I was in the process of analyzing the data below. The first 2 columns are correct. They represent a point in time and a value of a stock at that point. I decided to calculate the probability surrounding each value and calculated the average to be the Sum(price)/16 =4.6875. I calculated the mean as Sum(price * P(value=price)=E(y) and took the average of that last column. I expected that these to values to be close but E(y) was found to be 0.7617.
I want to know the following:
- Do the calculation look right (just take a single random row, I don't expect anyone to waste time checking all the numbers of course).
- Why is E(y) so different from AVG(y)? What is the statistical significance of that?
The list of y values (2nd column) is:
3, 4, 5, 6, 7, 8, 3, 4, 5, 6, 3, 1, 3, 7, 4, 6
The entire table is:
Time Price.y N.gt.y N.eq.y N.eq.y.1 P.gt.y P.eq.y P.eq.y.1 E.y
1 3 11 4 1 68.75% 25.00% 6.25% 0.7500
2 4 8 3 5 50.00% 18.75% 31.25% 0.7500
3 5 6 2 8 37.50% 12.50% 50.00% 0.6250
4 6 3 3 10 18.75% 18.75% 62.50% 1.1250
5 7 1 2 13 6.25% 12.50% 81.25% 0.8750
6 8 0 1 15 0.00% 6.25% 93.75% 0.5000
7 3 11 4 1 68.75% 25.00% 6.25% 0.7500
8 4 8 3 5 50.00% 18.75% 31.25% 0.7500
9 5 6 2 8 37.50% 12.50% 50.00% 0.6250
10 6 3 3 10 18.75% 18.75% 62.50% 1.1250
11 3 11 4 1 68.75% 25.00% 6.25% 0.7500
12 1 15 1 0 93.75% 6.25% 0.00% 0.0625
13 3 11 4 1 68.75% 25.00% 6.25% 0.7500
14 7 1 2 13 6.25% 12.50% 81.25% 0.8750
15 4 8 3 5 50.00% 18.75% 31.25% 0.7500
16 6 3 3 10 18.75% 18.75% 62.50% 1.1250