# Standard deviation as a percent?

1. Oct 9, 2014

### zeromodz

Say if I have a sample space 2,3, and 5. I want to find by what percent points deviate from the mean. So I would take the standard deviation as follows.

2+3+5 / 3 = 3.33

(2-3.33)^2 + (3-3.33)^2 + (5-3.33)^2 / 3 = 1.55

(1.55)^(1/2) = 0.775

So we get a standard deviation of 0.775. So how do I turn the standard deviation into a plus or minus percentage?

2. Oct 9, 2014

### mathman

Step 1: √1.55555 = 1.25
Step 2: 100(1.25/3.33)

3. Oct 9, 2014

### FactChecker

It's important that you say that the three points, 2, 3, and 5 are equally likely results. That is implied by your calculation of the mean = (2+3+5)/3, where the three points each have probability 1/3 of occurring.

As @mathman points out, your calculation of the standard deviation is wrong. You divided by 2 instead of taking the square root. The correct value is 1.24722.

You want to know what percentage of a sample will be within 1 standard deviation of the mean. That is between 3.33333 - 1.24722 and 3.33333 + 1.24722. (between 2.086 and 4.581. Only the results X=3 are in that range. That probability is 1/3 = 33.3%

Last edited: Oct 9, 2014