Average of vectors with unknowns

Question

I need to find an average of several vectors that denote the user profile. Here is the exmaple. '-' denotes that this element is empty. I computed the average, considering the '-' elements as well, so that for 1st element average is: $(1+9)/3=3.33$. Is it the correct way of doing it? I have doubts due to that empty elements. \begin{array}{llllllll} & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ v1 & 1 & - & 3 & 2 & 1 & - & - \\ v2 & - & 4 & 2 & 1 & 2 & - & 7 \\ v3 & 9 & - & 5 & - & - & 7 & 10 \\ ave & 3.3 & 1.3 & 3.3 & 1 & 1 & 2.3 & 5.66 \end{array}

Answer 1

Is that all the information that's provided? You might need to ask for some clarification on what the empty elements really signify.

If it's empty because there's no value (and not because the value is zero), you should probably divide by the number of non-empty values. For instance, for the first column, you would compute

$$ \frac{1+9}{2} = 5 $$

If it's empty because that's the convention for a zero, then you can divide by $3$. But that seems less likely to me.