A student worked for 20 days. For each of the amounts shown in the fir

Question

https://gmatclub.com/forum/download/file.php?id=50807 A student worked for 20 days. For each of the amounts shown in the first row of the table, the second row gives the number 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 table.gif Untitled.png

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=50807

A student worked for 20 days. For each of the amounts shown in the first row of the table, the second row gives the number 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

A student worked 20 days.

The median of a set with even number of terms is the average of the two middle terms when arranged in ascending  or descending  order. Since the data (amount earned per day) is already arranged in descending order there is no need to rearrange it.

The median will be the average of the 10th and 11th values (either in ascending or descending order) --> both of those values are 84 --> the median is (84+84)/2.

Answer: B.

ENAFEX · Answer

Arrange the amount in ascending order

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

Median = (Amount in 10th day+Amount in 11th Day)/2

= (84+84)/2
=84

B

ENAFEX · Answer

Expert..

Thanks Bunuel. I didn't notice that at all.. Got used to arranging a group in ascending order. :D

Swaminathan1986 · Answer

For people who want a make this one a "Quickie"

Look at the values given:

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

Both the highest values (84 and 96) have largest no. of days associated with them(7 and 4). Hence, your immediate reaction should be that the median is going to heavily lean towards the higher values. Now look at the options:

1)$96
2)$84
3)$80
4)$70
5)$48

It is obvious that it cannot be either of 96,48 (or) if you think about it even 70. The only decision now is between 84 and 80. Now out of these two 84 leans more towards the highest values and also has 7 days assigned to it. So........

P.S: Only meant for scenarios wherein you desperately want a " Quickie "

LogicGuru1 · Answer

20 days ... 20 is an even number so the median will be  \frac{10^{th}+11^{th} term}{2} 
Now the amount of money that corresponds to 10 and 11th day is 84. So it is the median 
ANSWER IS B

EMPOWERgmatRichC · Answer

Hi All,

We're told that a student worked 20 days - and the given table shows the number of days that the student earned each of 5 possible amounts of money. We're asked for the MEDIAN amount of money earned per day for those 20 days.

Since there are 20 total days, the MEDIAN will be the AVERAGE of the two 'middle days' (meaning the average of the 10th and 11th days). The table actually puts the values in 'reverse order' (from highest to lowest), but we don't have to rearrange any of that information. Working from 'left to right', we know that the first two columns will total 4+7 = the first 11 days... meaning that the 10th and 11th days will be in the second column. BOTH of those values are 84s, so the MEDIAN is 84.

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

ScottTargetTestPrep · Answer

There are 4 + 7 + 4 + 3 + 2 = 20 days that the student worked. The median is the average of the 10th and the 11th highest earnings. If we list the earnings from lowest to highest, we have:
 
1st to 2nd: 48 
 
3rd to 5th: 70
 
6th to 9th: 80
 
10th to 16th: 84
 
17th to 20th: 96
 
We see that both the 10th and the 11th highest earnings are 84. Therefore, the median is also 84.
 
Answer: B

CrackverbalGMAT · Answer

If the total observations is odd, then the median is the  \frac{n \space + \space 1}{2}th

If the number of observations are odd, then the median is the average of the  \frac{n}{2}th  and the next number.

In the question above, the frequencies are small enough for us to list out the numbers. If the frequencies are large, then we would create a 3rd table which would list the cumulative frequency as shown in the figure.

The last value of the cumulative frequency table tells us the total number of observations.

First arrange the numbers and their corresponding frequencies in ascending order

Here n = 20. The median is the average of the 10th and 11th numbers.

Looking at the cumulative frequency table, the 10th and 11th numbers are when x = 84

The median =  \frac{84 + 84 }{ 2} = 84

Option B

Arun Kumar

Kinshook · Answer

https://gmatclub.com/forum/download/file.php?id=50807

Given: A student worked for 20 days. For each of the amounts shown in the first row of the table, the second row gives the number of days that the student earned that amount.

Asked: What is the median amount of money that the student earned per day for the 20 days?

After rearranging table in increasing amount of money earned per day: -

Amount earned per day  $48  $70  $80  $84  $96  Total days  
  Number of days  2  3  4  7  4  20

Median amount of money = (10th data + 11th data) / 2 = $84

IMO B

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A student worked for 20 days. For each of the amounts shown in the fir

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Amount earned per day	$48	$70	$80	$84	$96	Total days
Number of days	2	3	4	7	4	20

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A student worked for 20 days. For each of the amounts shown in the fir

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