Mixing
Average calculation
$begingroup$
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 $$ left[
begin{array}{cc|c}
160&16&20
end{array}
right] $$
average percentages
edited Jan 25 at 9:57
Mohammad Zuhair Khan
1,6742625
asked Jan 25 at 9:44
PaulPaul
31
$endgroup$
add a comment |
$begingroup$
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 $$ left[
begin{array}{cc|c}
160&16&20
end{array}
right] $$
average percentages
edited Jan 25 at 9:57
Mohammad Zuhair Khan
1,6742625
asked Jan 25 at 9:44
PaulPaul
31
$endgroup$
1
$begingroup$
I think the mistake you made is to assume that $$ frac{sum text{actual}}{sum text{target}} = sum frac{text{actual}}{text{target}} $$ Which is not true.
$endgroup$
– Matti P.
Jan 25 at 9:50
$begingroup$
You well summarized my mistake
$endgroup$
– Paul
Jan 25 at 18:27
add a comment |
$begingroup$
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 $$ left[
begin{array}{cc|c}
160&16&20
end{array}
right] $$
average percentages
edited Jan 25 at 9:57
Mohammad Zuhair Khan
1,6742625
asked Jan 25 at 9:44
PaulPaul
31
$endgroup$
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 $$ left[
begin{array}{cc|c}
160&16&20
end{array}
right] $$
average percentages
average percentages
edited Jan 25 at 9:57
Mohammad Zuhair Khan
1,6742625
asked Jan 25 at 9:44
PaulPaul
31
edited Jan 25 at 9:57
Mohammad Zuhair Khan
1,6742625
asked Jan 25 at 9:44
PaulPaul
31
edited Jan 25 at 9:57
Mohammad Zuhair Khan
1,6742625
edited Jan 25 at 9:57
Mohammad Zuhair Khan
1,6742625
edited Jan 25 at 9:57
Mohammad Zuhair Khan
1,6742625
1,6742625
asked Jan 25 at 9:44
PaulPaul
31
asked Jan 25 at 9:44
PaulPaul
31
asked Jan 25 at 9:44
PaulPaul
31
31
1
$begingroup$
I think the mistake you made is to assume that $$ frac{sum text{actual}}{sum text{target}} = sum frac{text{actual}}{text{target}} $$ Which is not true.
$endgroup$
– Matti P.
Jan 25 at 9:50
$begingroup$
You well summarized my mistake
$endgroup$
– Paul
Jan 25 at 18:27
add a comment |
1
$begingroup$
I think the mistake you made is to assume that $$ frac{sum text{actual}}{sum text{target}} = sum frac{text{actual}}{text{target}} $$ Which is not true.
$endgroup$
– Matti P.
Jan 25 at 9:50
$begingroup$
You well summarized my mistake
$endgroup$
– Paul
Jan 25 at 18:27
1
1
$begingroup$
I think the mistake you made is to assume that $$ frac{sum text{actual}}{sum text{target}} = sum frac{text{actual}}{text{target}} $$ Which is not true.
$endgroup$
– Matti P.
Jan 25 at 9:50
$begingroup$
I think the mistake you made is to assume that $$ frac{sum text{actual}}{sum text{target}} = sum frac{text{actual}}{text{target}} $$ Which is not true.
$endgroup$
– Matti P.
Jan 25 at 9:50
$begingroup$
You well summarized my mistake
$endgroup$
– Paul
Jan 25 at 18:27
$begingroup$
You well summarized my mistake
$endgroup$
– Paul
Jan 25 at 18:27
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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.
answered Jan 25 at 9:56
Thomas LesgourguesThomas Lesgourgues
1,145219
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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.
answered Jan 25 at 9:56
Thomas LesgourguesThomas Lesgourgues
1,145219
$endgroup$
add a comment |
$begingroup$
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.
answered Jan 25 at 9:56
Thomas LesgourguesThomas Lesgourgues
1,145219
$endgroup$
add a comment |
$begingroup$
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.
answered Jan 25 at 9:56
Thomas LesgourguesThomas Lesgourgues
1,145219
$endgroup$
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.
answered Jan 25 at 9:56
Thomas LesgourguesThomas Lesgourgues
1,145219
answered Jan 25 at 9:56
Thomas LesgourguesThomas Lesgourgues
1,145219
answered Jan 25 at 9:56
Thomas LesgourguesThomas Lesgourgues
1,145219
answered Jan 25 at 9:56
Thomas LesgourguesThomas Lesgourgues
1,145219
1,145219
add a comment |
add a comment |
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1
$begingroup$
I think the mistake you made is to assume that $$ frac{sum text{actual}}{sum text{target}} = sum frac{text{actual}}{text{target}} $$ Which is not true.
$endgroup$
– Matti P.
Jan 25 at 9:50
$begingroup$
You well summarized my mistake
$endgroup$
– Paul
Jan 25 at 18:27