The merits and demerits of the positional averages viz. quartiles, deciles and percentilers can be outlined as under:
- They are easy to determine especially in case of the individual and discrete series.
- They do not need all the data relating to a series like the mathematical averages viz. AM… G.M. and H.M.
- 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.
- They are useful in the computation of the measures of dispersion and skewness.
- 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.
- They are not affected very much by the extreme values of a series.
- They can be located both graphically and tabularly.
- These averages are not easily understood by a common man.
- The determination of their values in case of continuous series becomes cumbersome as it involves application of the formula of interpolation.
- They are not based on all the observations of a series.
- They need the rearrangement of series in the ascending order if given otherwise.
- 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.
- They are not capable of further algebraic treatment except in the computation of quartile deviation and coefficient of skewness.
- They are affected very much by fluctuatin of sampling.
- They are influenced much by the number of items rather than their values.