# Mean and standard deviation of Gaussian Distribution

I have some random numbers which are generated from Gaussian Distribution. But I don't know the mean, standard deviation of that distribution. How can I find them using random numbers?

• If the only thing you have available to you is the sample of random numbers, this is impossible. But you can estimate them by computing the empirical mean and standard deviation. Jan 8, 2012 at 9:08
• @ocram Yeah, I have only large amount of random numbers generated from Gaussian Distribution.
– user
Jan 8, 2012 at 9:21
• Then, both the mean and variance can be estimated from your sample. @David Robinson has clarified that point. Jan 8, 2012 at 9:42

$$\bar{x} = \frac{1}{n}\sum_{i=1}^nx_i$$
$$\bar{s} = \sqrt{\frac{1}{n-1}\sum_{i=1}^n\left(x_i - \bar{x}\right)^2}.$$
Here, $x_i$ is the $i^\text{th}$ number in your sample. See Wikipedia for details.