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Measures of Dispersion — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Dispersion6 Marks
Question
Discuss merits and demerits of standard deviation.
✓

Answer

Merits of Standard Deviation: Among all measures of dispersion Standard Deviation is considered superior because it possesses almost all the requisite characteristics of a good measure of dispersion. It has the following merits:
  1. This is the most rigidly defined measure of dispersion and therefore is dependable.
  2. 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.
  3. Unlike Mean Deviation, Combined S.D. for given two or more series can be computed if Xs and S.D. are given.
  4. It is based on all the terms or observation hence is more reliable.
  5. As sum of squares of deviations from X is minimum, so it is the best measure.
  6. Standard Error of the different methods are also based on S.D.
  7. 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.
  8. As it is based on A.M.; It has vast good qualities of A.M.
  9. 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:
  1. As compared with other measures of dispersion it is more difficult to compute 1925 and not so easy to understand.
  2. 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.
  3. 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.
  4. 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.
  5. It cannot be exactly calculated for a distribution with open-ended classes.

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