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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]

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19 Feb 2012, 16:04
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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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19 Feb 2012, 16:47
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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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19 Feb 2012, 16:54
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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19 Feb 2012, 17:21
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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]

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19 Feb 2012, 22:28
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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.

Similar questions to practice:
a-vending-machine-is-designed-to-dispense-8-ounces-of-coffee-93351.html#p718208
the-mean-and-the-standard-deviation-of-the-8-numbers-shown-98248.html
statistics-108665.html
math-questions-mean-score-88502.html
the-standard-deviation-of-a-normal-distribution-of-data-is-99221.html
arithmetic-mean-and-standard-deviation-of-a-certain-normal-104117.html
70-75-80-85-90-105-105-130-130-130-the-list-shown-consist-of-100361.html

PS questions on standard deviation with tips: ps-questions-about-standard-deviation-85897.html

Math Book Chapter on Standard deviation: math-standard-deviation-87905.html

Hope it helps.
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Re: If a certain sample of data has a mean of 20.0 and a [#permalink]

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26 May 2013, 05:47
Bumping for review and further discussion.
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Re: If a certain sample of data has a mean of 20.0 and a [#permalink]

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06 Jan 2015, 16:41
Hello from the GMAT Club BumpBot!

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Re: If a certain sample of data has a mean of 20.0 and a [#permalink]

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06 Jan 2015, 18:54
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Hi All,

As a math subject, Standard Deviation comes from the broader category of statistics. It's essentially about how "spread out" a group of individual numbers is, relative to the average of that group. There's a lot of interesting ways that Standard Deviation can impact decision-making processes in big business, but that's something you'll learn about in Business School. In real life, calculating the Standard Deviation of a group of numbers involves a big calculation (and you probably would NOT want to do that calculation by hand). Thankfully, the GMAT will NEVER ask you to actually calculate the Standard Deviation of a group of numbers. You're likely to be tested on the CONCEPT though.

Any time you're given the average (arithmetic mean) of a group of numbers and the Standard Deviation, then you can easily calculate Standard Deviations "away" from the mean.

In this question, we're given an average of 20 and an S.D. of 2. Standard Deviations go in "BOTH directions" on a Number Line, so.....

1 Standard Deviation "up" = 20 + 2 = 22
1 Standard Deviation "down" = 20 - 2 = 18

2 Standard Deviations "up" = 20 + 2 + 2 = 24
2 Standard Deviations "down" = 20 - 2 - 2 = 16
Etc.

The above example is a common way for the GMAT to test you on the concept.

Another way to test you is to see if you understand how to "increase" or "decrease" an S.D. by adding in new numbers to an existing group of numbers.

Using this same prompt as an example, since we have an average of 20, if we were to include ANOTHER value that = 20 (or was really close to it), then the overall group of numbers would be LESS "spread out" and the S.D. would decrease. In that same way, if we were to include ANOTHER value that was FAR from 20, then the overall group of numbers would be MORE "spread out" and the S.D. would increase.

Standard Deviation is not a big part of the GMAT, but you'll likely see it in one question. As such, it's not a big "point gainer" or "point loser" on this Test. The ways in which the GMAT will Test you on the concept are relatively simple though, so this can be an easy pick up on Test Day as long as you're clear on the concepts.

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Re: If a certain sample of data has a mean of 20.0 and a [#permalink]

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29 Feb 2016, 09:56
Hello from the GMAT Club BumpBot!

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Re: If a certain sample of data has a mean of 20.0 and a [#permalink]

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11 May 2017, 19:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a certain sample of data has a mean of 20.0 and a   [#permalink] 11 May 2017, 19:54
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