I'm not sure in what context you are using this task average or using weighting but here is a starting point:
First you need to determine if you data set is normally distributed.
Here's a good resource:
Assuming your data set is normally distributed, the 3 most common "averages" will be your mean, median, or mode.
If you're not sure what these are, here's a resource:
Anyways, a data set that is normally distributed with very little skew will have a mean, median, and mode that are pretty close.
To identify/remove outliers, you may want to look at a histogram of your data or look at min/max values. the range, and 90 or 95% confidence intervals. Another way is to do random sampling of the entire population.
Lastly choose which "average" is most appropriate for your data set. Median and mode averages are more resistant to outliers.
If you determine your dataset is not normally distributed, its a good time to start searching the web about non-normal stats.