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# Math Questions Mean Score

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Math Questions Mean Score [#permalink]  28 Dec 2009, 10:58
00:00

Difficulty:

5% (low)

Question Stats:

80% (01:34) correct 20% (01:26) wrong based on 5 sessions
Hello,

Here is the statement:

"For a certain examination, a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean, what was the mean score for the examination?"
Choices: 74, 76, 80, 82

I am not familiar with deviation.

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Re: Math Questions Mean Score [#permalink]  28 Dec 2009, 11:24
Definition and properties of StDev are not crucial for this problem.

let's denote deviation with x

Quote:
a score of 58 was 2 standard deviations below the mean

58=mean-2x

Quote:
a score of 98 was 3 standard deviations above the mean

98=mean+3x

We have 2 equations and 2 variables. So this linear system of equations can be solved. let's just subtract Statement1 from Statement 2:
98-58=mean +3x-mean+2x
40=5x
x=8
mean=98-3x=98-24=74
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Re: Math Questions Mean Score [#permalink]  28 Dec 2009, 11:29
Thanks very much Shalva !!!

Indeed with the definition of Mean, the problem is solving by himself.

I need to review some maths concepts
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Re: Math Questions Mean Score [#permalink]  28 Dec 2009, 11:29
Expert's post
nailgmattoefl wrote:
Hello,

Here is the statement:

"For a certain examination, a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean, what was the mean score for the examination?"
Choices: 74, 76, 80, 82

I am not familiar with deviation.

A score of 58 was 2 standard deviations below the mean --> 58=Mean-2d
A score of 98 was 3 standard deviations above the mean --> 98=Mean+3d

Solving above for Mean=74

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Standard Deviation [#permalink]  01 Jun 2010, 04:28
Can anyone help me with this problem please? It comes from the Gmat Testprep.

For a certain examination, a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?

A. 74
B. 76
C. 78
D. 80
E. 82

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Re: Standard Deviation [#permalink]  01 Jun 2010, 05:41
1
KUDOS
Let d stand for Standard Deviation, M - for mean. We can construct a system of equations:

\begin{cases} M - 2d = 58 \\ M + 3d = 98 \end{cases}

After you subtract the first equation from the second, you get this equation:

5d = 40
d = 8

After plugging the value of d in the first equation, you get the value of M:

M = 58 + 2*8 = 74

I hope it helps you.
jessicavanessa wrote:
Can anyone help me with this problem please? It comes from the Gmat Testprep.

For a certain examination, a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?

A. 74
B. 76
C. 78
D. 80
E. 82

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Re: Standard Deviation [#permalink]  01 Jun 2010, 07:21
Thank you !
Very useful
Re: Standard Deviation   [#permalink] 01 Jun 2010, 07:21
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