[Math] is it possible to calculate the standard deviation with a given mean and sample size

probabilitystandard deviationstatistics

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.:

$M = \frac{\Sigma X}{N}$

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, $S^2$ and $X$ in this formula:

$S^2 = \frac{\Sigma(X-M)^2}{N – 1}$

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?

Best Answer

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

Related Solutions

[Math] Calculating mean and standard deviation of very large sample sizes

Posting as an answer in response to comments.

Here's a way to compute the mean and standard deviation in one pass over the file. (Pseudocode.)

n = r1 = r2 = 0;
while (more_samples()) {
    s = next_sample();
    n += 1;
    r1 += s;
    r2 += s*s;
}
mean = r1 / n;
stddev = sqrt(r2/n - (mean * mean));

Essentially, you keep a running total of the sum of the samples and the sum of their squares. This lets you easily compute the standard deviation at the end.

[Math] Calculating missing data points from standard deviation and mean

Hint: The mean is the sum of the scores divided by the number, so if the mean is 20 the total is 200. Let the remaining scores be $x$ and $y$ and this gives you $x+y$. Then the standard deviation is the square root of the variance. The variance is the sum of the squares of the difference of each square from the mean. So you have $(13-20)^2+(11-20)^2+\ldots+(x-20)^2+(y-20)^2=$what?

Best Answer

Related Solutions

[Math] Calculating mean and standard deviation of very large sample sizes

[Math] Calculating missing data points from standard deviation and mean

Related Question