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What is the average (arithmetic mean) height of the n people

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What is the average (arithmetic mean) height of the n people [#permalink] New post 14 Jul 2010, 13:35
What is the average (arithmetic mean) height of the n people in a certain group?

(1) The average height of the n/3 tallest people in the group is 6 feet and 2.5 inches and the average height of the rest of the people in the group is 5 feet 10 inches

(2) the sum of the heights of the n people is 178 feet 9 inches
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Re: Mean of group [#permalink] New post 14 Jul 2010, 15:40
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zisis wrote:
what is the average (arithmetic mean) height of the n people in a certain group?

(1) The average height of the n/3 tallest people in the group is 6 feet and 2.5 inches and the average height of the rest of the people in the group is 5 feet 10 inches

(2) the sum of the heights of the n people is 178 feet 9 inches


pranrasvij wrote:
zisis wrote:
pranrasvij wrote:
A is easily the right choice since it gives info about the rest (1-n/3) and n/3 => we dont need the final value of "n" in that case.

B gives us total height but no way to get the mean without more on "n".



so the mean height is the heights given at a ration 1:2 ????

please explain....


yep... all you have to do is the add the 2 heights and divide by 2 to get the mean height => easy to calculate (IMHO!)


Answer to the question is A, but you shouldn't divide the "sum" by 2, you should divide by n.

Weighted \ average=\frac{sum \ of \ weights}{# \ of \ data \ points}, or in our case average \ height=\frac{sum \ of \ heights}{# \ of \ people}.

(1) The average height of \frac{n}{3} people is 74.5 inches and the average height of \frac{2n}{3} people (the res of the people in the group n-\frac{n}{3}=\frac{2n}{3}) is 70 inches --> average \ height=\frac{sum \ of \ heights}{# \ of \ people}=\frac{74.5*\frac{n}{3}+70*\frac{2n}{3}}{n} --> n cancels out --> average \ height=74.5*\frac{1}{3}+70*\frac{2}{3}. Sufficient.

(2) Sum of heights equals to 178 feet 9 inches --> only nominator is given. Not sufficient.

Answer: A.

Hope it helps.
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Re: Mean of group [#permalink] New post 09 Oct 2010, 12:54
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Orange08 wrote:
Bunuel wrote:
(1) The average height of \frac{n}{3} people is 74.5 inches and the average height of \frac{2n}{3} people (the res of the people in the group n-\frac{n}{3}=\frac{2n}{3}) is 70 inches --> average \ height=\frac{sum \ of \ heights}{# \ of \ people}=\frac{74.5*\frac{n}{3}+70*\frac{2n}{3}}{n} --> n cancels out --> average \ height=74.5*\frac{1}{3}+70*\frac{2}{3}. Sufficient.

(2) Sum of heights equals to 178 feet 9 inches --> only nominator is given. Not sufficient.

Answer: A.

Hope it helps.


Hi Bunuel,
The fact that confused me is the word tallest in statement 1.
It says "average height of n/3 [highlight]tallest[/highlight] people in the group is 6 feet 2.5 inches.

Isn't this bit ambiguous? We have no clue how many people to consider in tallest category?


It means that if we order these n people from shortest to tallest and consider \frac{n}{3} tallest people, then their average height would be 74.5 feet.
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Re: Mean of group [#permalink] New post 14 Jul 2010, 13:43
A is easily the right choice since it gives info about the rest (1-n/3) and n/3 => we dont need the final value of "n" in that case.

B gives us total height but no way to get the mean without more on "n".
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Re: Mean of group [#permalink] New post 14 Jul 2010, 13:50
pranrasvij wrote:
A is easily the right choice since it gives info about the rest (1-n/3) and n/3 => we dont need the final value of "n" in that case.

B gives us total height but no way to get the mean without more on "n".



so the mean height is the heights given at a ration 1:2 ????

please explain....
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Re: Mean of group [#permalink] New post 14 Jul 2010, 14:06
zisis wrote:
pranrasvij wrote:
A is easily the right choice since it gives info about the rest (1-n/3) and n/3 => we dont need the final value of "n" in that case.

B gives us total height but no way to get the mean without more on "n".



so the mean height is the heights given at a ration 1:2 ????

please explain....


yep... all you have to do is the add the 2 heights and divide by 2 to get the mean height => easy to calculate (IMHO!)
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Re: Mean of group [#permalink] New post 14 Jul 2010, 16:33
thanks Bunuel.... this is a v good explanation. Sorry- I messed up the divide part!....I knew i was wrong somewhere and came back to fix it !!
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Re: Mean of group [#permalink] New post 15 Jul 2010, 01:20
Bunel - I need one help. This is not a difficult question and it's easy to see that A is sufficient. However I thought B is suf too because the stimulus says N. Now N could be anything. Is it not sufficient to say avg height = sum of heights (given in the second option)/N - N is mentioned in the stem. Why do we have to concern with the actual value of N?
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Re: Mean of group [#permalink] New post 15 Jul 2010, 08:06
dwivedys wrote:
Bunel - I need one help. This is not a difficult question and it's easy to see that A is sufficient. However I thought B is suf too because the stimulus says N. Now N could be anything. Is it not sufficient to say avg height = sum of heights (given in the second option)/N - N is mentioned in the stem. Why do we have to concern with the actual value of N?


Official Guide:

In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity.

Hope it helps.
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Re: Mean of group [#permalink] New post 09 Oct 2010, 12:46
Bunuel wrote:
(1) The average height of \frac{n}{3} people is 74.5 inches and the average height of \frac{2n}{3} people (the res of the people in the group n-\frac{n}{3}=\frac{2n}{3}) is 70 inches --> average \ height=\frac{sum \ of \ heights}{# \ of \ people}=\frac{74.5*\frac{n}{3}+70*\frac{2n}{3}}{n} --> n cancels out --> average \ height=74.5*\frac{1}{3}+70*\frac{2}{3}. Sufficient.

(2) Sum of heights equals to 178 feet 9 inches --> only nominator is given. Not sufficient.

Answer: A.

Hope it helps.


Hi Bunuel,
The fact that confused me is the word tallest in statement 1.
It says "average height of n/3 [highlight]tallest[/highlight] people in the group is 6 feet 2.5 inches.

Isn't this bit ambiguous? We have no clue how many people to consider in tallest category?
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Average Height of N people [#permalink] New post 21 Mar 2012, 11:55
What is the average height of n people in a certain group?

1. The average height of the n/3 tallest people in the group is 6 feet and the average height of the rest of the group is 5 feet.

2. The sum of the heights of the n people is 178 feet.

How come the answer is A and not C?
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Re: Average Height of N people [#permalink] New post 21 Mar 2012, 12:15
enigma123 wrote:
What is the average height of n people in a certain group?

1. The average height of the n/3 tallest people in the group is 6 feet and the average height of the rest of the group is 5 feet.

2. The sum of the heights of the n people is 178 feet.

How come the answer is A and not C?


Merging similar topics. Please ask if anything remains unclear.
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Re: Average Height of N people   [#permalink] 21 Mar 2012, 12:15
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