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If a certain sample of data has a mean of 20.0 and a

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If a certain sample of data has a mean of 20.0 and a [#permalink] New post 19 Feb 2012, 15:04
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If a certain sample of data has a mean of 20.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?

(A) (14.0; 16.5)
(B) (14.5; 21.0)
(C) (14.0; 26.5)
(D) (16.5; 26.0)
(E) (21.0; 26.5)

Guys - any idea how to solve this? Also, the thing that really drive me crazy is 2.5 standard deviations from the mean?. What does this mean?
[Reveal] Spoiler: OA

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Re: SD above mean [#permalink] New post 19 Feb 2012, 15:47
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You know the standard deviation is 2, so 2.5 standard deviations would be 2 times 2.5=5. Then you just look for the numbers that are at least that far from the mean (20). The answer in this case will be C, because 14 and 26.5 are each at least that far away from 20.
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Re: If a certain sample of data has a mean of 20.0 and a [#permalink] New post 19 Feb 2012, 21:28
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enigma123 wrote:
If a certain sample of data has a mean of 20.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?
(A) (14.0; 16.5)
(B) (14.5; 21.0)
(C) (14.0; 26.5)
(D) (16.5; 26.0)
(E) (21.0; 26.5)

Guys - any idea how to solve this? Also, the thing that really drive me crazy is 2.5 standard deviations from the mean?. What does this mean?


2.5 standard deviation equals to 2.5*2=5;

2.5 standard deviations from the mean, so 5 points, from the mean is the range from {mean-5} to {mean+5}, so from 15 to 25: (15, 25).

The correct answer choice must cover all this range: only answer choice C (14.0; 26.5) does this.

Answer: C.

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PS questions on standard deviation with tips: ps-questions-about-standard-deviation-85897.html
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Math Book Chapter on Standard deviation: math-standard-deviation-87905.html

Hope it helps.
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Re: SD above mean [#permalink] New post 19 Feb 2012, 15:54
A similar (or perhaps the same) question appears on OG 11th edition. The key here is the phrase "2.5 standard deviations away". Since SD is 2, you understand that phrase as 2.5 times SD, which is 5. So the answer is one where numbers fall outside the range of 15 to 25(i.e +/- 5 of the average 20. Choice C is where this happens.
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Re: SD above mean [#permalink] New post 19 Feb 2012, 16:21
What does "2.5 Standard Deviations from the mean" mean?
A Standard Deviation is simply the amount by which a number in a given set differs from the average of that set. Say, on average, you make 20 dollars an hour waiting tables but sometimes you get a mean customer and make 18 an hour or get a generous one and make 22. In this case the amount you are making ranges between 18 and 22, which is plus minus 2 dollars from your average 20 per hour pay. Say, one day, you spilled water on your customer and he/she left you no tip whatsoever and that hour you only made $16 per hour. How off is 16 from your average pay of 20? 4 dollars. What's the normal amount (SD) it is usually off by? 2. So, you would say, you earned a sum that deviated 2 times what it normally deviates from the average. In other words, your pay was 2 Standard deviations from the mean. If you had only made 15 dollars that hour, your pay was 2.5 SD away from the mean of 20 dollars.

So "X standard deviations from the mean" just means, x many times more different than what it is normally different, or x times the SD.

Hope this helps!
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Re: If a certain sample of data has a mean of 20.0 and a [#permalink] New post 26 May 2013, 04:47
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Re: If a certain sample of data has a mean of 20.0 and a   [#permalink] 26 May 2013, 04:47
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