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01 Sep 2009, 15:10
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In a company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than$40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn$49,000 a year. What is the median salary for the company?

60% of the employees earn less than $50,000 a year => 40% earn greater than 50,000 a year. 60% of the employees earn more than$40,000 a year
=> 40% earn less than 40,000 a year..

Let there are 100 employess
then, to calculate median we need salary of 50th employee and 51th employee.

Then, median = (salary of 50th employee + salary of 51th employee)/2
40 people<40000 $40,000 20 people$50,000 40 people > 50,000
--------------------------*----------------*----------------------

Salary of 11 people = 43,000
Salary of 5 people = 49,000
whtever, be the case, 50th and 51th salary would be 43,000 and 43,000

Hence, $$median = \frac{(2*43000)}{2}$$
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20 Oct 2009, 18:37
Absolutly did'nt grasp the concept guys..Please explain..

In a company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than$40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn$49,000 a year. What is the median salary for the company?

Quote:
60% of the employees earn less than $50,000 a year => 40% earn greater than 50,000 a year. 60% of the employees earn more than$40,000 a year
=> 40% earn less than 40,000 a year..

Let there are 100 employess
then, to calculate median we need salary of 50th employee and 51th employee.

Then, median = (salary of 50th employee + salary of 51th employee)/2

I understood till here..after that it all went above my head:(
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Re: In a company 60% of the employees earn less than $50,000 [#permalink] ### Show Tags 20 Oct 2009, 19:32 2 This post received KUDOS Expert's post tejal777 wrote: Opening this thread again.. Absolutly did'nt grasp the concept guys..Please explain.. In a company 60% of the employees earn less than$50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn$43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company? Quote: 60% of the employees earn less than$50,000 a year
=> 40% earn greater than 50,000 a year.

60% of the employees earn more than $40,000 a year => 40% earn less than 40,000 a year.. Let there are 100 employess then, to calculate median we need salary of 50th employee and 51th employee. Then, median = (salary of 50th employee + salary of 51th employee)/2 I understood till here..after that it all went above my head:( Let's consider this problem in the following way: 1. We have set of 100 terms: a1, a2, ..a100. 2. 60 terms are <50 3. 60 terms are >40 4. 11 terms =43 5. 5 terms =49. Q what is median of the set? Clearly as we have even number of terms (100) in the set, the median would be (a50+a51)/2. So we should determine a50 and a51. From 2 and 3 we can conclude that 20 terms: from a41 to a60 are in the range 40-50. Or 40<a41<=a42<=...<=a60<50. From this it's already clear that median will be <50. Plus we know 16 terms from this 20 terms (a41-a60): 11 terms=43 and 5 terms=49. 4 terms out of 20 (a41-a60) are unknown: they can be in the range 40-43, 43-49 or 49-50 (all or any combination of them in any of these three ranges). BUT they doesn't matter because in ANY case a50 and a51 would be 43. You can not move 11 terms, which are 43, in the range of a41 to a60, so that a50 and a51 not to be 43. a50=43, a51=43 --> median=43 Answer: A. _________________ Manager Joined: 19 Apr 2010 Posts: 210 Schools: ISB, HEC, Said Followers: 4 Kudos [?]: 75 [0], given: 28 Re: In a company 60% of the employees earn less than$50,000 [#permalink]

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07 Oct 2010, 07:18
Hi Bunuel,

I am not able to understand this problem

You are saying From 2 and 3 we can conclude that 20 terms: from a41 to a60 are in the range 40-50 how it is so?
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07 Oct 2010, 07:54
Got it Bunuel.. Thanks a lot
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19 May 2011, 00:30
good concept used here.
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08 Sep 2014, 02:23
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24 Nov 2015, 01:35
I reasoned like this:

40% over 50
40% less than 40

So we only care about the middle, 40 - 50. To see which one would be in the middle.

From the above, we know that 20% are from 40 to 50.
Also, 11% are 43

11 is more than half of 20. It means 43 will always appear in the middle, no matter what.

So the median is 43.
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Re: In a company 60% of the employees earn less than $50,000 [#permalink] ### Show Tags 28 Dec 2015, 03:59 I used a number line method here. 60 percent make more than 40,000. THis implies, 40 percent make less than 40,000 60 percent make less than 50,000 There is this 20 percent that makes between 40 and 50K and is in the mid 20 percentage, of which 11 percent is 43,000 So, 43,000 is always at the 50th position. Hence, the median _________________ Fais de ta vie un rêve et d'un rêve une réalité Re: In a company 60% of the employees earn less than$50,000   [#permalink] 28 Dec 2015, 03:59
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