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# A set has an average (arithmetic mean) of 42 and a standard deviation

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Math Expert
Joined: 02 Sep 2009
Posts: 62553
A set has an average (arithmetic mean) of 42 and a standard deviation  [#permalink]

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15 Aug 2016, 03:02
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Difficulty:

5% (low)

Question Stats:

83% (00:49) correct 17% (01:11) wrong based on 112 sessions

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A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean?

A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6

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A set has an average (arithmetic mean) of 42 and a standard deviation  [#permalink]

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15 Aug 2016, 04:06
Bunuel wrote:
A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean?

A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6

AM is 42 and SD is 1.8...

Now, we need to count all numbers greater than 42+2(1.8) = 45.6 or 42-2(1.8) = 38.4 (we are asked to find the value that is two SD away from the mean..so multiply the SD by 2)

Only B is in the list..

IMO option B is correct answer..

OA please...will correct if I missed anything..
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A set has an average (arithmetic mean) of 42 and a standard deviation  [#permalink]

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Updated on: 22 Jan 2020, 16:23
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Top Contributor
Bunuel wrote:
A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean?

A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6

A little extra background on standard deviations above and below the mean

If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc

So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
etc.
-----------------------------
For this question, if the standard deviation is 1.8, then two standard deviations = (2)(1.8) = 3.6
So, two standard deviations BELOW the mean = 42 - 3.6 = 38.4
And two standard deviations ABOVE the mean = 42 + 3.6 = 45.6
This means there are two correct answers.
Now check the answer choices for one of the two possible answers.

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Originally posted by GMATPrepNow on 15 Aug 2016, 06:24.
Last edited by GMATPrepNow on 22 Jan 2020, 16:23, edited 1 time in total.
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Re: A set has an average (arithmetic mean) of 42 and a standard deviation  [#permalink]

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13 Sep 2017, 07:47
Bunuel wrote:
A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean?

A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6

42-x= 2*1.8
x= 42-3.6 = 38.4

Ans:B
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Re: A set has an average (arithmetic mean) of 42 and a standard deviation  [#permalink]

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09 Feb 2020, 04:15
Bunuel wrote:
A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean?

A. 36
B. 38.4
C. 40.2
D. 43.8
E. 75.6

Two standard deviations above the mean is 42 + 2 x 1.8 = 42 + 3.6 = 45.6.

Two standard deviations below the mean is 42 - 2 x 1.8 = 42 - 3.6 = 38.4.

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Re: A set has an average (arithmetic mean) of 42 and a standard deviation   [#permalink] 09 Feb 2020, 04:15
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