# is it possible to calculate the standard deviation with a given mean and sample size?

I have been going in rounds with this problem... I may be thinking "complicated", any advice?

I have the mean and total sample size (=number of data points) and I need to know what is the standard deviation (SD).

I know I can calculate back the sum of individual scores from the formal formula for calculation of the mean, i.e.:

M = Σ(X) / N

where X=individual data points N=number of data points

However after this step I am stuck. To find the SD using the variance I need to know the individual data points and which I don't have.

I then end up with two "unknown" variables, S2 and X in this formula:

S2 = Σ(X-M) 2 / N - 1

Thanks!

Thank you André and Jonathan. I now got some extra information: I am given the N and mean(maximum), e.g.: N=596, mean(maximum): 5.86(39.1); any extra advice?

-
You are stuck. If the data points are all equal (they might be) your sample variance would be $0$. If they wiggle all over the place, the sample variance would be high. – André Nicolas Dec 1 '12 at 21:46
What do you mean by "mean(maximum)"? – alex.jordan Dec 1 '12 at 23:20

If all you know is the mean and sample size, then no. The standard deviation could be 6 or $1.5\times 10^{10^{10}}$.