Set 22 Q2 Averages

[VIP]

What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?

(1) The average height of the students in class X is 120 centimeters.
(2) The average height of the students in class X and class Y combined is 126 centimeters.

I picked "C", but the OA is E. My logic was that you could do (120 + Y)/2=126. Find Y and then have the ratio.

I guess since they do not specify the size of each class...the average of the two combined classes combined could be skewed, so you can not use the equation i used.
Is this right?

[LegoLife]

My answer is E.

Let
X = {120,120}
Y = {132,132}

Total average = 126.
Ratio = 120/132.

Now, if another student of height 126 joins class Y.
X = {120,120}
Y = {132,132,126}

Total average = 126.
Ratio = 120/130.

Now, you can see that though the total average is the same, the ratio will differ according to the average within each class.

[VIP]

Cool...Thanks!

[bads123]

Originally Posted by VIP

Cool...Thanks!

Your logic would be correct if number of students in both class is same.

Yes, this is the case with weighted average. In "average" if weights are all equal we can use the formula a+b + .../ (number of observations), but if we donot know the weights we can never assume them to eb the same