Hi this one is from page 160.
The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4 inches.
Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the students in the class?
Indicate all such statements
A) The tallest male student in the class is 5.8 inches taller than the tallest female student in the class.
B) The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class.
C) The average (arithmetic mean) height of the male students in the class is 4.6 inches greater than the average height of the female students in the class.
How to go about this one?
Thanks
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- jen
- Manhattan Prep Staff
- Posts: 51
- Joined: Mon Mar 28, 2011 9:50 am
Re: Heights
Hi there,
That's a great question. We begin with the range for the males and the range for the females. That's great, but we need to know how (or if) the ranges overlap. Here's what I mean:
Imagine I say that the Smith children have an age range of three years and the Jones children have an age range of five years. That's nice, but ... maybe the Smith kids are 1 and 4, and the Jones kids are 1 and 6 (so there's a pretty big overlap), or maybe the Smith kids are 1 and 4 and the Jones kids are 10 and 15 (so no overlap at all). We need to know the overlap of the ranges in order to know the overall range. In order to know the overlap of the ranges, any of the following would be sufficient:
gap between shortest female and shortest male
gap between shortest female and tallest male
gap between tallest female and shortest male
gap between tallest female and tallest male
Any of those quantities would tell us how the two ranges line up!
A) Gives us exactly the information we need! If the tallest male is 5.8 inches than the tallest female, then the range is simply whatever the range for the females is, plus another 5.8. (This is true because we can also verify that the shortest female is indeed shorter than the shortest male.)
B) Medians just aren't going to tell us ranges. Ever.
The median is really just the middle person's height. There is nothing in the problem about the heights being equally distributed. That is, if the range of female heights is 13.2 and it turns out that the actual heights range from 60 to 73.2 (for example), the median could actually be anything in that range (for instance, maybe there are three females with heights 60, 60, and 73.2, so the median would actually be 60!)
C) An average can't tell you a range. Ever.
Range is the difference between the highest and lowest values. Just as the sets 5, 5, 5, and 0, 5, 10 have the same average but different ranges, knowing an average just can't tell you a range.
I have seen a lot of GRE questions that test the idea that "stats don't tell you other stats." Except in special cases, such as a set in which all the numbers are identical, a mean won't tell you a median, a median won't tell you a range, a range won't tell you a mean, etc. The GRE seems actually pretty obsessed with testing this concept.
Sincerely,
Jen
That's a great question. We begin with the range for the males and the range for the females. That's great, but we need to know how (or if) the ranges overlap. Here's what I mean:
Imagine I say that the Smith children have an age range of three years and the Jones children have an age range of five years. That's nice, but ... maybe the Smith kids are 1 and 4, and the Jones kids are 1 and 6 (so there's a pretty big overlap), or maybe the Smith kids are 1 and 4 and the Jones kids are 10 and 15 (so no overlap at all). We need to know the overlap of the ranges in order to know the overall range. In order to know the overlap of the ranges, any of the following would be sufficient:
gap between shortest female and shortest male
gap between shortest female and tallest male
gap between tallest female and shortest male
gap between tallest female and tallest male
Any of those quantities would tell us how the two ranges line up!
A) Gives us exactly the information we need! If the tallest male is 5.8 inches than the tallest female, then the range is simply whatever the range for the females is, plus another 5.8. (This is true because we can also verify that the shortest female is indeed shorter than the shortest male.)
B) Medians just aren't going to tell us ranges. Ever.
The median is really just the middle person's height. There is nothing in the problem about the heights being equally distributed. That is, if the range of female heights is 13.2 and it turns out that the actual heights range from 60 to 73.2 (for example), the median could actually be anything in that range (for instance, maybe there are three females with heights 60, 60, and 73.2, so the median would actually be 60!)
C) An average can't tell you a range. Ever.
Range is the difference between the highest and lowest values. Just as the sets 5, 5, 5, and 0, 5, 10 have the same average but different ranges, knowing an average just can't tell you a range.
I have seen a lot of GRE questions that test the idea that "stats don't tell you other stats." Except in special cases, such as a set in which all the numbers are identical, a mean won't tell you a median, a median won't tell you a range, a range won't tell you a mean, etc. The GRE seems actually pretty obsessed with testing this concept.
Sincerely,
Jen
- mkamony
- Students
- Posts: 14
- Joined: Sun May 22, 2011 11:47 am
Re: Heights
Thanks Jen! Appreciate your help
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: Heights
Jen's the best! Glad your question was answered!
-t
-t
4 posts Page 1 of 1