What is variance in statistics?

Variance is a crucial concept in statistics that measures the degree of spread or dispersion of a set of data points. It is calculated by taking the average of the squared differences between each data point and the overall mean of the dataset. More formally, variance quantifies how far each number in the set is from the mean and thus from every other number.

To find the variance, one first computes the mean (average) of the data points, then for each data point, one calculates the squared deviation from the mean, and finally, the sum of these squared deviations is divided by the number of items in the dataset. This method highlights how much variability exists within the data. As a result, the correct definition depicts the variance as the sum of squared deviations divided by the number of items, which captures the essence of how data is distributed around the mean.

The understanding of variance is essential because it is utilized in various statistical applications, including standard deviation (which is derived from variance) and is foundational for inferential statistics.