What is variance?

Variance is defined as the average of the squared differences from the mean. This quantifies how spread out the values in a data set are in relation to the mean. To calculate variance, you take each data point, subtract the mean from it, square the result, and then take the average of those squared differences. This process ensures that both positive and negative deviations from the mean contribute positively to the variance, thus reflecting the overall variability in the data.

In contrast to other statistical measures, variance specifically relates to the distribution of the values around the mean rather than just the extremes or most common values. The range of values in a data set only gives a sense of the spread between the highest and lowest values without accounting for the values in between. The most frequently occurring value, known as the mode, does not provide insight into overall variability, and the total sum of data values simply provides a cumulative measure without addressing the spread of the individual values. Thus, variance stands out as a key measure for assessing variability in a data set.