# Distribution and Expected value

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?