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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, \text{Quartile Deviation }=\frac{Q_3-Q_1}{2}

where, Q_1 = \text{ Lower Quartile and, }

Q_3 = \text{ Upper Quartile.}

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

1. Quartile deviation is easy to calculate. This is beacuse we only need to calculate two value – 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.

1. The quartile deviation is an absolute measure of dispersion and hence cannot be used to compare variability of two or more data sets. In such cases a relative measure such as 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 changes wildly depending on the different sample taken. On the other hand, the sample variance can be mathematically shown to be an unbiased estimator of the population variance.

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