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The arithmetic mean of a data set is 46 and the standard deviation of 13 Mar 2017, 01:31
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77% (00:40) correct 23% (00:46) wrong based on 106 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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B
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The arithmetic mean of a data set is 46 and the standard deviation of 13 Mar 2017, 03:53
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SajjadAhmad
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
Show more

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

Answer is B .
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The arithmetic mean of a data set is 46 and the standard deviation of 13 Mar 2017, 06:31
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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 13 Mar 2017, 07:53
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SajjadAhmad
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
Show more
\(Range\) \(=\) \(Mean\) + \(2*SD\)

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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The arithmetic mean of a data set is 46 and the standard deviation of 15 Mar 2017, 16:44
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SajjadAhmad
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
Show more

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.

Answer: B
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The arithmetic mean of a data set is 46 and the standard deviation of 27 Apr 2019, 07:42
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SajjadAhmad
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
Show more

-----------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.
----------------------------------

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?

2 standard deviations ABOVE the mean = 46 + 2(4) = 54
2 standard deviations BELOW the mean = 46 - 2(4) = 38

The range = 38 to 54

Answer: B

Cheers,
Brent
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