We have to proceed to Coefficient of S.D. or C.V. for this purpose.
- The extreme terms make the impact two much, therefore in some cases Coefficient of Q.D. or of M.D. has a certain edge over it. If extreme item differ largely, then they make a heavy change when deviations are squared.