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Table 1

1   -5
12  -4
14  -3
13  -2
9   -1
11  0
10  1
10  2
8   3
6   4
6   5

First column above is frequency, second is data. Sum is -22, Count is 100, Mean is -.22 and std dev is 2.769

13  -2
9   -1
11  0
10  1
10  2

Above is a snippet of Table 1 between one std dev. Here the sum is -5 and it represent 53% of all the data.

1   -5
12  -4
14  -3
8   3
6   4
6   5

Above is a snippet of Table 1 beyond one std dev. Here the sum is -17 and it represent 47% of all the data.

If I do this : .47 * -17 + .53 * -5 = -10.64

Three questions: What does this number -10.64 represent? why does it not equal the mean? Why is it wrong to say "53% (within one std dev) of the data gives a sum of -5 and 47% (in the tail ) of the data gives a sum of -17 and hence the expected value is: -10.64"?

Robert Thanks for the response. Since the two sums are -17 and -5 is the number -10.64 an expected value of the sums? How do I interpret this number?

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The means of your two subsets are, respectively, -0.0934 and and -0.3167. Adding these in proportion to their relative sample size: (0.53*-0.09434)+(0.47*-0.3167) = -0.22 which is the correct mean for the total population (there is a minus sign missing in the original question)

Alternatively, observe that the -17 and -5 sum to -22, the sum of the observations.

You can't add two sums together and end up with a mean, in short.

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