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Old 2007 September 5th, 02:49 AM   #1 (permalink)
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Standard Deviation Problems 2

  • For a certain exam a score of 58 is 2 standard deviations below the mean and a score of 98 is 3 standard deviations above mean. What was the mean score of the exam?
a) 16
b) 40
c) 72
d) 74
82

Could anyone give me step by step solution?

Thanks
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Old 2007 September 5th, 05:26 AM   #2 (permalink)
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Answer is d.

74 - 58 = 16. so the sd is 8. 8 *3 + 74 = 98.
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Old 2007 September 9th, 06:42 PM   #3 (permalink)
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M=> mean, S.D=> Standard Deviation

M-58 = 2 * S.D
M+3 * SD =98

Rearranging ..,
M-58=2SD
M-98 = -3SD

=> 5 SD = 40 => SD = 5

Subst. SD in anyone of the above eqn. will give you the mean.It is 74
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Old 2007 September 10th, 08:33 PM   #4 (permalink)
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D.

The way I figured it out was to take the difference between 58 & 98
98 - 58 = 40. This corresponds to 5 standard deviations for the question.

Hence, 40/5 = 8 is one standard deviation....

So Mean = 58 + 2*8 = 74; 98 - 3*8 = 74.

Hence D.
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Old 2007 September 12th, 03:49 PM   #5 (permalink)
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Can someone por favor, El Seņor list the formulae for standard deviation!

Thanks
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Old 2007 September 12th, 11:47 PM   #6 (permalink)
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[Sum (Variable - Mean ) ] / n

n= number of variables.
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Old 2007 September 13th, 01:01 AM   #7 (permalink)
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Quote:
Originally Posted by Prawler View Post
[Sum (Variable - Mean ) ] / n

n= number of variables.
Not correct.

std dev = sqrt(Sum([Variable-Mean]^2)/n)
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Old 2007 September 13th, 08:50 PM   #8 (permalink)
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You don't need to know std dev to solve this problem. 58 is 2*stuff down, 98 is 3*stuff up. Whatever this "stuff" might be, the answer is 74.
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Old 2007 September 24th, 04:09 AM   #9 (permalink)
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avg = 58 + 2d
avg = 98 - 3d
d = 8
avg = 74
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Old 2007 September 25th, 05:42 AM   #10 (permalink)
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I agree 98-85 = 40 ---> 40/5=8 ----> 58+2*8=74
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