Which statement is true regarding variance in statistics?

• A. It can be computed directly from the original scores
• B. It measures the average distance from the mean
• C. It is always a negative value
• D. It is computed after finding the mean

Answer: (D)

Variance is a statistical measure that quantifies the degree to which scores in a dataset vary or spread out from the mean. To compute variance, one must first calculate the mean of the data set. After obtaining the mean, the next step involves determining the squared differences between each data point and the mean. These squared differences are then averaged, which results in the variance.

The process starts with calculating the mean because variance is fundamentally based on how far each score deviates from this central value. If one does not find the mean first, it would not be possible to determine the variance accurately, as the deviations would be relative to an unknown reference point. Therefore, stating that variance is computed after finding the mean accurately captures the necessary steps in the calculation of variance, highlighting the interdependence of these two statistical concepts.