# Thread: Compute standard deviation given mean, sample size and sum of squares.

1. ## Compute standard deviation given mean, sample size and sum of squares.

Hello All:

I'm afraid that I'm not sure what to do here. I am given the following information:

Sample size: 5
Mean: 3.0
Sum of squared values: 65

I am asked to compute the standard deviation, given these data. Could someone please suggest a formula with a step-by-step solution?

Thank you for your time,

Panglot

2. ## Re: Compute standard deviation given mean, sample size and sum of squares.

$s = \sqrt{\frac{\sum (x-\bar{x})^2}{n-1}}$

3. ## Re: Compute standard deviation given mean, sample size and sum of squares.

Thank you, pickslides,

My only difficulty here is that I cannot seem to get an answer of 2.24 when I attempt to solve this problem using the standard equation. If possible, could you walk me through this particular problem so that I will know exactly what goes where?

Thank you,

Panglot

4. ## Re: Compute standard deviation given mean, sample size and sum of squares.

Root of (sum of squares/n -mean^2) So in this case Root of (65/5 -9) = 2

5. ## Re: Compute standard deviation given mean, sample size and sum of squares.

Multiply my answer 2 by root(5/4) to get the required answer.
What's happening is that if they ask for the sample SD the answer is 2 but if they want an estimate of the population SD you multiply the sample SD by root(n/n-1) which in your case is root(5/4)