Q:

How to estimate the "average number"?

I have many numbers representing some survey results, namely the number of siblings of each respondent (usually 0, 1, or 2 in this sample). The assignment is to estimate the average number of siblings.
Could you please clarify the problem? I suppose it would not be enough if I just compute the sample mean? How such problems are usually solved? Perhaps some data transformation could be convenient?

A:

Be careful how you interpret this question.
Families don't have "siblings", people have siblings. A family can have children in it, and each child will have one fewer siblings than than the number of children in the family. 
So the question is unclear -- what is it asking for? 

Is it asking for the average number of children in a family including those with no children? 
Is it asking for the average number of children in a family that has children? 
Is it asking for one less than the average number of children in a family that has children (e.g. if we surveyed one child in each family with children, how many siblings would they report?)
Or does it seek the number of siblings that is possessed on average by a person?

If you're interested in the question "what's the average number of siblings reported by survey respondents?", that's all well and good, but that's usually* not a very interesting quantity -- people who have the information from such a survey might be tempted to use it to answer a slightly more practical question.
Imagine you are interested in trying to infer "average number of children per family that has children" from those answers. It seems like you should just take the average and add 1, right? (+1 for the respondent, who didn't count themselves in their siblings, so their answer is one smaller than the number of children in their family)
Not so!
Consider an island with three families that have children. Family 1 has one child. Family 2 has 1 child. Family 3 has 10 children. Imagine that we ask all 12 children how many siblings they have.
the answers are:
0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9
with mean 7.5; adding 1 for the respondent gives 8.5
But the average number of children per family is 4.
* If we were (say) trying to identify the average number of "Happy birthday, sibling" cards bought per child on the island, the straight average from the survey works perfectly well (if every child buys one for every sibling each year, 7.5 cards per child is the average). If we're trying to infer something that's actually related to some form of children-per-household, we would be quite wrong to just average it.
For that, we'd need to adjust our formula for calculating the average.
The reason for the discrepancy is that the 10 children (9 +1 for the respondent) in the larger family gets counted repeatedly (ten times). In the end, we actually estimated the ratio of average squared family size to average children per family (that actually is 8.5, if both are conditioned on there being children at all)
[Such "over-representation" mistakes can sometimes be quite subtle.]

Now notice that if we're interested in average number of children per family (including those with no children), that our survey of children will have missed all the 0-children families. What if we imagine our island has two more families, with no children?
Now the average number of children per family is 12/5 = 2.4
But our island-survey of children gives us no direct way to estimate the proportion of families without children at all. 
We'd need to in some way estimate that; either via assumptions or by some model (itself containing more assumptions).
--
In short, you need to be very careful about what "average number of siblings per family" was actually intended to mean here. 

