Measure of dispersion which is affected most by extreme observations is :

Question

Accepted Answer

The correct option is 1:

The correct measure of dispersion that is affected most by extreme observations is the **Range**. The range is the simplest measure of dispersion and is calculated solely based on the difference between the maximum (highest) value and the minimum (lowest) value in a dataset ($Range = X\_{max} - X\_{min}$). Because its calculation depends entirely on these two extreme points, any unusually large or unusually small observation (an outlier) will immediately and significantly inflate the range. For example, if a dataset is 10, 12, 15, 18, 20, the range is 10. If we add an extreme observation, 100, the new range becomes 90, showing its extreme sensitivity to outliers. Therefore, while easy to compute, the range is generally considered a crude measure due to its reliance on only the endpoints of the data.

The incorrect option is 2:
Quartile Deviation (also known as the Semi-Interquartile Range) is far less affected by extreme observations because it is based only on the first quartile ($Q\_1$) and the third quartile ($Q\_3$). Since it ignores the lowest 25% and the highest 25% of the data, any extreme outlier outside this central 50% does not impact its value.

The incorrect option is 3:
Mean Deviation measures the average absolute distance of each observation from the mean or median. While it does use every value in the dataset, its absolute deviations make it less sensitive to the squaring effect of extreme values compared to the standard deviation.

The incorrect option is 4:
Standard Deviation uses all observations and involves squaring the deviations from the mean. Although standard deviation is significantly affected by outliers, as squaring magnifies the difference of extreme observations, it uses every data point for its calculation. The Range remains the most sensitive because it relies *only* on the two most extreme points, making it instantaneously and solely determined by them.