You should understand the difference between the parameters and properties of a distribution and the estimators for these parameters and properties. For instance 

 - The true mean, $\mu = E[X]$ is the the expected value of a stochastic variable $X$ and can not be calculated exactly.
 - The sample mean, $m = \sum{x_i/n}$ with $x_i$ your observations of $X$ is the usual estimator for $\mu$.

Chapters in text books and whole scientific articles discuss the quality of estimators. For variance

 - The true variance is $\sigma^2 = E[(X-\mu)^2]$
 - The sample variance actually is $\frac{1}{n} \sum{(x_i - m)^2}$, but it has a tendency to be smaller than $\sigma^2$, therefore it is said to be biassed. This is related to the fact that $m$ itself is estimated from the same sample.
 - The usual estimator, $s^2 = \frac{1}{n-1} \sum{(x_i - m)^2}$, does not have this disadvantage.

For skewness

 - The true skewness of the stochastic variable is $\gamma_1 = E[(\frac{X-\mu}{\sigma})^3]$

 - The sample skewness is $\frac{1}{n} \sum(\frac{x_i-m}{s})^3$, but again, it is biassed.
 - The usual estimator is $\frac{n}{(n-1)(n-2)} \sum(\frac{x_i-m}{s})^3$, in which $s$ is of course the square root of the estimator for the variance.

Have fun implementing this.
For further discussion, you might consult 

 - Wikipedia's article on [Bias of an estimator][1] 
 - [this discussion of SAS on descriptive statistics][2] or 
 - [this Cross Validate question on skewness and kurtosis][3]. 


  [1]: https://en.wikipedia.org/wiki/Bias_of_an_estimator
  [2]: http://support.sas.com/documentation/cdl/en/procstat/63104/HTML/default/viewer.htm#procstat_univariate_sect026.htm
  [3]: http://stats.stackexchange.com/questions/157895/unbiased-estimators-of-skewness-and-kurtosis