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

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If a certain sample of data has a mean of 24.0 and the value  [#permalink]

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New post Updated on: 28 May 2014, 11:06
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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

Originally posted by Raghunathnallu on 28 May 2014, 09:05.
Last edited by Bunuel on 28 May 2014, 11:06, edited 2 times in total.
Edited the question.
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Re: If a certain sample of data has a mean of 24.0 and the value  [#permalink]

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New post 28 May 2014, 11:11
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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


31.0 is more than 2.5 standard deviations from 24 --> 31 > 24 + 2.5*{SD} --> 2.5*{SD} < 7 --> {SD} < 2.8. Only option E offers the standard deviation less than 2.8.

Answer: E.
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Re: If a certain sample of data has a mean of 24.0 and the value  [#permalink]

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New post 28 May 2014, 11:17
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


31.0 is more than 2.5 standard deviations from 24 --> 31 > 24+2.5*{SD} --> 2.5*{SD} < 7 --> {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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Re: If a certain sample of data has a mean of 24.0 and the value  [#permalink]

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New post 28 May 2014, 22:54
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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Re: If a certain sample of data has a mean of 24.0 and the value  [#permalink]

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New post 29 May 2014, 18:59
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


31.0 is more than 2.5 standard deviations from 24 --> 31 > 24 + 2.5*{SD} --> 2.5*{SD} < 7 --> {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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Re: If a certain sample of data has a mean of 24.0 and the value  [#permalink]

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New post 30 May 2014, 00:15
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


31.0 is more than 2.5 standard deviations from 24 --> 31 > 24 + 2.5*{SD} --> 2.5*{SD} < 7 --> {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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Re: If a certain sample of data has a mean of 24.0 and the value  [#permalink]

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Re: If a certain sample of data has a mean of 24.0 and the value   [#permalink] 28 Mar 2017, 10:12
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