Advantages and Disadvantages of Quartile Deviation

The quartile deviation is a positional average that is used to measure the spread of data values. It can be calculated by subtracting the lower quartile from the upper quartile and dividing the result by 2. The quartile deviation can be calculated using the formula,

Quartile Deviation = Q₃ – Q₁/2.

We now list out some of the advantages and disadvantages of using quartile deviation as a measure of dispersion in statistics.

Advantages of Quartile Deviation:

1. Quartile deviation is easy to calculate. This is because we only need to calculate two values – lower and upper quartiles – in order to obtain the value of quartile deviation.
2. The quartile deviation takes into account the middle 50% of data values and is therefore much better compared to the range which only takes two values (highest and lowest values) into consideration.
3. The quartile deviation is much more resistant to the presence of outliers. This is because it ignores the topmost 25% values and bottommost 25% values. On the other hand, the range fluctuates wildly if the highest or lowest value is changed.
4. It cannot be calculated even with open-ended class intervals. Other measures of dispersion such as standard deviation, mean deviation, etc. cannot be calculated in this case.
5. The quartile deviation can be used to obtain the value of the coefficient of quartile deviation which is a relative measure of dispersion.

Disadvantages of Quartile Deviation:

1. The quartile deviation is an absolute measure of dispersion and hence cannot be used to compare the variability of two or more data sets. In such cases, a relative measure such as the coefficient of quartile deviation is much more appropriate.
2. It is not calculated on the basis of all data values. It only considers the middle 50% of data values and ignores the rest. Since it ignores some data values it is not an ideal measure of dispersion.
3. Quartile deviation is not suitable for mathematical treatment. This is in sharp contrast to measures such as the standard deviation whose formula is much more amenable to algebraic manipulation.
4. If we want to study a population by repeatedly taking random samples from it, then the quartile deviation is not a suitable measure of variability. This is because the values of quartile deviation change wildly depending on the different samples taken. On the other hand, the sample variance can be mathematically shown to be an unbiased estimator of the population variance.