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

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Manager
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What is the average (arithmetic mean) height of the n people [#permalink]  14 Jul 2010, 12:35
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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
[Reveal] Spoiler: OA
Manager
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Re: Mean of group [#permalink]  14 Jul 2010, 12:43
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]  14 Jul 2010, 12:50
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 ????

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Re: Mean of group [#permalink]  14 Jul 2010, 13:06
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 ????

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]  14 Jul 2010, 14:40
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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 ????

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.

Hope it helps.
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Manager
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Re: Mean of group [#permalink]  14 Jul 2010, 15:33
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]  15 Jul 2010, 00:20
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]  15 Jul 2010, 07:06
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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]  09 Oct 2010, 11:46
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.

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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Re: Mean of group [#permalink]  09 Oct 2010, 11:54
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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.

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: What is the average (arithmetic mean) height of the n people [#permalink]  03 Jun 2013, 01:42
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Re: What is the average (arithmetic mean) height of the n people [#permalink]  03 Jun 2013, 04:37
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Stmt 1 : Average = Sum/Total number of items

Hence, Average * Total number of items = Sum

1 foot = 12 inches, therefore the average height of n/3 people is 74.5 inches

Sum of heights of n/3 people is 74.5n/3

Rest of the people = total – n/3 = (n – n/3) = 2n/3

Similarly, the average height of the 2n/3 people is 70 inches

Hence, the sum of the heights of 2n/3 people is 140n/3

Sum of both groups = (74.5n/3)+ (140n/3) = 214.5n/3

Average = Sum/Total number of items

therefore, (214.5n/3)/n = 214.5n/3n = 71.5 inches

Hence, stmt 1 is sufficient

Stmt 2 : This statement gives us the sum of the heights of all the people in the group but the exact value of n is unknown

Since we can not determine the average height of the group, this statement is insufficient

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Re: What is the average (arithmetic mean) height of the n people [#permalink]  03 Aug 2014, 18:03
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Re: What is the average (arithmetic mean) height of the n people   [#permalink] 03 Aug 2014, 18:03
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