The standard deviation of a collection of numbers is the square root of the variance which is, intuitively, a measure of how much the individual numbers differ from the average (mean) of the collection.

Your steps describe the formula for calculating the standard deviation but the numbers you are using are not applicable to the formula. You need the individual scores to calculate deviation. The deviation of the subgroup could be much smaller than that of the whole group or much larger depending on the nature of the subgroup and the individual answers. For example consider the following distribution:

{0,1,1,1,1,1,1,2,3,3,3,3,3,3,4}

The mean is 2, the standard deviation of the whole group is 1.15 If we choose the subgroup {0,1,2,3,4} the mean is 2 but the standard deviation is 1.41. Choosing the subgroup {2} leads to a mean of 2 and stanard deviation of 0.

Now with that being said if you are looking for the standard deviation of the 2 averages, your procedure is almost correct:

1. Find the average of the 2 averages: (5.09 + 3.83)/2 = 4.46

2. Find the difference between the average and each number and square it.

(4.46-5.09)^2 = .3969

(4.46-3.83)^2 = .3969

3. add the numbers .3969+.3969 = 0.7938

4. Divide by the number of values inthe collection (2) = 0.7938/2 = .3969

5. square root the number: sqrt(.3969) = .63

Notice that |4.46-5.09| = |4.46-3.83| = .63

For two numbers the standard deviation is just the difference between either number and the average. Intuitively this makes sense.

Is the standard deviation of the two averages what you are after?