How is variance defined in a statistical context?

• A. Average of the squared differences from the mean
• B. Sum of the mean values
• C. Difference between maximum and minimum values
• D. Square root of individual values

Answer: (A)

Variance is a measure of how much the values in a data set deviate from the mean of that data set, providing insight into the spread or dispersion of the data. Specifically, it is defined as the average of the squared differences from the mean. This squaring is critical because it ensures that all differences are positive, thus preventing cancellation that would occur if positive and negative differences were summed directly.

By averaging these squared differences, variance quantifies the extent to which each data point varies from the mean. A high variance indicates that data points are spread out over a wider range of values, while a low variance suggests that they are closer to the mean. This measure is foundational in statistics because it forms the basis for many statistical analyses and is pivotal in the calculation of standard deviation, which is the square root of the variance and provides a more interpretable measure of dispersion.