Which measure indicates the variability or dispersion of a random variable?

The measure that indicates the variability or dispersion of a random variable is variance. Variance quantifies how much the values of a random variable differ from the mean of that variable. It is calculated as the average of the squared differences between each value and the mean, making it an effective indicator of spread. A higher variance indicates a wider spread of values, while a lower variance reflects that the values are closer to the mean.

While standard deviation is also a measure of dispersion and is derived from the variance (being the square root of variance), it emphasizes the concept of variability directly in the same units as the original data. However, variance itself is fundamentally the core measure that defines the degree of spread within a dataset. The other options, such as median and mean, do not provide information on variability; instead, they reflect central tendency measures that describe the center of the data distribution.