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#### A student worked for 20 days....

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 Post subject: A student worked for 20 days....  Posted: Sat Mar 27, 2010 7:58 am
 Students

Posts: 3
 A student worked for 20 days. For each of the amounts shown in the 1st row of the table, the 2nd row gives the no. of days at the student earned that amount. What is the median amount of money that the student earned per day for 20 days?amt earned/day : 96 84 80 70 48no. of days...... : 4 7 4 3 2a) 96b) 84c) 80d) 70e) 48How do i go about to calculate the median in this case..is there something called weighted median as well..please explain..

 Post subject: Re: Median..  Posted: Sat Mar 27, 2010 8:11 am
 Students

Posts: 33
 Arranging amount earned in ascending order with the number of days,48-270-380-484-796-4median = (amount earned in 10th day + amount earned in the 11th day)/2 = (84+84)/2 = 84.

 Post subject: Re: A student worked for 20 days....  Posted: Sat Mar 27, 2010 10:20 am
 Students

Posts: 3
 thanks..

 Post subject: Re: A student worked for 20 days....  Posted: Tue Apr 27, 2010 12:41 pm
 ManhattanGMAT Staff

Posts: 6864
Location: San Francisco
 Thanks, thoppaepriyanka, if it's confusing to look at the list in the way that thoppae wrote it, you can also just literally list them all out, from smallest to largest, and count your way to the middle. (And, of course, in this case, you actually need to average the middle two numbers beacuse you have an even number of terms.) _________________Stacey KoprinceInstructorDirector of Online CommunityManhattanGMAT

 Post subject: Re: A student worked for 20 days....  Posted: Mon Dec 12, 2011 11:15 am
 Forum Guests

Posts: 29
 The only way to go about solving this question is to know the concept of median. I somehow forgot to apply that while attempting the question. (I got carried away by that caution-"Always arrange the numbers in ascending before calculating the median".)But anyway-the way to solve it is this:The total number of days are 20 (this is given in the question, but if you want, you can also add the number of days).The "rule" says that if the number is even, the median will be the mean of the two middle terms. In this case the middle terms will be 10th and 11th terms. Now here comes the tricky part. Start by "adding" the days in a tabular format:4+7=11 (these are the "first two"). This means that the median will "lie in this range" (sorry for the language-can't find any other phrase).So the number that "lies in this range" is \$84. And that, is the answer.Perhaps Ron or Stacey can add more depth to this explanation. Also, they might explain why that "rule" of arranging numbers in ascending order is not used here (my guess is that the rule is not used because the "amount earned" has a "frequency" attached to it.)

 Post subject: Re: A student worked for 20 days....  Posted: Sun Dec 18, 2011 11:43 pm
 ManhattanGMAT Staff

Posts: 2394
 pratik.munjal wrote:Perhaps Ron or Stacey can add more depth to this explanation. Also, they might explain why that "rule" of arranging numbers in ascending order is not used here (my guess is that the rule is not used because the "amount earned" has a "frequency" attached to it.)Actually, Stacey did suggest listing out the values in ascending order. Please see what we have below. I would look at this and say to myself, "since there are twenty numbers the median will be the average of numbers 10 and 11. The three smallest pay numbers are two \$48s, three \$70s, and four \$80s. That is nine numbers. Thus, I know that numbers 10 and 11 must be the next two numbers, which will be in the \$84 category.Day Salary1 482 483 704 705 706 807 808 809 8010 8411 8412 8413 8414 8415 8416 8417 9618 9619 9620 96 _________________Jamie NelsonManhattanGMAT Instructor

 Post subject: Re: A student worked for 20 days....  Posted: Thu Jul 05, 2012 3:57 pm
 Forum Guests

