Merits and Demerits of Quartiles, Deciles and Percentiles etc.

The merits and demerits of the positional averages viz. quartiles, deciles and percentilers can be outlined as under:

Merits

1. They are easy to determine especially in case of the individual and discrete series.
2. They do not need all the data relating to a series like the mathematical averages viz. AM… G.M. and H.M.
3. They can be directly determined in case of an open end series without locating the lower limit of the lowest class, and the upper limit of the highest class.
4. They are useful in the computation of the measures of dispersion and skewness.
5. They give an idea about the character of a frequency distribution i.e. whether a series is symmetric, or asymmetric can be known by measuring their distance from the Median.
6. They are not affected very much by the extreme values of a series.
7. They can be located both graphically and tabularly.

Demerits

1. These averages are not easily understood by a common man.
2. The determination of their values in case of continuous series becomes cumbersome as it involves application of the formula of interpolation.
3. They are not based on all the observations of a series.
4. They need the rearrangement of series in the ascending order if given otherwise.
5. They do not study the entire data. For example, Q1, studies only, first 25%, Q2 only first 50%, and Q3 only first 75% of the data.
6. They are not capable of further algebraic treatment except in the computation of quartile deviation and coefficient of skewness.
7. They are affected very much by fluctuatin of sampling.
8. They are influenced much by the number of items rather than their values.