Financial Calculator HP 10bII - Standard Deviation with Probability

Question

I have a financial calculator and am trying to use it to calculate the standard deviation when probability is involved.

For a standard deviation question say on the numbers 1, 5, 6, 10

Press 1, E+
Press 5, E+
Press 6, E+
Press 10, E+
Press Stat Button - ox

Answer 3.2

However I have just been presented with a question in the format

Probability | Score
--------------------
0.1         | 1
0.3         | 5
0.4         | 6
0.2         | 10

With the forumla (sorry I don't know math format, feel free to edit)

stdev^2 = Sum of (Probability * (Score - Average Score))^2

How would I do this on my calculator?

Many thanks,

Answer 1

You have three choices:

1)make the list 1,5,5,5,6,6,6,6,10,10 which has the correct probabilities and do the same as you are doing

2) Calculate average score with one pass through the data, avg score=0.1*1+0.3*5+0.4*6+0.2*10=6, then make a second pass through the data doing the equation you present stdev^2=0.1*(1-6)^2+0.3*(5-6)^2+0.4*(6-6)^2+0.2*(10-6)^2 (note your square is one layer too far out-Probability should not be squared)

3)One one pass accumulate sum(data) and sum(data^2), then use stdev^2=(sum(data))^2-sum(data^2)