# puzzled with percentages

• Oct 31st 2007, 02:12 AM
tsatsos007
puzzled with percentages
hi everyone.. i have a simple but puzzling problem that i came across. just read the example:

say you have high-low-mid situation for say expectations for products..

so, you ll have :
Low:10
mid:20
high:30

total=60

Now, say we want to check what the 30% would be of that total (simple answer..) = 18

the problem begins now..:
say we assign some percentages for this low-mid-high averaging to 30%..just to check

so, say aagain that we assign further that:
low: 10% of the 10 above (=1)
mid:30% of the 20 (=6)
high:50% of 30..(=15)

the average of these percentages is 30% but the result is 22!!..
i can see that the last 30% does not represent the 30% of the total directly...but then again..it s 30%...well once again i am puzzled to explain it can u please tell me the reason?
• Oct 31st 2007, 02:52 AM
janvdl
You used 30% on all the numbers in your first calculation, not an AVERAGE of 30%.

You did the first one this way:

$\displaystyle ( \frac{30}{100} \times 10) + ( \frac{30}{100} \times 20) + ( \frac{30}{100} \times 30) = 18$

And the second one this way:

$\displaystyle ( \frac{10}{100} \times 10) + ( \frac{30}{100} \times 20) + ( \frac{50}{100} \times 30) = 22$

And therefore you will get two very different answers...
• Oct 31st 2007, 03:11 AM
tsatsos007
thanks.. i still got a little confused at the beginning but i figured out the whole thing with yr clue.
yes..indeed..that is how i first thought abt it,by using weight for each value.. but the wording trick is that since the first calculation represents 30% of the values...and then the second represents 30% of the values too...why not match!?i think i m getting confused again!lol
• Oct 31st 2007, 03:12 AM
janvdl
Quote:

Originally Posted by tsatsos007
thanks.. i still got a little confused at the beginning but i figured out the whole thing with yr clue.

You'll see I edited my post, check if it makes a little more sense now...
• Oct 31st 2007, 03:18 AM
tsatsos007
i think i found the explanation in words..it IS that it represents 30% in both cases..yet with different weighting for the values!right?
• Oct 31st 2007, 03:20 AM
janvdl
Quote:

Originally Posted by tsatsos007
i think i found the explanation in words..it IS that it represents 30% in both cases..yet with different weighting for the values!right?

No, my logic says it's not 30%.
It's 30% in the FIRST case yes.
In the second it's 10% , 30% , 50%.
• Oct 31st 2007, 03:24 AM
tsatsos007
why... since 10+30+50=90...then, 90/3=30..so, 30%..
• Oct 31st 2007, 03:26 AM
janvdl
Quote:

Originally Posted by tsatsos007
why... since 10+30+50=90...then, 90/3=30..so, 30%..

It just doesn't work that way. In the first one you applied 30% to every value.

In the second one you applied different percentages to every value. It just won't work. It's maths! :D
• Oct 31st 2007, 03:27 AM
tsatsos007
;-)