When a co-efficient is given for any variables, then it's always squared.
The problem is that the examiner may not be nice, and you have to form the equation yourself, in which case, things can go something like
X + X + X + X + X + Y + Y + Y
or
5X + 3Y.
This generally causes a lot of confusion.
In this case, coin toss =/= poisson so mean =/= variance.
Therefore you can't just find the mean and assume it's the same as the variance.
I think your question is, "To square or not to square, the variance co-efficient?"
Well, there is no straightforward answer.
Let's say, there is a long jumper, whose distances have a mean of 5m and s.d. of 0.5m.
No two jumps will ever be the same... (although they can be the same distance)
If you have currency, $50 will always = $50, so it is squared.
I'm sorry I haven't been more clear, but in time, you will be used to it.
I'll stick around this topic ^^