Math question from practice exam

[fbmagnumopus]

For Q 16 out of 20 on the second math section of the first practice exam, I had a question: How do you know that the number of women in a given age group equal the area under the graph? We only get area as a probabililty in normal distributions when we have relative frequency plotted against data on the x axis. So how come you found the area under the graph in the following explanation? Please advise:

Which of the following is closest to the median age of the U.S. female population in 2009?

29
38
45
53
62


The median age is the age of a person in the middle (half are younger, half are older) of the population stack.

Note that the female graph is on the RIGHT.

Notice that the 12 age groups from 45 to 49 through 100 + show almost a straight-line decline in population from a peak of around 120 hundred thousand 45 to 49 year olds down to essentially 0 100+ year olds. Because of this straight-line decline, we can approximate the number of women who are 45+ as the area under a right triangle:



Since each of the 9 population groups from under 5 through 40 to 44 has about 100 hundred thousand people, it is easy to estimate the total number of women under 45:




So the median age must be under 45, which rules out choices C, D, and E.

Removing100 hundred thousand from the younger group (the 40 to 44 year olds) and adding them to the older group would make the two groups approximately equal in size, so the age of the median U.S. woman in 2009 must be close to 40.

The correct answer is B.

[tommywallach]

Hey There,

Sections are different depending on the student, so I actually need your full name so I can look this one up. Mind popping that in here?

OR you can go into your review and give me the "name" of the question (as it's listed on the review page). I need it word for word to seek it out. Thanks!

-t

[fbmagnumopus]

Hey Tommy,

Here you go

Frank Barron

and just in case :
16 Median Female Age Medium-High 1:06 29:11 DI Stats - Mean & Median

[tommywallach]

Hey FB,

Another way to think of it is this. Add up ALL the age groups (i.e. about 5 people in the top category, then 10 people in the next group, etc.). Add them all up, then figure out where the "middlemost person would be". This will be your correct age group for the median.

Make more sense?

-t

[fbmagnumopus]

Hey Tommy,

I understand your solution and that's the strategy I would've opted for on first instinct myself but here's my problem-

I don't understand the solution given in the exam but I would like to because I feel it has to do with some misunderstanding on my part:

Now to find the number of people above 45 years old, how does finding the area lead to this? Could you please explain how we can apply this in another example?

[tommywallach]

Hey FB,

The truth is I don't dig that methodology either, so I'd avoid it. It doesn't speed things up in any way, and the notion of finding area under the curve is such a throw forward to calculus, which isn't REMOTELY tested on the GRE! I'd just do it the classic way. I can't say I know of a real question that requires the other understanding of things (though if you find one, definitely post it!).

-t

[fbmagnumopus]

Alrightie, shall stick to the simpler method then !

[tommywallach]

Always a good philosophy! : )

-t