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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 quartile $NESE$ deviation.
✓

Answer

MERITS OF QUARTILE DEVIATION:
  1. It is rigidly defined.
  2. It is superior to range as such its calculation is based on middle $50\%$ of the items of the series.
  3. It is easy to calculate especially in case of open end series.
  4. It is not very much affected by the extreme values of the series.
  5. In a moderately systematic series, it enables the computation of lower De quartile, upper quartile, standard deviation and mean deviation.
  6. It is the only method of dispersion applicable in case of 'open-end classes'.
DEMERITS OF QUARTILE DEVIATION:
  1. Since Quartile Deviation is based on Quartiles, sometimes it is not rigidly defined.
  2. It is not based on all the observations of the series. It does not take into account in all the observations in the series. Hence it is not representative.
  3. It is not capable of further algebraic treatment.
  4. It is not a stable measure of dispersion as it is affected very much by fluctuations son of sampling.
  5. In a symmetrical distribution, the value of the median which is the second Quartile of the distribution lies midway between $Q_1$ and $Q_3$. If however, the series in non-symmetrical, Md does not lie midway between $Q_1$ and $Q_3$​​​​​​​. If the series is symmetrical ma + Q.D should equal $Q_3$ and $Q_1$​​​​​​​.
  6. It is not understood by a common man.
  7. It is more time consuming.

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