What statistical measure indicates how spread out the numbers in a dataset are from their average value?

The statistical measure that indicates how spread out the numbers in a dataset are from their average value is variance. Variance quantifies the degree to which each number in the dataset differs from the mean (average) of the dataset. It achieves this by calculating the average of the squared differences between each data point and the mean. A higher variance indicates a greater spread of data points, signaling that the numbers are more dispersed from the mean, while a lower variance means the numbers are closer to the mean.

While both standard deviation and variance are measures of dispersion, variance specifically serves as the foundational concept that direct calculations of standard deviation are based on; standard deviation is simply the square root of variance. This relationship emphasizes the role of variance in understanding data spread. Other measures like mean absolute error and range provide different perspectives on data variability but are not as focused specifically on the spread relative to the mean as variance is.