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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
Joined: 16 Aug 2015
Posts: 6966
GMAT 1: 760 Q51 V42
GPA: 3.82
46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu  [#permalink]

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17 Dec 2017, 23:31
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:16) correct 33% (01:41) wrong based on 65 sessions

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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. $$9$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 27 Mar 2016 Posts: 13 Location: India Schools: IIM (S) GMAT 1: 590 Q49 V21 GPA: 3.9 Re: 46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu [#permalink] ### Show Tags 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. Retired Moderator Joined: 25 Feb 2013 Posts: 1216 Location: India GPA: 3.82 46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu [#permalink] ### Show Tags 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 Retired Moderator Joined: 25 Feb 2013 Posts: 1216 Location: India GPA: 3.82 Re: 46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu [#permalink] ### Show Tags 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? Intern Joined: 10 Dec 2017 Posts: 3 Re: 46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu [#permalink] ### Show Tags 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 _________________ Regards, Sneha Tatavarthy Math Facilitator International Baccalaureate Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6966 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: 46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: 46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 nu   [#permalink] 20 Dec 2017, 01:00
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