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

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

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22 May 2006, 04:03
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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?

1. -6 and 0
2. 0 and 0
3. 0 and 6
4. 0 and 12
5. 6 and 6
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22 May 2006, 05:06
See which one gives the smallest value for
totals of (number - mean)^2

Ans = E
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Re: PS - Standard Deviation (GMATPrep) [#permalink]

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23 May 2006, 09:06
ffgmat wrote:
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?

1. -6 and 0
2. 0 and 0
3. 0 and 6
4. 0 and 12
5. 6 and 6

E is true. since 6 is the mean, adding 6 twice lower the SD.
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23 May 2006, 13:27
Agree it should be E.

By adding elements close to the average, the spread/standard deviation should reduce.
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23 May 2006, 18:50
E as well

In order to lower the standard deviation the new data have to add nothing to the dispersion of the data. Thus, the new data must have the lowest squared value of the difference between the data and the mean.
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23 May 2006, 18:50
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# A certain list of 100 data has an average (arithmetic mean)

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