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Standard Deviation

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Standard Deviation

by Anahatha » Sun Aug 29, 2010 10:25 am
I have 2 doubts regarding SD:

[1]If two sets have equal number of terms and are evenly spaced , will their SDs be equal?
Please explain with an example

[2]The SD of an existing set is x. If we have to add more numbers to this set

a. without altering SD
b.reducing SD
c.increasing SD

how do we do it?

Please explain :(
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by TheGmatTutor » Sun Aug 29, 2010 6:08 pm
1) Not necessarily. The set

{6,8,10}

has a lower standard deviation than the set

{5,8,11}

However, the SD of the set

{6,7,8}

is equal to that of

{7,8,9}

Does that help?
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by Anahatha » Mon Aug 30, 2010 12:02 am
Thanks.. Please can you explain my second question too?For example, what is the solution for a problem like this


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

[A]-6,0

0,0

[C]0,6

[D]0,12

[E]6,6


Please explain
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by uwhusky » Mon Aug 30, 2010 12:25 am
I think to best understand SD is to know how to calculate SD.

The answer to your question is E, 6, 6, because it reduces SD by adding two more terms without increasing the variance.

To answer your previous question, I don't think you need to worry about not altering SD for GMAT. As for reducing SD, you can do so by adding numbers to the set that are closer to the average than the existing numbers, and for increasing SD, do the opposite, which is to add numbers that are larger than the average.
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