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

BTGmoderatorLU wrote: ↑

Thu May 28, 2020 10:32 am

Source: GMAT Prep

Untitled2.png

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

The OA is B

The no. of days = 20, so the average of the 10th and 11th day (Middle-most = (20 + 1)/2 = 10.5) earning would be the median earning of the student.

So, we must find out the earning for the 10th and the 11th day; but before that, we must arrange earnings in ascending or descending order. Since the earnings are already arranged in descending order (96 > 84 > 80 > 70 > 48), we are good to go.

The sum of the first two number of days = 4 + 7 = 11. So, the 10th, as well as 11th day, would fall in the 7 day cells. The value against 7 is $84, the median.

The correct answer: B

Hope this helps!

-Jay
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BTGmoderatorLU wrote: ↑

Thu May 28, 2020 10:32 am

Source: GMAT Prep

Untitled2.png

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

The OA is B

Solution:

We need to determine the median of the following data set:

96, 96, 96, 96, 84, 84, 84, 84, 84, 84, 84, 80, 80, 80, 80, 70, 70, 70, 48, 48

Since the median is the middle value, we use the formula (n + 1) /2 to determine which data point is the median. Thus, (20 + 1) / 2 = 10.5, so the median is halfway between the 10th and 11th data points. Since both the 10th and 11th data points are equal to 84, the median is 84.

Alternate Solution:

Rather than listing the 20 data points, we can use the table data to determine the median.

Since there are 20 daily earnings, the median will be the average of the 10th and the 11th highest daily earnings. Looking at the categories, we see that only 4 data points are $96, but the next category ($84) contains the 5th through the 11th data points. Thus, since both the 10th and 11th data points are $84, the median daily earning is also $84.

Answer: B