Absolute Difference and Proportional Difference

[jack2010]

Hi, first time here, hoping clear up my fuzzy thinking regarding 'absolute' and 'proportional' differences. Example question:

Table showing percentage of university & pre-school students fitting into particular category

	University	Pre-School
Cat A	36%	60%
Cat B	20%	10%
Cat C	12%	9%
Cat D	8%	2%
Cat E	3%	2%
Cat F	2%	2%
Cat G	1%	0%
Cat H	18%	16%
Total	379,000 (100%)	88,000 (100%)

Question 1: Excluding Cat A and Cat B, which Category showed the greatest proportional difference between University and Pre-School

My answer: I read this to mean what is the greatest ratio of Universityre-School so i looked at:

	University	Pre-School	Ratio	Value
Cat A	36%	60%	----	----
Cat B	20%	10%	----	----
Cat C	12%	9%	4:3	1.3
Cat D	8%	2%	4:1	4
Cat E	3%	2%	3:2	1.5
Cat F	2%	2%	2:1	2
Cat G	1%	0%	0	0
Cat H	18%	16%	9:8	1.125
Total	379,000 (100%)	88,000 (100%)

To me, the answer is Cat D. Am i right or way off the mark?

Question 2: Looking at the whole sample, which category, excluding Cat G, showed the smallest absolute difference between University and Pre-School

Again, to me, this is asking "what are the raw numbers and what is the smallest difference?"

So isnt this just Cat F - you can tell by looking at the chart but if not, my working would be turing everything into numbers and getting:

To me, the answer is Cat D. Am i right or way off the mark?

	University	Pre-School	Difference
Cat A	136440	52800	83640
Cat B	75800	8800	67000
Cat C	45480	7920	37560
Cat D	30320	1760	28560
Cat E	11370	1760	9610
Cat F	7580	880	6700
Cat G	3790	0%	3790
Cat H	68220	14080	54140
Total	379,000 (100%)	88,000 (100%)

Thanks in advance for any advice

 

[jack2010]

I think you are overcomplicating this. In my mind:

Question 1: The answer is Category D as you say because 8% - 2% = 6% and no other percentage difference is that great. The point is that a percentage already is a proportion between the number in that category and the total population.

Question 2: The answer is Category G. 3790 - 0 = 3790 is the smallest absolute difference there is. Why make it more complicated?

If I have it wrong, someone will be along to say so.

Thanks for the reply Jeff, I wouldn't be surprised if I was overcomplicating this - these are just meant to be 'relatively hard' test, so I'm sceptical of obvious answers!

Just a minor point to your answer to Q2 - the questions states 'excluding Cat G', therefore I would assume you get the same answer as me, Cat F

Thanks again.