3.2 The Arithmetic Mean
First, some notation:
Clearly, Equations (3.1) and (3.2) are “simple averages.”
Example 3.1
Suppose we have a sample of n = 5 observations on a variable X: 1, 4, 10, 8, 10. What is the arithmetic mean of X or the value of ? It is readily seen that
How should we interpret 6.6? A “physical” interpretation of the mean is that it represents X's center of gravity, that is, X's absolute frequency distribution will “balance” at the mean (Fig. 3.1).
So much for physics. How does the statistician interpret the word “balance?” To answer this question, let us introduce the concept of the ith deviation from the mean. Specifically, given a variable X:X1, X2,. . . , Xn, the ith ...
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