I know it will be a stupid question for somebody but I need to understand.
Below the matrix: $$ \left[ \begin{array}{cc|c} 55&0&0\\ 55&0&0\\ 15&8&53\\ 15&4&27\\ 10&2&20\\ 10&2&20 \end{array} \right] $$
The 1st column is the target, the 2nd is the actual and the 3rd is the percent achievment $\text{round} \left(\frac{\text {actual} \cdot 100}{\text{target}} \right)$
The question is:
Why I cannot calculate an average on the $3^{\text {rd}}$ column ?
Why do I have to use this formula :
$$\frac{\sum{ \text {actual}}*100}{\sum{ \text {target}}}$$
The result is $$ \left[ \begin{array}{cc|c} 160&16&10 \end{array} \right] $$
and not $$ \left[ \begin{array}{cc|c} 160&16&20 \end{array} \right] $$
Intuitively, this is because your target have different values, they have different "weights/importance" into your total target.
Imagine an extreme case, where you add another very high target : 1,000,000 for instance, and suppose you actually reach 0 on this target. The percentage of achievement for this task is 0, and overall you should be very close to 0% of total achievement. The other targets almost don't count compared to the new main one.
But if you compute the average directly on the percentage of achievement, then you suppose that the new task counts as much as the old one, only reducing the total achievement percentage by 1/7th.
In short : They are two possible goals. You should:
recalculate the total average from the total actual divided by total target if you want to know the average achievement of the total target
average on percentage of achievements if you want to know the average achievement of the different tasks, giving each task the same importance.