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A data set with a mean of 60 has a standard deviation of 3.5  [#permalink]

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Question Stats: 79% (00:46) correct 21% (00:42) wrong based on 232 sessions

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A data set with a mean of 60 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean?

A. 53
B. 56
C. 59
D. 63.5
E. 65

Originally posted by HarveyS on 04 Jan 2014, 18:54.
Last edited by Bunuel on 05 Jan 2014, 04:44, edited 1 time in total.
Edited the question.
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Re: A data set with a mean of 60 has a standard deviation of 3.5  [#permalink]

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Re: A data set with a mean of 60 has a standard deviation of 3.5  [#permalink]

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Mountain14 wrote:
A data set with a mean of 60 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean?

53

56

59

63.5

65

I guess the question is little ambiguous. I didn't understand what "one standard deviation" meant. I took at as a number.
As [(59-60)^2]^1/2 = 1
So 59 satisfies that criteria.
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Re: A data set with a mean of 60 has a standard deviation of 3.5  [#permalink]

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Bunuel wrote:

56 is smaller than 56.5 and does not lie in between 56.5 and 63.5 (the specified range here). I think you meant 59. Answer C. No?
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Re: A data set with a mean of 60 has a standard deviation of 3.5  [#permalink]

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gmatbugsme84 wrote:
Bunuel wrote:

56 is smaller than 56.5 and does not lie in between 56.5 and 63.5 (the specified range here). I think you meant 59. Answer C. No?

Yes. Edited the typo. Thank you.
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Re: A data set with a mean of 60 has a standard deviation of 3.5  [#permalink]

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Mountain14 wrote:
A data set with a mean of 60 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean?

A. 53
B. 56
C. 59
D. 63.5
E. 65

One standard deviation of the mean = 60 - 3.5 = 56.5 OR 60 + 3.5 = 63.5

From the answer options only 59 falls in this criteria hence answer is C.
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Re: A data set with a mean of 60 has a standard deviation of 3.5  [#permalink]

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HarveyS wrote:
A data set with a mean of 60 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean?

A. 53
B. 56
C. 59
D. 63.5
E. 65

Range is = $$Mean$$ + $$SD$$

$$Range = 60$$ + $$3.5$$

Ie, Range is 56.5 to 63.5

Thus, among the given options only (C) 59 falls within the given range, answer will be (C)

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Re: A data set with a mean of 60 has a standard deviation of 3.5  [#permalink]

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HarveyS wrote:
A data set with a mean of 60 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean?

A. 53
B. 56
C. 59
D. 63.5
E. 65

-----------ASIDE-----------------------
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.
-----------ONTO THE QUESTION-----------------------

A data set with a mean of 60 has a standard deviation of 3.5.
So, 1 standard deviation ABOVE the mean = 60 + 3.5 = 63.5
And 1 standard deviation BELOW the mean = 60 - 3.5 = 56.5

Which of the following is the smallest number that falls within one standard deviation of the mean?
The values within one standard deviation of the mean are all values that are greater than or equal to 56.5 AND less than or equal to 63.5
So, when we check the answer choices, we see that 59 is the smallest value that fits with the above range of values.

Cheers,
Brent
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Re: A data set with a mean of 60 has a standard deviation of 3.5  [#permalink]

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HarveyS wrote:
A data set with a mean of 60 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean?

A. 53
B. 56
C. 59
D. 63.5
E. 65

Since one standard deviation below the mean is 60 - 3.5 = 56.5, 53 and 56 will fall outside one standard deviation of the mean. So 59 is the smallest number in the given answer choices that falls within one standard deviation of the mean.

Alternate Solution:

One standard deviation below the mean is 60 - 3.5 = 56.5, and one standard deviation above the mean is 60 + 3.5 = 63.5. Thus, we are looking for the smallest data value that falls in the interval from 56.5 to 63.5. We see from the answer choices that 59 meets the requirement.

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Re: A data set with a mean of 60 has a standard deviation of 3.5  [#permalink]

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_________________ Re: A data set with a mean of 60 has a standard deviation of 3.5   [#permalink] 05 Feb 2020, 13:01
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