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median

by cuty » Thu Mar 03, 2011 7:28 am
Amt earned per day No of days
$96 4
$84 7
$80 4
$70 3
$48 2
A student worked for 20 days for each of the amounts shown inthe first row of the table, th 2nd row gives the No of days that the student earned that amount. What is the median amount of money that the student earned per day for the 20 days?

a) 96
b) 84
C) 80
D)70
E)48
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by Rich@VeritasPrep » Thu Mar 03, 2011 7:37 am
The median simply refers to the middle term in an ORDERED list of numbers. For example, if you were given this list...

3, 8, 2, 1, 6

...first you'd order the numbers, then pick the middle value...

1,2,3,6,8

The median would be 3, because 3 is located at the center of the list.

Or, if the number of terms is even, then the median is the AVERAGE OF THE MIDDLE TWO TERMS. For example...

3,5,9,11,16,20

...the middle two terms are 9 and 11. Their average is 10, so the median of the list is 10.

In this problem, the student has worked 20 days, so once we've put the numbers in order, the median will be the average of the 10th and 11th terms.

The student earned $48 for 2 of the days, $70 for 3 of the days, and $80 for 4 of the days. That's a total of 9 days, so all we need to do is find the next dollar amounts in the list (10th and 11th items).

The next 4 items in the list will be $84, so both the 10th and 11th items are $84, which means the average of the two terms is $84. That is our median.

Ans: B

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by Night reader » Thu Mar 03, 2011 7:41 am
:) plz reveal the source (ambiguity involved)
this problem can be solved by only keeping the order given in a table --> the number of 20 days makes its median within 7 days (4+7=11) - hence $84 is our answer

IOM B
cuty wrote:Amt earned per day No of days
$96 4
$84 7
$80 4
$70 3
$48 2
A student worked for 20 days for each of the amounts shown inthe first row of the table, th 2nd row gives the No of days that the student earned that amount. What is the median amount of money that the student earned per day for the 20 days?

a) 96
b) 84
C) 80
D)70
E)48
wanna help guyz
[/list][/quote]
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
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by Night reader » Thu Mar 03, 2011 7:44 am
@razz, this problem cannot be solved unless additional assumption is made by test-taker :( We are given number of values in the table but are not suggested that the values are ordered!
raz1024 wrote:The median simply refers to the middle term in an ORDERED list of numbers. For example, if you were given this list...

3, 8, 2, 1, 6

...first you'd order the numbers, then pick the middle value...

1,2,3,6,8

The median would be 3, because 3 is located at the center of the list.

Or, if the number of terms is even, then the median is the AVERAGE OF THE MIDDLE TWO TERMS. For example...

3,5,9,11,16,20

...the middle two terms are 9 and 11. Their average is 10, so the median of the list is 10.

In this problem, the student has worked 20 days, so once we've put the numbers in order, the median will be the average of the 10th and 11th terms.

The student earned $48 for 2 of the days, $70 for 3 of the days, and $80 for 4 of the days. That's a total of 9 days, so all we need to do is find the next dollar amounts in the list (10th and 11th items).

The next 4 items in the list will be $84, so both the 10th and 11th items are $84, which means the average of the two terms is $84. That is our median.

Ans: B

Hope this helps!
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by Rich@VeritasPrep » Thu Mar 03, 2011 8:00 am
Hey Night reader,

A median by it's very definition is the midpoint of an ordered list. So when we're asked specifically for a median, we don't have to assume that the list we'll look at is ordered. We know it must be ordered.

The list given in the prompt does not specify on which days the student earned which amounts. But it doesn't matter, because once we're asked for the median, we know we MUST put the dollar amounts in ascending order.
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by Night reader » Thu Mar 03, 2011 8:21 am
A student worked for 20 days for each of the amounts shown in the first row of the table, the 2nd row gives the No of days that the student earned that amount. What is the median amount of money that the student earned per day for the 20 days?

a) 96
b) 84
C) 80
D)70
E)48
raz1024 wrote:Hey Night reader,

A median by it's very definition is the midpoint of an ordered list. So when we're asked specifically for a median, we don't have to assume that the list we'll look at is ordered. We know it must be ordered.

The list given in the prompt does not specify on which days the student earned which amounts. But it doesn't matter, because once we're asked for the median, we know we MUST put the dollar amounts in ascending order.
$96 4
$84 7
$80 4
$70 3
$48 2
as you see from above intercept in the problem we are given NOT ascending order BUT descending order, shall we put them in ascending order?
we MUST put the dollar amounts in ascending order
then how we take our table as ordered in the value set?

anyway, we are on different pages about this question

@cuty please reveal the source
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by Rich@VeritasPrep » Thu Mar 03, 2011 8:33 am
Again, the list you're given might not be ordered in its original form, but if you are asked for the median, you must put the list in order before finding the result.

As an example, if I gave you this list...

2, 78, 22, 4, 8

...and then I asked you for the median, the correct answer would NOT be 22. A median is by definition the middle of an ordered list. So first rearrange...

2, 4, 8, 22, 78

...then pick the median, in this case 8.

And it does not matter whether the list is ascending or descending. The result will be the same. The geographic center of an ordered list of numbers does not vary if you change the numbers from ascending to descending.

You can test this with basic examples:

2,4,7,12,13 or 13,12,7,4,2 (median is 7 either way)

3,5,7,9,12,15 or 15,12,9,7,5,3 (median is 8 either way)

Hope this makes sense!
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by Night reader » Thu Mar 03, 2011 8:45 am
apparently this question was rephrased
NOT row BUT column
no need to dig more into this question, for example MGMAT experts on their website never provide their comments/solutions until the source is revealed
cuty wrote:Amt earned per day No of days
$96 4
$84 7
$80 4
$70 3
$48 2
A student worked for 20 days for each of the amounts shown inthe first row of the table, th 2nd row gives the No of days that the student earned that amount. What is the median amount of money that the student earned per day for the 20 days?

a) 96
b) 84
C) 80
D)70
E)48
wanna help guyz
[/list][/quote]
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
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by cuty » Fri Mar 04, 2011 12:19 am
@ night reader.. This is from GMAT PREP official software , Practice test No-1
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by BarryLi » Fri Mar 04, 2011 12:23 am
Interesting, on the Practice Test I got for GMAT software I had a similar question, but instead of amounts earned over 20 days it was a range of scores (i.e. 96-100%, 84-95%) from 20 students.
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