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555-605 Level|   Statistics and Sets Problems|                     
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KarishmaB
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The 10 students in a history class recently took an examination. What 13 Jul 2025, 21:30
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Let me ask you this - why do you think every value should be 5 units away from mean? Think about how SD of a list is calculated. Think about what is meant when we say a value is 2SD away or 3SD away etc.

Komal324
Hello KarishmaB

Hope you are doing well. Can you pleas tell me that why is every value not 5 units way from the mean? What is the logic behind it?

Thank you in advance.

Best,
Komal

KarishmaB
Bunuel
The 10 students in a history class recently took an examination. What was the maximum score on the examination?

(1) The mean of the scores was 75.
(2) The standard deviation of the scores was 5.


NEW question from GMAT® Official Guide 2019


(DS02939)

Mean tells you the average and SD tells you how far or close to the mean the distribution of values is. Neither tells you what the ACTUAL maximum or minimum value is. You can have mean 75 and SD 5 in various different distributions.

70, 70, 70, 70, 70, 80, 80, 80, 80, 80
68,69,69,73,74,76, 77, 81,81,82
67,69,70,74,75,75, 76, 80,81,83

We don't know which is these is the actual case and hence we cannot say what the actual greatest score is. Hence answer is (E).


There is a maximum value that the greatest score can take under these constraints. That will happen in case of this list:

(75 - a), 75, 75, 75, 75, 75, 75, 75, 75, (75 + a)

Most values are at mean so that difference from mean is minimised. Most of the deviation will come from the maximum value but since we need the mean to be 75, we need to balance out the maximum value with the minimum value.

\(Sd = 5 = \sqrt{2a^2/10}\)
a = 11.18

So the maximum value that any one number can take is 75 + 11.18 = 86.18

In this case too
63.82, 75,75,75,75,75,75,75,75,86.18
mean = 75, SD = 5

But here is the thing - the question does not ask you the maximum value any number CAN take. The question only asks you the maximum value it does take. We cannot say what that is because the actual scenario could be any one of the 4 given above or any one of the many many others possible (within these constraints).

Answer (E)
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The 10 students in a history class recently took an examination. What 03 Oct 2025, 20:35
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standard deviation is the AVERAGE DISTANCE FROM THE MEAN.
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