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# A certain list of 100 data has an average (arithmetic mean)

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Joined: 01 Aug 2007
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A certain list of 100 data has an average (arithmetic mean) [#permalink]  28 Aug 2007, 05:12
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A certain list of 100 data has an average (arithmetic 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 standard deviation less than d?

a) -6 and 0
b) 0 and 0
c) 0 and 6
d) 0 and 12
e) 6 and 6
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Joined: 27 Aug 2007
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E

as per SD formula
SD = sqrt( sum(square(each term - average))/n-1)

6,6 does not increases the numerator, but denominator increase for all: from 99 to 101

so, overall SD decreases
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