July 2012
Intermediate to advanced
400 pages
9h 33m
English
Content preview from Statistical Inference: A Short Course
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3.5 The Range
We previously defined the range of a variable X as range = max Xi − min Xi. Clearly, the range is a measure of the total spread of the data. However, knowing the total spread of the data values tells us nothing about what is going on between the extremes of max Xi and min Xi. To specify a more appealing measure of dispersion, let us consider the spread or scatter of the data points about the mean. In particular, let us consider the “average variability about the mean.” This then takes us to the concept of the standard deviation of a variable X.
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