Weighting a Percent of Change

  • Thread starter Thread starter Jessica
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Jessica

Hi Everyone,

I need to weight my percent of change by province. E.g.

2004 2005 2005 Distribution % Change Weight
AB 182 268 6% 47% 2.8%
MB 1,285 1,295 29% 1% 0.2%
SK 784 887 20% 13% 2.6%
TOTAL 4255 4455 4.7% 5.7%

I see that MB has 29% of the market share, but only a % change of 1% in
volume.
AB has a small market share 6%, but is pulling the % change way up. But why
doesn't my weight formulas add up to total % change 4.7<>5.7?
My weight formula is 2005 Distribution times % Change.
 
I need to weight my percent of change by province.  E.g.
        2004    2005    2005 Distribution       % Change        Weight
AB      182     268     6%                            47%           2.8%
MB      1,285   1,295   29%                            1%           0.2%
SK      784     887     20%                            13%          2.6%
TOTAL   4255    4455                                  4.7%         5.7%

[....] why doesn't my weight formulas add up to total % change
 4.7<>5.7?
Click to expand...

Mostly because AB+MB+SK does not equal TOTAL. Either you have a
computation in those columns, or there are categories contributing to
TOTAL that you have not included in the table above.

Oh, I think I see your problem: your TOTAL includes the year title,
2004 and 2005 respectively. The correct totals are 2251 and 2450. So
you total change is about 10.9%.

Of course, changing the totals affects the "distribution" (proportion)
and weighted averages. But using the numbers above, it appears that
your "distribution" and "weight" formulas are correct.

So if you fix the TOTAL formula, I think everything will work out --
especially if you fix the format so that it consistently shows tenths
of a percent.

HTH.
 
Ok, i fixed the totals.

2004 2005 2005 Distribution % Change Weight
AB 182 268 11% 47% 5.2%
MB 1,285 1,295 53% 1% 0.4%
SK 784 887 36% 13% 4.8%
TOTAL 2251 2450 8.8% 10.3%

8.8% still does not equl the sum of the weighted percentages 10.3%
Is should equal my total % change right?

joeu2004 said:
I need to weight my percent of change by province. E.g.
2004 2005 2005 Distribution % Change Weight
AB 182 268 6% 47% 2.8%
MB 1,285 1,295 29% 1% 0.2%
SK 784 887 20% 13% 2.6%
TOTAL 4255 4455 4.7% 5.7%

[....] why doesn't my weight formulas add up to total % change
4.7<>5.7?
Click to expand...

Mostly because AB+MB+SK does not equal TOTAL. Either you have a
computation in those columns, or there are categories contributing to
TOTAL that you have not included in the table above.

Oh, I think I see your problem: your TOTAL includes the year title,
2004 and 2005 respectively. The correct totals are 2251 and 2450. So
you total change is about 10.9%.

Of course, changing the totals affects the "distribution" (proportion)
and weighted averages. But using the numbers above, it appears that
your "distribution" and "weight" formulas are correct.

So if you fix the TOTAL formula, I think everything will work out --
especially if you fix the format so that it consistently shows tenths
of a percent.

HTH.
Click to expand...
 
Ok, i fixed the totals.

        2004    2005    2005 Distribution       % Change        Weight
AB      182     268     11%                     47%     5.2%
MB      1,285   1,295   53%                      1%     0.4%
SK      784     887     36%                      13%    4.8%
TOTAL   2251    2450                            8.8%   10.3%

8.8% still does not equl the sum of the weighted percentages 10.3%
Is should equal my total % change right?
Click to expand...

First, sorry for saying the total change was 10.9%. Silly misreading
of the calculator.

And sorry for not recognizing your other mistake initially: you want
to look at the proportion ("distribution") of the 2004 numbers, not
the 2005 numbers. For example, for AB, instead of 268/2450, compute
182/2251.

As for the reason why.... The way my wife explains it might make the
best sense: since the base for the %Change is the 2004 numbers, the
base for the proportion should be the 2004 numbers.

If that works for you, great. Stop here.

I need to look at it mathematically, but I arrive at the same
conclusion. For the total %Change, we compute (b1+b2+b3)/(a1+a2+a3) -
1, where the "b's" are 2005 and the "a's" are 2004. For the
individual %Change, we compute b1/a1, for example. So in order for
the sum of the weighted averages to equal the total %Change, we need
to have a1+a2+a3 in the denominator. Therefore, we multiply b1/a1 - 1
by a1/(a1+a2+a3). The "a1's" cancel, giving us b1/(a1+a2+a3) - a1/
(a1+a2+a3). When we sum that "b1 term" with the b2 and b3 terms, we
do indeed get (b1+b2+b3)/(a1+a2+a3) - 1.

Whew! That should be clear as mud ;-). Now go back and read my
wife's explanation :-).

HTH.
 
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