If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviation from the mean ?
* 12.0 ( right Answer )
* 13.5
* 17.0
* 23.5
* 26.5
Thanks.
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Mean and standard Deviation
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penumbra547
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I assume you are asking why the answer is (a).
if so, here is why.
Think of standard deviation(sd) as distance from the mean. So in this case, 2.5 times the sd is 2.5x3=7.5. <=== that's the distance from the mean.
therefore, you add and subtract 7.5 to the mean in order to get both extremes. in this case, it is 20+7.5=27.5, and 20-7.5=12.5. so imagine this range, from 27.5 and 12.5, and see which of the given values fall outside the range.
Voila! (A) is the answer.
if so, here is why.
Think of standard deviation(sd) as distance from the mean. So in this case, 2.5 times the sd is 2.5x3=7.5. <=== that's the distance from the mean.
therefore, you add and subtract 7.5 to the mean in order to get both extremes. in this case, it is 20+7.5=27.5, and 20-7.5=12.5. so imagine this range, from 27.5 and 12.5, and see which of the given values fall outside the range.
Voila! (A) is the answer.
