VolatilitySmile wrote:
Using the method
KarishmaB had written about a long time ago.
(Cannot add the article here because of some technical issue but do checkout Bunuel's Ultimate GMAT Quantitative Megathread under "Stats Made Easy" and you can find her article there.)
We will solve this problem using the number line.
So, the question is asking us to find a mean.
The two numbers provided are 750 and 780.
Assume a mean between these, I'm gonna go with 765 because it is
equidistant from 750 and 780.
Now, given it is equidistant how far out is 750 from 765 and 780? 15 spaces on either side i.e. $15 on either side in this case.
They also gave information regarding it's
weights:
6 pay cheques for $750
20 pay cheques for $780
Side tracking for a moment :You can
intuitively say that the weight towards $780 is
greater than towards $750 so the
first three options are out of the question right away.
Now,
The left side of $765 we have six pay cheques, hence...
6 pay cheques x $15= $90
On the right side of $765 we have twenty pay cheques, hence...
20 pay cheques x $15 = $300
(While using this method ALWAYS subtract the RHS with the LHS, if it's negative then you need to move down the number line instead of up)
Now $300 - $90 = $210
We need to "evenly spread" this $210 over the 26 pay cheques.
So $210 / 26 = 8.07 ~ 8
We need to move up the number line.
Now move 8 spaces right to $765 to get $773.
Final answer $773.
I suggest you give Karishma's article a read.
VolatilitySmileThat's great use of the deviations from mean concept.
A couple of further notes:
Since we know that there are more numbers at 780, let's start with the assumed mean as 770. It will lead to smaller calculations. Of course the method followed and the answer obtained would be the same.
Also an interesting way to apply your weighted average formula to reduce calculations would be to shift the scale 750 units to the left.
750 ----- Avg --- 780
Let me move it 750 units to the left: 0 ------- Avg ---30
\(\frac{6}{20} = \frac{(30 - Avg)}{(Avg - 0)} \)
\(\frac{26}{20} = \frac{30}{Avg}\)
Avg = 600/26 = 23
So the actual average = 750 + 23 = 773 (move it back 750 units to the right)
Think about why it works.