Goodness of fit - explaining standard deviations

Evening folks.

Hopefully someone can help me with this as stats isn't my forte and hours of internet trawling hasn't been any help!

I've performed an experiment to find out whether a certain scenario fits a negative binomial distribution. After collecting the data, I performed a chi-squared goodness of fit test. The result of this was that there was was no evidence to reject the null, so it was likely that the data did fit a Neg. Bin. Distribution.

My problem lies with the mean and standard deviations. The mean for the observed data and the expected are equal. Why is that so? Is it because the expected values are calculated from the observed values??

Secondly, the standard deviations of the observed and expected are not equal (but are close: 5.6 and 6.5 approximately). Why is there a difference in the SD?

*Edit* - just to clarify, I know what SD is, it's just the reasoning behind the observed and expected SDs being different that I'm unclear on.

Thanks in advance.