weighted average

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weighted average

by mehrasa » Sun Sep 11, 2011 4:44 am
could anyone explain for me the weighted average and its formula based on this question

A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefits costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993?
a. 16.5%
b. 20%
c. 35%
d. 55%
e. 65%

Note that one element increased 3% and another one 5.5% and weighted average increase is closer to smaller increment so clearly that has higher weight. Weightage of fringe benefits is
(3.5 - 3.0)/ (5.5 - 3.0)*100 = %20

I know another formula:
proportion of one element = absolute value (proportion of another element - proportion of mixture)

we can find both proportion of two element of mixture then find its ratio.... but about above formula, plz a bit clarification
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by sl750 » Sun Sep 11, 2011 9:43 am
Can you explain what you did here?

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by mehrasa » Sun Sep 11, 2011 10:38 am
Note that one element increased 3% and another one 5.5% and weighted average increase is closer to smaller increment so clearly that has higher weight. Weightage of fringe benefits is
(3.5 - 3.0)/ (5.5 - 3.0)*100 = %20


this is the explanation that I also did not understand and do not have any idea which formula has been used..

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by shankar.ashwin » Sun Sep 11, 2011 10:44 am
Well, your explanation is using rule of allegations.

When you mix 2 solutions A & B of different concentration (say 10% and 20%) to form a solution which is say 18% concentration, you can determine the ratio in which they are mixed by.

20-18/18-10 = 2:8 (or) 1:4.

Similarly here,

You get (5.5-3.5)/(3.5-3) = 4:1.

4:1 is nothing but 80%:20%.

Hope you get it.
mehrasa wrote:could anyone explain for me the weighted average and its formula based on this question

A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefits costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993?
a. 16.5%
b. 20%
c. 35%
d. 55%
e. 65%

Note that one element increased 3% and another one 5.5% and weighted average increase is closer to smaller increment so clearly that has higher weight. Weightage of fringe benefits is
(3.5 - 3.0)/ (5.5 - 3.0)*100 = %20

I know another formula:
proportion of one element = absolute value (proportion of another element - proportion of mixture)

we can find both proportion of two element of mixture then find its ratio.... but about above formula, plz a bit clarification

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by mehrasa » Sun Sep 11, 2011 11:03 am
thnx shankar