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If a certain sample of data has a mean of 24.0 and the value

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Raghunathnallu
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If a certain sample of data has a mean of 24.0 and the value [#permalink] New post   Updated on: 28 May 2014, 12:06
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If a certain sample of data has a mean of 24.0 and the value 31.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample

A. 3.75
B. 3.50
C. 3.25
D. 3.00
E. 2.75
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E

Originally posted by Raghunathnallu on 28 May 2014, 10:05.
Last edited by Bunuel on 28 May 2014, 12:06, edited 2 times in total.
Edited the question.
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Bunuel
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If a certain sample of data has a mean of 24.0 and the value [#permalink] New post   28 May 2014, 12:11
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Raghunathnallu wrote:
If a certain sample of data has a mean of 24.0 and the value 31.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample

A. 3.75
B. 3.50
C. 3.25
D. 3.00
E. 2.75


Since 31.0 is more than 2.5 standard deviations from 24, we have 31 > 24 + 2.5*{SD}. This implies 2.5*{SD} < 7, and consequently, {SD} < 2.8. Only option E offers the standard deviation less than 2.8.

Answer: E.
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Bunuel
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If a certain sample of data has a mean of 24.0 and the value [#permalink] New post   28 May 2014, 12:17
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Bunuel wrote:
Raghunathnallu wrote:
If a certain sample of data has a mean of 24.0 and the value 31.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample

A. 3.75
B. 3.50
C. 3.25
D. 3.00
E. 2.75


Since 31.0 is more than 2.5 standard deviations from 24, we have 31 > 24 + 2.5*{SD}. This implies 2.5*{SD} < 7, and consequently, {SD} < 2.8. Only option E offers the standard deviation less than 2.8.

Answer: E.


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Hope this helps.
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Raghunathnallu
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Re: If a certain sample of data has a mean of 24.0 and the value [#permalink] New post   28 May 2014, 23:54
It definitely does Bunuel. Your explanations are so apt and crisp which are easy to understood for a student who is coming from a non mathematical background. Thx a ton again
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AliciaSierra
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If a certain sample of data has a mean of 24.0 and the value [#permalink] New post   29 May 2014, 19:59
Bunuel wrote:
Raghunathnallu wrote:
If a certain sample of data has a mean of 24.0 and the value 31.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample

A. 3.75
B. 3.50
C. 3.25
D. 3.00
E. 2.75


Since 31.0 is more than 2.5 standard deviations from 24, we have 31 > 24 + 2.5*{SD}. This implies 2.5*{SD} < 7, and consequently, {SD} < 2.8. Only option E offers the standard deviation less than 2.8.

Answer: E.


Bunuel,

Could you little explain how "2.5 standard deviations from the mean" is 2.5*SD. Why we are multiplying.

Regards,
Ammu
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Bunuel
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If a certain sample of data has a mean of 24.0 and the value [#permalink] New post   30 May 2014, 01:15
Expert Reply
ammuseeru wrote:
Bunuel wrote:
Raghunathnallu wrote:
If a certain sample of data has a mean of 24.0 and the value 31.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample

A. 3.75
B. 3.50
C. 3.25
D. 3.00
E. 2.75


Since 31.0 is more than 2.5 standard deviations from 24, we have 31 > 24 + 2.5*{SD}. This implies 2.5*{SD} < 7, and consequently, {SD} < 2.8. Only option E offers the standard deviation less than 2.8.

Answer: E.


Bunuel,

Could you little explain how "2.5 standard deviations from the mean" is 2.5*SD. Why we are multiplying.

Regards,
Ammu


How much is 2 standard deviations? Isn't it {SD} + {SD} = 2*{SD}?
How much is 2.5 standard deviations? Isn't it {SD} + {SD} + {SD}/2 = 2.5*{SD}?

Check the links to similar questions in my post above, they should help to understand this problem better.
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Hasini22
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Re: If a certain sample of data has a mean of 24.0 and the value [#permalink] New post   05 Dec 2023, 18:37
Is the problem related to standard deviation curve. Can anyone explain it clearly

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Bunuel
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Re: If a certain sample of data has a mean of 24.0 and the value [#permalink] New post   06 Dec 2023, 00:07
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Hasini22 wrote:
Is the problem related to standard deviation curve. Can anyone explain it clearly

Posted from my mobile device


If by "standard deviation curve" you mean the bell curve of a normal distribution then the answer is no. The question is explained clearly here: HERE, with further elaboration in a few subsequent posts.. Also, HERE several similar problems are given for practice. Please review carefully. If still not clear, please ask specific questions.

Hope it helps.
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Re: If a certain sample of data has a mean of 24.0 and the value [#permalink]
06 Dec 2023, 00:07
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