How is variance calculated?

Variance is a statistical measurement that quantifies the degree of variation or spread in a set of data points. To calculate variance, one must first determine how far each data point deviates from the mean (average) of the data set. This involves finding the difference between each score and the mean, squaring each of those differences to eliminate any negative values, and then averaging those squared differences.

This process captures not only the magnitude of deviation but also the nature of variance as a measure that gives more weight to larger deviations. Thus, by squaring the differences, variance effectively emphasizes outliers more than smaller deviations, providing a comprehensive view of variability in the data set. Ultimately, this leads to a more accurate understanding of how scores are distributed around the mean.

The other approaches, such as averaging scores, finding the mid value, or counting the frequency of values, do not contribute to the calculation of variance. Averaging scores yields the mean, finding the mid value indicates the median, and counting frequencies relates to frequency distribution analysis, none of which capture the spread of data in the way variance does.