The graph shows, for 7 groupsGroups A through Gthe relationship

Question

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The graph shows, for 7 groups—Groups A through G—the relationship between the median and the arithmetic mean of annual salaries for members of that group. All 7 groups have the same number of employees and each group plans to hire a new worker at the group's median salary.

Based on the information provided, select from each drop-down menu the option that creates the most accurate statement.

For exactly  GRAPH_1_PLACEHOLDER  of the groups, the addition of the new worker will result in an increase in the arithmetic mean salary for the group. For Group  GRAPH_2_PLACEHOLDER , the increase (as a percentage of the previous arithmetic mean) will be the greatest.

ID: 101123

scrantonstrangler · Accepted Answer

This question requires the use of the following basic property of Statistics:
Adding a value to a set, that is   greater than the mean  , will  increase  the overall   mean(average)   value of the set.

Here, we are adding the median value of each group, as a new person's salary.
To understand how the mean would get affected by this new addition, we require the relationship between the mean and the median of that particular group.

Hence, if Median is greater than the Mean, we can safely, say that the overall value of the Mean will increase.

You can see that the median is greather than the mean in case of Groups A, C & G. Hence, these groups will see a rise in Mean after the addition of their respective Medians.

The answer to the first blank is 3.

The highest increase will be in group G, since there, the median is around 109% of the Mean. Larger than any other group. Hence, the answer to the second question is G.

KanikaJain · Answer

Shouldn't the answer to the second question be G?

guddo · Answer

You are correct. OFFICIAL EXPLANATION: https://gmatclub.com/forum/download/file.php?id=82281 RO1: For each of the 7 groups, adding a worker will increase the group’s mean salary if and only if that worker’s salary exceeds the group’s current mean salary. Each group plans to hire a new worker at the group’s median salary. So, assuming no other relevant factors change, adding the worker as planned will increase the group’s mean salary if and only if the group’s median salary now exceeds its mean salary. The graph shows that this holds for exactly three of the groups—Group A, Group C, and Group G. So, for each of exactly 3 of the groups, adding a worker as planned will increase the group’s mean salary. The correct answer is 3. RO2: Each of the groups has the same number of workers. So, if each group adds exactly one worker, the resulting percentage increase in mean salary will be highest for the group for which the new worker’s salary is highest as a percentage of that group’s current mean salary. Each group plans to add a worker at its own median salary. Thus, assuming no other relevant factors change, adding the worker as planned will yield the greatest percentage increase in the group’s mean salary for the group whose median salary is now the highest as a percentage of its mean salary. The graph shows that this is Group G, whose median salary is almost 110% of its mean salary. The correct answer is G. GMAT-Club-Forum-q4b0yh33.png

mayankdgmat · Answer

Let arithmetic mean be A and Median be x% of A and T be total employee

New salary = (AT+x%*A)/(T+1) ; so New Salary= A(T+x%)/(T+1)

so X is more than 100% than new salary will be greater than A and further greater the x higher the % increase.

SR4896 · Answer

For group A, Median is equal to Mean. So, adding employee with median salary shall not increase the mean salary. So, answer should be 2

scrantonstrangler · Answer

Hi  SR4896 ,
For Group A, you would find that the median is more than 100% (slightly). Thus it becomes greater than the mean.

nikitathegreat · Answer

karishma   GMATNinja   marty  - Can you please explain this one.
How are we applying the concept of Mean and Median in this question and also how do we solve this one

bb · Answer

It seems  scrantonstrangler  has a good explanation above as well as the official explanations posted. Is there something not clear?

Nipunh · Answer

I was able to do this in 30 seconds, and here is how you can do it as well:

Observe (eyeball) that any new median that is above 100% of the mean will definitely be greater than the mean (basically saying median is 1.xx times the mean. Hence, by eyeballing we have 3 groups (1st answer). Now the greatest positive change/deviation from the mean will be observed with the greatest value as a percentage to the mean.. clearly G is ~110% of its mean.. (also visually the tallest) (Answer 2)

Hope it helps!

Nipunh · Answer

I was able to do this in 30 seconds, and here is how you can do it as well:

Observe (eyeball) that any new median that is above 100% of the mean will definitely be greater than the mean (basically saying median is 1.xx times the mean). Hence, by eyeballing we have 3 groups (1st answer). Now the greatest positive change/deviation from the mean will be observed with the greatest value as a percentage to the mean.. clearly G is ~110% of its mean.. (also visually the tallest) (Answer 2)

Hope it helps!

RishiSpi · Answer

It's pictorially very ambiguous to dentify if A is equal to 100% or greater. Spent good one minute to figure it out.

Similarly in many questions it's difficult to make out if the count is eg 2.6 or 2.7.

Any clues for this please.

Bunuel · Answer

It might not be very clear in this image, but in the actual high-resolution graph, it’s quite clear that A is above 100%. On the real exam, the visuals are much sharper, so this kind of ambiguity shouldn’t be an issue. https://gmatclub.com/forum/download/file.php?id=86333 GMAT-Club-Forum-pcylesne.png

The graph shows, for 7 groupsGroups A through Gthe relationship

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