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From Prep - Standard Deviation

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From Prep - Standard Deviation

by mocha » Sat Mar 07, 2009 5:26 pm
Hi All,

Can any of you please explain the below question ?

A certain set of 100 data has a mean of 6 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 102 data with a SD less than d ?

A. -6 and 0
B. 0 and 0
C. 0 and 6
D. 0 and 12
E. 6 and 6

I know that SD is the distribution from the center point or Avg of the data.

I cant understand what the question is asking ?

Also, how can I black out the OA ?

Thanks a lot everyone for looking in. Appreciate your help.
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by Feep » Sat Mar 07, 2009 7:50 pm
The answer should be E. The question is asking what two points can you add to the set to lower the standard deviation.

Adding two (or one, or a hundred) data points at the exact mean cannot possibly raise the standard deviation. It could technically leave it the same, if the standard deviation was zero, but we know from the question that it had some non-zero value to start. So, this must necessarily lower the standard deviation.

Remember, standard deviation can be thought of as a measure of how closely to the mean the data is clustered. -200 -100 0 100 200 has a much larger standard deviation than -0.2 -0.1 0 0.1 0.2.
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