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# Median problem

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Intern
Joined: 28 Oct 2010
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Median problem [#permalink]  28 Oct 2010, 14:44
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Question Stats:

0% (00:00) correct 100% (00:59) wrong based on 3 sessions
Hello,

Q:125 passengers commute everyday. Is the median commute per day less than 40km ?

1) 62 passengers commute within 35 kms from their house
2) 63 passengers commute within 45 kms from their house

What I understand from this question is :
what is the average communte. So can we calculate it like this --->

62*35 = 2170
63*45 = 2835

then add them up and divide it by 125 to get the answer 40.04

So the median commute per day is not less than 40. .. Answer

IS IT RIGHT?

Thanks
Intern
Joined: 28 Oct 2010
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Re: Median problem [#permalink]  28 Oct 2010, 14:47
I found this explanation on some forum. I dont understand what this guy is saying.

For this question, you will need to know that the median is the middle number of a series of numbers arranged from smallest to largest.

From the statement, we know that we're dealing with 125 commuters. The median is the middle number, which is 63. Thus, the question is asking "Does the 63rd commuter travel less than 40km per day ?"

Using statment (1), all we know is 62 passengers commute within 35km from their house. But we do not know how these 62 passengers are picked (It could be any order, such as, 1st, 4th, 7th, 9th commuter)

The same problem with statement (2).

Using both (1) and (2), we can re-arrange the commuters from 1st to 125th and only know that the median, which is the 63rd commuter could be travelling anywhere between 35km and 45km (since we do not know if this 63rd commuter originally came from the 62 passenger that lived within 35km of their house, or he/she came from the 63 passengers that lived within 45km of their house), and so we do not know if the 63rd commuter does less than 40km a day.
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Re: Median problem [#permalink]  28 Oct 2010, 15:03
Expert's post
abdullahkhan19 wrote:
Hello,

Q:125 passengers commute everyday. Is the median commute per day less than 40km ?

1) 62 passengers commute within 35 kms from their house
2) 63 passengers commute within 45 kms from their house

What I understand from this question is :
what is the average communte. So can we calculate it like this --->

62*35 = 2170
63*45 = 2835

then add them up and divide it by 125 to get the answer 40.04

So the median commute per day is not less than 40. .. Answer

IS IT RIGHT?

Thanks

You are calculating the mean (average). The question asks for the median, not the average.

Here we have a set of 125 values. The median, the number in the middle of our set, will be the 63rd largest (or 63rd smallest - that's the same thing). We know from Statement 1 that 62 values are less than 35, but we don't know about the 63rd smallest value. From Statement 2, we know that we have 63 values which are less than 45, but we don't know if the 63rd smallest is less than 40. Even combined, while we know the 63rd smallest is somewhere between 35 and 45, we don't know if it's less than 40, so the answer is E.
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Intern
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Re: Median problem [#permalink]  28 Oct 2010, 15:36
Okay .. Now I get it .. Thanks alot
Re: Median problem   [#permalink] 28 Oct 2010, 15:36
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