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# For a certain exam,a score of 58 was 2 standard deviations b

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Intern
Joined: 20 Nov 2011
Posts: 2
For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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06 Mar 2012, 04:06
5
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Difficulty:

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Question Stats:

82% (01:08) correct 18% (00:58) wrong based on 903 sessions

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

A. 74
B. 76
C. 78
D. 80
E. 82
Math Expert
Joined: 02 Sep 2009
Posts: 47981
Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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06 Mar 2012, 04:11
9
16
MaithiliGokarn wrote:
For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score for the exam?

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

Welcome to GMAT Club. Below is a solution to your question.

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.

For more about the Standard Deviation please check: Standard Deviation.

Hope it helps.
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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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14 Aug 2013, 10:37
Bunuel wrote:
MaithiliGokarn wrote:
For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score for the exam?

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

Welcome to GMAT Club. Below is a solution to your question.

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.

Can someone please elaborate as how is this solved?
Math Expert
Joined: 02 Sep 2009
Posts: 47981
Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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14 Aug 2013, 11:35
1
2
patternpandora wrote:
Bunuel wrote:
MaithiliGokarn wrote:
For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score for the exam?

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

Welcome to GMAT Club. Below is a solution to your question.

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.

Can someone please elaborate as how is this solved?

Please elaborate what exactly didn't you understand. Thank you.

Meanwhile check similar questions to practice:
70-75-80-85-90-105-105-130-130-130-the-list-shown-consist-of-100361.html
the-standard-deviation-of-a-normal-distribution-of-data-is-99221.html
given-that-the-mean-of-set-a-is-10-what-is-the-range-of-two-141964.html

Hope it helps.
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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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17 Apr 2014, 08:59
2
2
patternpandora wrote:
Bunuel wrote:
MaithiliGokarn wrote:
For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score for the exam?

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

Welcome to GMAT Club. Below is a solution to your question.

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.

Can someone please elaborate as how is this solved?

you can either solve as Bunuel did or exploit number properties and plug in from the answer choices:

58 = Mean - 2d -----> 2d = Mean - 58
98 = Mean + 3d -----> 3d = 98 - Mean

Thus your d must be both a multiple of 2 (2n) or a multiple of 3 (2n+1). Giving a fast glance at the answer choices, since E-E = E, the first equation is satisfied in every answer choice. The second equation, however, is satisfied in two answers only, respectively A and D.

Now, since d is a unique value for both equations, calculating d must yield the same result. It does but for one choice only and that choice is A.

$$d=\frac{74-58}{2}=\frac{98-74}{3}$$

This is intended to be a back-up method, for sure not as fast as that one Bunuel came up with but when you're under pressure everything that pops up in your mind is useful.
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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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17 Apr 2014, 19:19
13
6
MaithiliGokarn wrote:
For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score for the exam?

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

These are concepts of normal distribution. You don't need to delve much into details but you must understand what 1 SD, 2 SD etc mean.

Say you have a distribution of weights in a class of children. The mean weight of the class is, say 46 kgs. If I tell you that 1 standard deviation is of 5 kgs, it means that 1 SD below mean is 5 kgs less than 46 kgs which is 41 kgs. This also means that 34% children have weight ranging from 46 kgs to 41 kgs but you don't have to worry about that.

So 2 SD below mean will be 2*5 = 10 kgs less than 46 i.e. 36 kgs.

Similarly, 3 SD above mean will be 3*5 = 15 kgs more than 46 i.e. 61 kgs.

In the original question, you are given that 58 is 2 SD below mean and 98 is 3 SD above mean. So from 58 to 98, we have 5 SDs.
$$\frac{{98 - 58}}{5} = 8$$ = SD

Since SD is 8 so mean is at $$58 + 2*8 = 74$$
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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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13 Sep 2014, 19:38
3
Every list of numbers has a mean. every number on the list has a deviation from the mean: that is how far that number is from the mean.
deviation from the mean = (value) – (mean)
Or
Value= Mean - Deviation
58 = M - 2d
98 = M - 3d
Solve it
M = 74

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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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08 Dec 2014, 16:44
3
For those confused like myself, 58=M-2d and 98=M+3d is a system of equations. We want the value of M, so isolate D in one of the equations. then plug that value of d into the other equation and solve for M.
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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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15 Mar 2015, 00:18
I am getting m=-22. I will be glad is someone point out the mistake i have committed.

58=m-2d 1
98=m-3d 2

subtracting 2 from 1

d=-40.

substituting d in 1

m =-22.
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Joined: 02 Aug 2009
Posts: 6549
Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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15 Mar 2015, 00:33
1
manishbhusal wrote:
I am getting m=-22. I will be glad is someone point out the mistake i have committed.

58=m-2d 1
98=m-3d 2

subtracting 2 from 1

d=-40.

substituting d in 1

m =-22.

hi manishbhusal,
98 is 3 deviation above ..
so 98=m+3d and not m-3d..
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For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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23 Jul 2016, 02:46
3
MaithiliGokarn wrote:
For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score for the exam?

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

Mean -2 SD = 58 ..... eq 1
Mean +3SD =98 ........eq 2

Subtract eq 2 from eq1
5SD= 40
SD = 40/5--> 8

So the standard deviation is 8
now to find the mean
either add 2*SD to 58 = 2*8+58 = 18+58=74
Or subtract 3*SD from 98 = 98-3*8 = 98-24 = 74
THE ANSWER IS DEFINITELY A = 74
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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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05 Aug 2016, 10:01
This question looks deceiving easier than it is. Still need to setup the correct system of equations :/
Intern
Joined: 01 Mar 2017
Posts: 14
Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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21 Mar 2017, 12:58
I solved that with Ratios.
Range from 98 to 58 is 40. There are 5 SD in between, 2 SD from 58 and 3 SD for 98. (2:3:5 -> Total 40)
Therefore 2/5 * 40 = 16 (or 3/5*40 = 24)
Add/Subtract any of these values to find the mean.
Intern
Joined: 07 Dec 2016
Posts: 2
Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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10 Dec 2017, 10:20
2
Quick solution --> please see below
58=M-2D
98=M+3D
98-58=M+3D-M-2D
40=5D
D=8 so, One SD =8

58=M-2D
58+2D=M
58+(2x8)=M
58+16=M
So M = 74

apply the same for the other equation and you will get to M=74.

Thanks!
Intern
Joined: 05 Jun 2017
Posts: 2
For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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23 Jan 2018, 14:44
1
The easiest approach ever:
98-58=40
there are 5 SD in between; hence,
40/5=8
58+2(SD) i.e. 58+16=74
or
98-3(SD) i.e. 98-24=74
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Posts: 307
Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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25 Jul 2018, 18:55
1
For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score for the exam?

The range in given question is 98-58 = 40

58 is 2 SD below mean
90 is 3 SD above mean

So there is 5 SD in between 58 and 98. 5 SD=40 , SD = 8

The mean score is 74
Ans :A
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