What does the term "variance" specifically measure?

Variance specifically measures the spread of data points around the mean of a data set. It quantifies how much the individual data points deviate from the mean value, providing insight into the degree of variability within the data. When variance is calculated, each data point's distance from the mean is squared to ensure that negative and positive deviations do not cancel each other out. This squaring amplifies larger differences, indicating a greater impact on the overall variability. A higher variance indicates a wider spread of data points, while a lower variance suggests that the data points are closer to the mean.

The other options refer to different statistical concepts. For instance, the central point of a data set is typically determined by measures like the mean or median, not variance. The difference between each data point and the range does not represent variance; it relates more to the overall distribution of values rather than their individual deviations from the mean. Lastly, identifying the common value in a data set refers to the mode, which is the most frequently occurring value, and is not related to variance at all. Therefore, the definition and purpose of variance are accurately captured by its measurement of the spread of data points around the mean.