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Senior Manager  Joined: 21 Oct 2013
Posts: 408
M is a certain set of numbers with an average (arithmetic  [#permalink]

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4
15 00:00

Difficulty:   45% (medium)

Question Stats: 67% (01:58) correct 33% (01:50) wrong based on 229 sessions

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M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 2.5. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?

A. {3, 4, 5, 10, 14}
B. {3, 6, 7, 10, 12}
C. {3, 5, 5, 10, 16}
D. {1, 5, 7, 10, 18}
E. {5, 6, 7, 10, 12}
Math Expert V
Joined: 02 Sep 2009
Posts: 61549
M is a certain set of numbers with an average (arithmetic  [#permalink]

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5
goodyear2013 wrote:
M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 2.5. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?

A. {3, 4, 5, 10, 14}
B. {3, 6, 7, 10, 12}
C. {3, 5, 5, 10, 16}
D. {1, 5, 7, 10, 18}
E. {5, 6, 7, 10, 12}

Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 5 to 10 + 2*{SD} = 15.

A. {3, 4, 5, 10, 14} --> only 3 numbers are in this range. Discard.
B. {3, 6, 7, 10, 12} --> 4 numbers are in this range. OK.
C. {3, 5, 5, 10, 16} --> only 3 numbers are in this range. Discard.
D. {1, 5, 7, 10, 18} --> only 3 numbers are in this range. Discard.
E. {5, 6, 7, 10, 12} --> all 5 numbers are in this range. Discard.

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Hope this helps.
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Manager  B
Joined: 29 Jan 2018
Posts: 52
Concentration: Marketing, Strategy
Re: M is a certain set of numbers with an average (arithmetic  [#permalink]

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10 - 2*{SD} = 5 to 10 + 2*{SD} = 15

Thanks
Intern  B
Joined: 20 Oct 2019
Posts: 4
M is a certain set of numbers with an average (arithmetic  [#permalink]

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Ratnaa19 wrote:
10 - 2*{SD} = 5 to 10 + 2*{SD} = 15

Thanks

If anyone else is confused: SD is 2.5. Being that we're looking for numbers that are outside 2 of the SD, it's 2.5 * 2 in both higher and lower from the mean i.e. 5 and 15

IMO the confusing part of that statement is the "to". Those are two separate statements. Within the 2 SD deviation we have 5, and then we have 15, or otherwise 5 to 15. The way I'd phrase it is as such:

Low End: 10 - 2*{SD} = 5
High End: 10 + 2*{SD} = 15

Total range that's within 2 SD: 5 to 15.

i.e. Ans. B

Hope that's helpful to anyone, I'm currently doing my best to avoid my actual job by answering random posts!

Originally posted by conormdr203 on 03 Jan 2020, 06:42.
Last edited by conormdr203 on 03 Jan 2020, 08:21, edited 1 time in total.
SVP  V
Joined: 03 Jun 2019
Posts: 2025
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
Re: M is a certain set of numbers with an average (arithmetic  [#permalink]

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goodyear2013 wrote:
M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 2.5. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?

A. {3, 4, 5, 10, 14}
B. {3, 6, 7, 10, 12}
C. {3, 5, 5, 10, 16}
D. {1, 5, 7, 10, 18}
E. {5, 6, 7, 10, 12}

Terms in Q = 5
80% *5 = 4 terms are located within 10 +-5, i.e between 5 & 15.

Only B{3,6,7,10,12} satisfy the condition.

IMO B
SVP  V
Joined: 03 Jun 2019
Posts: 2025
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
Re: M is a certain set of numbers with an average (arithmetic  [#permalink]

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Ratnaa19 wrote:
10 - 2*{SD} = 5 to 10 + 2*{SD} = 15

Thanks

Mean = 10
S. D. = 2.5
2 SD = 2*2.5 = 5
2 SD around mean is 10 - 5 to 10+5, i.e. between 5 and 15 Re: M is a certain set of numbers with an average (arithmetic   [#permalink] 03 Jan 2020, 08:08
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