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

Question

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

Bunuel · Answer

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 · Answer

Raghunathnallu · Answer

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

AliciaSierra · Answer

Bunuel,

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

Regards,
Ammu

Bunuel · Answer

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.

Hasini22 · Answer

Is the problem related to standard deviation curve. Can anyone explain it clearly

Posted from my mobile device

Bunuel · Answer

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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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

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