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The 10 students in a history class recently took an examination. What

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The 10 students in a history class recently took an examination. What  [#permalink]

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New post 24 Jun 2018, 21:15
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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.


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(DS02939)

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Re: The 10 students in a history class recently took an examination. What  [#permalink]

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New post 25 Jul 2018, 10:58
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Mo2men wrote:
GMATGuruNY wrote:
NandishSS wrote:
HI EgmatQuantExpert , GMATGuruNY

Can you please help me with this problem?

Standard deviation of the scores was 5 means it is 5 score variation, So if we combine 1 & 2 Mean = 75 Highest might be 80 & Least might be 70?


For the purposes of the GMAT, we can consider standard deviation to be the AVERAGE DISTANCE FROM THE MEAN.

Quote:
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.


Statement 1 implies that the sum of the 10 scores = 10*75 = 750.
Statement 2 implies that the average distance from the mean = 5.
Given these two facts, we cannot determine the maximum score.
INSUFFICIENT.



GMATGuruNY

1- Why the distance (mean) is not enough? Can't we say max = 80?

2-Can you please shed light when the two statement would be sufficient? what is the missing info here?

Thanks


Hello Mo2men

I will try to explain. If 75 is the mean and SD is 5, it means that on average, every value deviates from mean by 5 units. That doesnt mean every value necessarily deviates from mean by 5 units. Its possible that few values deviate from mean by 8 or 10 units also but other values deviate from mean by 1 or 2 units only. Lets take example.

{70, 70, 80, 80}. For this set, mean is 75, and since every value deviates from mean by 5 only, SD of this set is also 5. And here the MAX value is 80.

Now consider {65, 75, 75, 75, 75, 75, 75, 85}. For this set, mean is 75, SD is 5 only. But here the MAX value is 85.
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Re: The 10 students in a history class recently took an examination. What  [#permalink]

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New post 24 Jun 2018, 22:11
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Bunuel wrote:
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)


As the question stem doesn't make it clear where to start, we'll first try a few examples.
This is an Alternative approach.

(1) OK, but how much is the maximum? Could be 80, 85, 90, anything above the mean.
Insufficient.

(2) Still no useful information.... though finding specific examples is time consuming (as the equation for std is involved), we can think of the std as an expression with 10 variables representing the 10 different scores. So the maximum could, as above, be any number, such as 50, 30, 90, etc...
Insufficient.

Combined: Still not helpful, as we now have two equations for 10 variables (our 10 scores): std = 5 and mean = 75. So we cannot solve.

(E) is our answer.
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Re: The 10 students in a history class recently took an examination. What  [#permalink]

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New post 24 Jun 2018, 22:28
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IMO E
Can have outliers
Normal distribution is approximation and not exact separate data
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Re: The 10 students in a history class recently took an examination. What  [#permalink]

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New post 24 Jul 2018, 04:48
HI EgmatQuantExpert , GMATGuruNY

Can you please help me with this problem?

Standard deviation of the scores was 5 means it is 5 score variation, So if we combine 1 & 2 Mean = 75 Highest might be 80 & Least might be 70?
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Re: The 10 students in a history class recently took an examination. What  [#permalink]

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New post 24 Jul 2018, 05:36
NandishSS wrote:
HI EgmatQuantExpert , GMATGuruNY

Can you please help me with this problem?

Standard deviation of the scores was 5 means it is 5 score variation, So if we combine 1 & 2 Mean = 75 Highest might be 80 & Least might be 70?


For the purposes of the GMAT, we can consider standard deviation to be the AVERAGE DISTANCE FROM THE MEAN.

Quote:
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.


Statement 1 implies that the sum of the 10 scores = 10*75 = 750.
Statement 2 implies that the average distance from the mean = 5.
Given these two facts, we cannot determine the maximum score.
INSUFFICIENT.


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Re: The 10 students in a history class recently took an examination. What  [#permalink]

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New post 24 Jul 2018, 15:13
GMATGuruNY wrote:
NandishSS wrote:
HI EgmatQuantExpert , GMATGuruNY

Can you please help me with this problem?

Standard deviation of the scores was 5 means it is 5 score variation, So if we combine 1 & 2 Mean = 75 Highest might be 80 & Least might be 70?


For the purposes of the GMAT, we can consider standard deviation to be the AVERAGE DISTANCE FROM THE MEAN.

Quote:
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.


Statement 1 implies that the sum of the 10 scores = 10*75 = 750.
Statement 2 implies that the average distance from the mean = 5.
Given these two facts, we cannot determine the maximum score.
INSUFFICIENT.



GMATGuruNY

1- Why the distance (mean) is not enough? Can't we say max = 80?

2-Can you please shed light when the two statement would be sufficient? what is the missing info here?

Thanks
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Re: The 10 students in a history class recently took an examination. What &nbs [#permalink] 24 Jul 2018, 15:13
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