Below is the distribution for a data set.

Question

Below is the distribution for a data set.

xP(x)
3	0.12
4	0.71
10	0.04
11	0.13

Calculate the standard deviation of the data set from this probability distribution.

σ� =
[three decimal accuracy]

Answer 1

Have you tried putting the data into Excel, or Numbers, and calculating it that way?

Column A: these are your "x" outcomes

Column B: these are your P(x) probabilities of each outcome

Choose a cell in which you will calculate the mean using the SUM of all the x's divided by 4. Let's say this is in cell B7

Column C: Use a formula to calculate the following: (x-mean)^2 * p(x) for each x. Don't forget to put ( ) before squaring. This is very important because of "order of operations" rules. There are only four calculations to make; if there were more, I could show you how to type a formula in once and then "fill down" to the rest of the data.

In cell C7, SUM all of these calculated values. This is variance.

To get the standard deviation, take the square root of the number in C7.

Your instructor may have asked you to use a specific calculator/tool for this problem. As someone who likes to see it in front of me, I prefer a spreadsheet over a hand-held calculator any day.