Statistics in CR - per unit of something

[aditya20012005]

Hi,
In the Critical Reasoning Problems that deal with Numbers and Statistics what does the "per unit of something" imply?

Eg, If we have the premise such as -
"In 1990 the cars per 1000 residents in a city X was 10% . In 2012 the cars per 1000 residents is the city X was 5%."

Can the conclusion be - the number of cars in city X has declined.

I am confused in comprehending the conclusion.

1. The conclusion seems correct because in 1990 there were 10% cars and in 2012 that fell to 5% per 1000 residents. The fact that the number of residents is standardized (1000) so the ratio of cars/residents for 1990 and 2012 seem comparabe.

2. On the other hand the conclusion seems incorrect because in 1990 there were 100 cars for 1000 residents and in 2012 there were 50 cars for 1000 residents.

-Point 2 seems incorrect, if the population of city X in 1990 was 1000 residents and in 2012 the population increased to 4000 residents then the number of cars in 2012 become 200, which is more than the number of cars in 1990.

I think I am missing a concept here.

And does the reasoning change if percentage is repalced by numbers:
"In 1990 the cars per 1000 residents in a city X was 10. In 2012 the cars per 1000 residents is the city X was 5."

Please help.. Thanks!!

[tim]

your explanation of point 2 gets to the heart of this issue. if the population more than doubles, then there could still be more cars in absolute terms even if the rate drops from 10 to 5. "per unit" implies division - a ratio - as you have correctly identified. as to your final question, you would actually need to use numbers rather than percentages. the use of percentages in the original example turns it into nonsense..

[aditya20012005]

Hi Tim,

Thank you for the explanation. My thought process is now somewhat more better regarding the stats in CR...

I am going to view "Thursday's With Ron' videos that deal with "Problems with Numbers and Statistics in CR" for the same.

I have one more question: (sorry to ask this before viewing the video)

What role does the "per unit of something" play in an argument?
I have heard that it removes the effect of changing denominator form the equation.

Can you please elaborate.

[jlucero]

I'm not 100% sure I understand your question. The units will make all the difference in a conclusion, but it depends on what information they give you and what conclusion they are trying to make. From the example you gave, you picked out that the unit "cars per 1000 residents", which is helpful if you are looking at a "per 1000 residents" statistic, but less helpful if you are looking at the actual number of cars, residents, or anything else that is an absolute number.

[aditya20012005]

Hi Joe,

I do get your point here.

Let me articulate my comprehension of the following argument:
"In 1990 the cars per 1000 residents in a city X was 10. In 2012 the cars per 1000 residents is the city X was 5.

This argument sufficiently provided the data that the Car density in city X reduced from 10 to 5 in the time period starting 1990 to 2012.

But we can not derive the conclusion that the absolute number of cars in city x fell or grew in the time period starting from 1990 to 2012.

[RonPurewal]

aditya, there's little point in trying to memorize "rules" for these kinds of things (if indeed that's what you're trying to do here). instead, just find the right examples - i.e., instances of the same kinds of statistics that happen to be more intuitive for you - and then just make the appropriate analogies.

e.g.
the total GDP (= roughly, the total output of the whole economy) of the US is approximately US$15 trillion.
the total GDP of Canada is approximately US$1.7 trillion.
it should be clear, though, that these statistics do not tell us that Canada is dirt poor compared to the US; rather, they just indicate how much bigger the US is.

if you look at the GDP per capita, on the other hand, that's US$50,500 for Canada and US$48,300 for the US. These are comparable numbers, indicating that, on a per-person level, the economies are comparable.

to make this example more like the one in the problem, you could look at "GDP per 1000 people" instead. that'd be the same thing as the latter statistic above, except magnified by 1000 times (i.e., US$50.5 million for Canada, US$48.3 million for the US). still measures the per-person figures.

if you understand these examples, then just internalize the examples -- our brains work much, much better with analogies than with "rules", which are rarely useful unless you're trying to program a computer.

[aditya20012005]

Hi Ron,

Thank you for that insight.
And, yes I was trying to create a rule based approach to the statistical CR problems. (I am a software professional, so it might explain....)

I am now trying to comprehend arguments in a more real world way, but sometimes confusion is too much, and so I look for some rule based way that might satisfy GMAT.

Even when typing this response, I am trying to be as GMAT correct as possible. I hope that in my reply there are very few grammatical mistakes...

Back to the topic, Statistics in CR. I thought of a real world situation. Please let me know whether I make sense with this one:

Argument is:
On the GMAT test, over past few years, there has been an increase in the number of people who have a score of 700+.
From the online forums and online testimonials also we can see a significant increase in number of people reporting a 700+ score. It shows that the proportion of people getting a 700+ score has increased over the past few years.

The flaws that I have noticed are:
1. The actual number of 700+ scoring people is not compare to the proportional increase. And also because 700+ score means 90th percentile, which has been the same in the past few years, it means that the proportion is fixed.
It can be the case that earlier 1 out of 10 got a 700+ and now 10 out of 100 get a score of 700+. So numerically 10 greater than 1 is correct, as stated in the argument.

2. There is a statistical flaw. The survey sample is limited to online forums and online testimonials. Maybe a few years back people had less access to internet. Also, maybe only those people share their scores who get a 700+ and other do not, implying a bias in the survey.

Thanks

[tim]

you did a fairly good job with the grammar in your post BTW. thanks for trying; it makes your post easier to read and is good practice!

from your example, you seem to have a good handle on the issues at work here. good job, and let us know if you have any further questions..