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# The arithmetic mean of a data set is 46 and the standard deviation of

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The arithmetic mean of a data set is 46 and the standard deviation of  [#permalink]

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13 Mar 2017, 00:31
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77% (00:44) correct 23% (00:43) wrong based on 59 sessions

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The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the interval two standard deviations from the mean of the set?

(A) 38 to 46
(B) 38 to 54
(C) 42 to 50
(D) 44 to 48
(E) 46 to 50

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Re: The arithmetic mean of a data set is 46 and the standard deviation of  [#permalink]

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13 Mar 2017, 02:53
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The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the interval two standard deviations from the mean of the set?

(A) 38 to 46
(B) 38 to 54
(C) 42 to 50
(D) 44 to 48
(E) 46 to 50

Arithmetic Mean = 46
SD = 4 (One Interval )
Two SD intervals means 38__42__46 __50__54

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Re: The arithmetic mean of a data set is 46 and the standard deviation of  [#permalink]

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13 Mar 2017, 05:31
Mean 46
SD = 4

We need to find the interval which lies within 2 SDs of the mean value. That is on either side of the mean, we need to find the extremes which are 2 SDs away from the mean.

2 SDs = 4*2=8

Left extreme = 46 - 2*SD = 46-8=38
Right extreme = 46+2*SD = 46+8 = 54

Hence the interval is 38 to 54. Answer B
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The arithmetic mean of a data set is 46 and the standard deviation of  [#permalink]

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13 Mar 2017, 06:53
The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the interval two standard deviations from the mean of the set?

(A) 38 to 46
(B) 38 to 54
(C) 42 to 50
(D) 44 to 48
(E) 46 to 50

$$Range$$ $$=$$ $$Mean$$ + $$2*SD$$

Or, $$Range$$ $$=$$ $$46$$ + $$2*4$$

Or, $$Range$$ $$=$$ $$46$$ + $$8$$

Or, $$Range$$ $$=$$ $$38 \ to \ 54$$

Hence, the correct answer must be (B) $$38 to 54$$
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Re: The arithmetic mean of a data set is 46 and the standard deviation of  [#permalink]

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15 Mar 2017, 15:44
The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the interval two standard deviations from the mean of the set?

(A) 38 to 46
(B) 38 to 54
(C) 42 to 50
(D) 44 to 48
(E) 46 to 50

Two standard deviations above the mean is 46 + 2(4) = 46 + 8 = 54.

Two standard deviations below the mean is 46 - 2(4) = 46 - 8 = 38.

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Re: The arithmetic mean of a data set is 46 and the standard deviation of  [#permalink]

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02 Jul 2018, 15:54
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The arithmetic mean of a data set is 46 and the standard deviation of &nbs [#permalink] 02 Jul 2018, 15:54
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