# Financial Calculator HP 10bII - Standard Deviation with Probability

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

$$\begin{array}{l|l} \text{Probability}&\text{Score}\\ \hline 0.1&1\\ 0.3&5\\ 0.4&6\\ 0.2&10 \end{array}$$

With the forumla:

$$\text{stdev}^2 = \sum (\text{Probability} \times (\text{Score} - \text{Average Score}))^2$$

How would I do this on my calculator?

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## 1 Answer

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)

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It's a shame to not have this feature, for ease of memory I've just learnt your first option, which is not ideal but works! –  Pez Cuckow Sep 3 '11 at 10:38