median Question from GMAC GMAT Prep test

[arawamis]

Can somebody please explain me how to solve the question below?

Thanks

Amount Earned per day: $96 $84 $80 $70 $48
Number of Days: 4 7 4 3 2

A student worked for 20 days. For each of the amount showed in the first row above, the second row gives the number of days that the student earned that amount (e.g. he earned $96 for 4 days, $84 for 7 days etc.). What is the median amount of money that the student earned per day for the 20 days?
A. $96
B. $84
C. $90
D. $70
E. $48

[sibbineni]

The Ans is B...

I will provide the explanation.. if the ans is correct.

Suggest if iam wrong

[Stuart@KaplanGMAT]

B is the right answer.

The median of a set of numbers is the middle term (if there are an odd # of items) or the average of the two middle terms (if there are an even # of items).

The set in this question has 20 terms, so the median will be the average of the 10th and 11th terms.

If we rearrange the terms from lowest to highest, we see that the first 3 figures (48, 70. 80) account for 9 of the 20 terms. Therefore, the 10th and 11th terms in the set will both be 84, so the median will also be 84.

You could also just write out the set:

{48, 48, 70, 70, 70, 80, 80, 80, 80, 84, 84, 84, 84, 84, 84, 84, 96, 96, 96, 96}

and count from the left (or the right, it doesn't matter) until you hit the 10th and 11th terms, then take the average of those two.

[sibbineni]

Amount Earned per day: $96 $84 $80 $70 $48
Number of Days: 4 7 4 3 2

A student worked for 20 days. For each of the amount showed in the first row above, the second row gives the number of days that the student earned that amount (e.g. he earned $96 for 4 days, $84 for 7 days etc.). What is the median amount of money that the student earned per day for the 20 days?
A. $96
B. $84
C. $90
D. $70
E. $48



Median Definition:

The middle measurement after the measurements are ordered
by size (or the average of the two middle measurements if the number
of measurements is EVEN)

Given:

There are 20 set of numbers... so the median would be the average of the 10 and the 11 the term as the set of numbers were
EVEN

arrange the given data According to positions....

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 7 18 19 20
96 96 96 96 84 84 84 84 84 84 84 80 80 80 80 70 70 70 48 48

median is the average of the 10 and 11 th term

so ans is 84

ans is (B)

[RyanDe680]

The question is worded oddly, saying that he earned $96 for 4 days implies to me that he earned $24 per day totaling $96 for 4 days....

I so hate GMAT wording....