How is variance defined in a statistical context?

In a statistical context, variance is defined as the average squared deviation of each number from its mean. This measure quantifies how much individual data points differ from the mean of the dataset. By squaring the differences, variance ensures that negative and positive deviations do not cancel each other out and provides a clear measure of dispersion.

To calculate variance, one would first find the mean of the data set, then compute the deviation of each data point from this mean (subtracting the mean from each point), square each of these deviations, and finally calculate the average of these squared values. This process highlights how spread out the numbers in the dataset are around the mean.

In contrast, other options do not accurately define variance. The square root of the mean does not reflect how data points disperse. The total sum of the scores divided by the number of observations describes the mean, not variance. Likewise, the difference between the median and the mode does not relate to the measure of dispersion that variance represents. Thus, understanding variance as the average squared deviation from the mean is essential for analyzing the spread of data in statistics.