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46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu

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Math Revolution GMAT Instructor
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46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu  [#permalink]

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New post 17 Dec 2017, 23:31
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[GMAT math practice question]

\(46, 47, 48, 49, 50, 51, 52, 53, 54\)
The standard deviation of the \(9\) numbers in the above list lies between \(2\) and \(3\). How many of the \(9\) numbers are within one standard deviation of the average (arithmetic mean)?

A. \(5\)
B. \(6\)
C. \(7\)
D. \(8\)
E. \(9\)

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Re: 46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu  [#permalink]

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New post 18 Dec 2017, 06:35
Although I have marked the correct answer, I just want to confirm my approach.

I have calculated s.d of the series 48,49, 50,51,52 (sqrt2.5) and 47,48,49,50,51,52,53(sqrt7)

Please correct me whether my approach is correct.
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46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu  [#permalink]

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New post 18 Dec 2017, 09:12
1
MathRevolution wrote:
[GMAT math practice question]

\(46, 47, 48, 49, 50, 51, 52, 53, 54\)
The standard deviation of the \(9\) numbers in the above list lies between \(2\) and \(3\). How many of the \(9\) numbers are within one standard deviation of the average (arithmetic mean)?

A. \(5\)
B. \(6\)
C. \(7\)
D. \(8\)
E. \(9\)


The mean of the above set is the middle value \(= 50\)

\(2<SD<3\), as \(1 SD = 1*SD\)

so one \(SD\) will also be between \(2\) and \(3\). SD will be \(2.nnn\) (2.something). for the sake of calculation let \(SD = 2.5\)

lower limit: \(Mean - S.D = 50 - 2.5 = 47.5\)

upper limit: \(Mean + S.D = 50 + 2.5 = 52.5\)

So numbers lying within 1 \(SD\) will range from \(48\) to \(52\) which are 48, 49, 50, 51 & 52 \(=5\)

Option A
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Re: 46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu  [#permalink]

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New post 18 Dec 2017, 09:14
ushasi wrote:
Although I have marked the correct answer, I just want to confirm my approach.

I have calculated s.d of the series 48,49, 50,51,52 (sqrt2.5) and 47,48,49,50,51,52,53(sqrt7)

Please correct me whether my approach is correct.


Hi ushasi

Could not get your approach. Can you explain your reason for calculating SD for two different sets as mentioned by you?
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Re: 46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu  [#permalink]

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New post 18 Dec 2017, 10:25
MathRevolution wrote:
[GMAT math practice question]

\(46, 47, 48, 49, 50, 51, 52, 53, 54\)
The standard deviation of the \(9\) numbers in the above list lies between \(2\) and \(3\). How many of the \(9\) numbers are within one standard deviation of the average (arithmetic mean)?

A. \(5\)
B. \(6\)
C. \(7\)
D. \(8\)
E. \(9\)


Solution:
1.The standard deviation of 9 numbers lies between 2 and 3
2. considering standard deviation 2.5 approx. .
3. Mean of the above 9 numbers is 50.
4.Hence numbers lying between Mean + (1 Standard deviation ) = 52.5 and Mean - (1 Standard deviation) = 47.5 are 48,49,50,51 and 52
5. Hence 5 numbers are lying within 1 standard deviation from the Mean. Hence answer is A
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Re: 46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu  [#permalink]

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New post 20 Dec 2017, 01:00
=>
The average of the \(9\) numbers is \(50\). So, if n lies within one standard deviation of the mean, then
\(50 – 2.xxx < n < 50 + 2.xxx\)
\(47.xxx < n < 52.xxx\)
and \(n = 48, 49, 50, 51, or 52.\)
There are five numbers in this range.

Therefore, the answer is A.
Answer : A
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Re: 46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu &nbs [#permalink] 20 Dec 2017, 01:00
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