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 48
no. of days...... : 4 7 4 3 2


a) 96
b) 84
c) 80
d) 70
e) 48

How do i go about to calculate the median in this case..is there something called weighted median as well..please explain..

Arranging amount earned in ascending order with the number of days,

48-2
70-3
80-4
84-7
96-4

median = (amount earned in 10th day + amount earned in the 11th day)/2 = (84+84)/2 = 84.

thanks..

Thanks, thoppae

priyanka, 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.)

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Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

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.)

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 Salary
1 48
2 48
3 70
4 70
5 70
6 80
7 80
8 80
9 80
10 84
11 84
12 84
13 84
14 84
15 84
16 84
17 96
18 96
19 96
20 96

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Jamie Nelson
ManhattanGMAT Instructor