Which measure of dispersion is least affected by the extreme values of the series ?

Question

Accepted Answer

The correct option is 3:

The correct answer is Quartile Deviation. Measures of dispersion quantify the extent to which data points vary around a central value. The robustness of a measure refers to its resistance to being unduly influenced by extreme values, or outliers, in the dataset. Quartile Deviation (QD) is fundamentally based on the values of the first quartile ($Q_1$) and the third quartile ($Q_3$). It is calculated as half the difference between these two points: $QD = (Q_3 - Q_1) / 2$. Since the calculation only involves the central 50% of the data, it completely ignores the lowest 25% and the highest 25% of the observations. This intentional exclusion of the tails makes the Quartile Deviation an inter-percentile measure and hence the measure least affected by any unusually large or small values in the extreme ends of the series.

The incorrect option is 1 (Standard Deviation):
Standard Deviation requires every single observation in the series for its calculation, as it measures the deviation of each value from the arithmetic mean. Since it squares these deviations, extreme values are amplified, making the Standard Deviation highly sensitive to outliers.

The incorrect option is 2 (Mean Deviation):
Mean Deviation is calculated by averaging the absolute deviations of all data points from a central value (usually the mean or median). Because it incorporates every single observation, any extreme value will pull the central value (mean) and increase the resulting deviations, thus making the Mean Deviation affected by outliers.

The incorrect option is 4 (Range):
The Range is the simplest measure of dispersion, defined as the difference between the maximum and minimum values in the series. Since it is calculated solely using the two most extreme values, it is the measure *most* affected by any single extreme value (outlier).