Posts: 125
 jnelson0612 wrote:pratik.munjal wrote:Perhaps Ron or Stacey can add more depth to this explanation. Also, they might explain why that "rule" of arranging numbers in ascending order is not used here (my guess is that the rule is not used because the "amount earned" has a "frequency" attached to it.)Actually, Stacey did suggest listing out the values in ascending order. Please see what we have below. I would look at this and say to myself, "since there are twenty numbers the median will be the average of numbers 10 and 11. The three smallest pay numbers are two \$48s, three \$70s, and four \$80s. That is nine numbers. Thus, I know that numbers 10 and 11 must be the next two numbers, which will be in the \$84 category.Day Salary1 482 483 704 705 706 807 808 809 8010 8411 8412 8413 8414 8415 8416 8417 9618 9619 9620 96Hi,I got this approach that you mentioned and I thought of the same. At the same time, I have a doubt. Why do we consider that the days given in the second line are consecutive days. For eg, the student could have earned 80\$ on one day say the 10th and the next one on 12th. I am a little unsure of whether we can arrange the days consecutively since the question statement doesn't mention it anywhere. But otherwise, since the answer would be 80 and the number of days would be a data without purpose, that seems a little too easy and therefore doubtful.Do I seem to make any sense or am I confusing myself here?

 Post subject: Re: A student worked for 20 days....  Posted: Fri Jul 06, 2012 8:38 am
 ManhattanGMAT Staff

Posts: 4410
Location: Southwest Airlines, seat 21C
 they don't have to be literally consecutive days, but when we order them according to which day was worked, after we talk about the 10th day he worked, the next one must be the 11th day he worked. :) let me know if you have any other questions about this one.. _________________Tim SandersManhattan GMAT Instructor

 Post subject: Re: A student worked for 20 days....  Posted: Fri Jul 06, 2012 11:54 am
 Forum Guests

Posts: 125
 Thanks for the explanation but what I don't understand is why do those two days have the wage of 84. They might also have wage of 80 and 96 and then the median might be 88.

 Post subject: Re: A student worked for 20 days....  Posted: Sat Jul 07, 2012 5:03 pm
 ManhattanGMAT Staff

Posts: 2394
 krishnan.anju1987 wrote:Thanks for the explanation but what I don't understand is why do those two days have the wage of 84. They might also have wage of 80 and 96 and then the median might be 88.Hi Krishnan,The median is the absolute middle value of a set of numbers. When we determine a median, we have to first order the numbers in order from smallest to largest. The median is either the middle number (if we have an odd number of numbers) or the average of the two middle numbers) if we have an even number of numbers.I have listed out the values again below. Notice that I listed them from smallest to largest. That is absolutely necessary to be able to identify the median. You can't just have random numbers popping up in different positions. You must put the smallest number and every other identical number, then the next smallest (and every other identical number if there are any, etc.).Please let us know if you need further clarification.Day Salary1 482 483 704 705 706 807 808 809 8010 8411 8412 8413 8414 8415 8416 8417 9618 9619 9620 96 _________________Jamie NelsonManhattanGMAT Instructor

 Post subject: Re: A student worked for 20 days....  Posted: Sat Jul 07, 2012 9:06 pm
 Forum Guests

Posts: 125
 Hi Jamie,Thanks for the clarification. That point is clear to me. We need to sort the elements in ascending order to be able to determine the median. However, I guess I failed to express my doubt clearlyIn the below orderDays Salaries1 482 483 704 705 706 807 808 809 8010 8411 8412 8413 8414 8415 8416 8417 9618 9619 9620 96How do we know the days are related to the salaries? I mean it doesn't mention anywhere in the question that the dates consecutive or the wages are earned in the order mentioned. So the order could as well be as mentioned below1 482 803 844 705 486 807 808 849 7010 8411 8012 7013 8414 8415 8416 8417 9618 9619 9620 96or something like this. I know this would make the question ridiculously unsolvable and I solved it in a manner similar to the one you took up but have this doubt lingering in my mind.

 Post subject: Re: A student worked for 20 days....  Posted: Sun Jul 08, 2012 12:08 pm
 ManhattanGMAT Staff

Posts: 4410
Location: Southwest Airlines, seat 21C
 your concern does not have to do with the specifics of this problem; you seem to be fundamentally misunderstanding what the definition of a median is. put these numbers in order (without the numbers 1-20 if that's what's confusing you), and find what the middle number is. this is what a median is.. _________________Tim SandersManhattan GMAT Instructor

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