Which statistic measures the average distance of data points from the mean?

Which statistic measures the average distance of data points from the mean?

• A. Range
• B. Mean
• C. Median
• D. Standard Deviation

Answer: (D)

The concept being tested is how we quantify the spread of data around the center. The standard deviation measures, on average, how far each data point lies from the mean. It does this by taking each deviation from the mean, squaring them, averaging those squares, and then taking the square root. This gives a value in the same units as the data that reflects typical distance from the mean, i.e., the dispersion of the dataset. The range, by contrast, only shows the total span from minimum to maximum and can be heavily influenced by outliers, without describing how data are generally distributed around the mean. The mean is just the average value and tells you the central tendency, not how far values tend to deviate from it. The median is the middle value and likewise conveys central position rather than spread. Therefore, standard deviation best captures the average distance of data points from the mean.

The concept being tested is how we quantify the spread of data around the center. The standard deviation measures, on average, how far each data point lies from the mean. It does this by taking each deviation from the mean, squaring them, averaging those squares, and then taking the square root. This gives a value in the same units as the data that reflects typical distance from the mean, i.e., the dispersion of the dataset.

The range, by contrast, only shows the total span from minimum to maximum and can be heavily influenced by outliers, without describing how data are generally distributed around the mean. The mean is just the average value and tells you the central tendency, not how far values tend to deviate from it. The median is the middle value and likewise conveys central position rather than spread. Therefore, standard deviation best captures the average distance of data points from the mean.