M43-34

Question

At the Olympic Games, 10 gymnasts must perform two routines, compulsory and free, each gymnast receiving a separate score for each routine. If the standard deviation of the 10 scores for the compulsory routine was 0.7 points, what was the standard deviation of the 20 scores for both routines combined?

(1) The standard deviation of the 10 scores for the free routine was also 0.7 points.
 
(2) The range of scores for each of the compulsory routine and free routine was 3 points.

Bunuel · Answer

Official Solution:

At the Olympic Games, 10 gymnasts must perform two routines, compulsory and free, each gymnast receiving a separate score for each routine. If the standard deviation of the 10 scores for the compulsory routine was 0.7 points, what was the standard deviation of the 20 scores for both routines combined? 
 
(1) The standard deviation of the 10 scores for the free routine was also 0.7 points.
 
Having two lists with the same standard deviation does not mean that the combined list will have the same standard deviation. The lists might be very far apart. For example, {0, 1} and {100, 101} both have the same standard deviation. However, {0, 1, 100, 101} is far more widespread than either of the lists and thus will have a much higher standard deviation than the initial lists. Therefore, this information is not sufficient.
 
(2) The range of scores for each of the compulsory routine and free routine was 3 points.
 
The range alone does not help to determine the standard deviation. Therefore, this information is also not sufficient.
 
(1)+(2) Using the same example from (1): {0, 1} and {100, 101} both have the same standard deviation and range. However, {0, 1, 100, 101} is far more widespread than either of the lists and thus will have a much higher standard deviation than the initial lists. Therefore, we cannot determine the range of both routines combined. Not sufficient.

Answer: E

chandan_13 · Answer

I like the solution - it’s helpful.

utkarsh_atri · Answer

I like the solution - it’s helpful.

NikunjC · Answer

I did not quite understand the solution. Hello bb,
Does such type of complex standard deviation question is common in GMAT exam ?

Bunuel · Answer

This question tests the general concept of standard deviation, so it’s 100% aligned with the GMAT syllabus, as are all questions in GMAT Club Tests. You won’t get too many questions on standard deviation on test day, at most one or maybe two. What exactly is unclear in the question?

HowCanIDoThis · Answer

Hello bunuel, thanks for the question and the solution. It's very helpful.

I'd like to ask something: What should the statement be so that we can determine the standard deviation in this question?

Bunuel · Answer

For example, if statement (2) were:

"Each gymnast received the same score on the free routine as on the compulsory routine."

Then the 20 scores would simply be the 10 compulsory scores listed twice. Duplicating every value does not change the standard deviation, so the standard deviation of all 20 scores would still be 0.7, and the answer would be B.

Advait01 · Answer

I like the solution - it’s helpful.

ZeroSquare · Answer

Quick question - if the question had mentioned that scores given in between 0-1 or 0-10 as in if the range for both was mentioned and the same ....then would solution be different??

Bunuel · Answer

No. Even if all scores were restricted to a fixed scale, such as 0 to 10, the answer would still be E.

A fixed scale limits the scores, but it does not tell us how far apart the two averages are. The combined standard deviation depends on that.

M43-34

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