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

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Manager
Joined: 14 Nov 2005
Posts: 67
Followers: 1

Kudos [?]: 0 [0], given: 0

A certain list of 100 data has an average (arithmetic mean) [#permalink]  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
Director
Joined: 24 Oct 2005
Posts: 660
Location: London
Followers: 1

Kudos [?]: 7 [0], given: 0

[#permalink]  22 May 2006, 05:06
See which one gives the smallest value for
totals of (number - mean)^2

Ans = E
VP
Joined: 29 Dec 2005
Posts: 1349
Followers: 7

Kudos [?]: 30 [0], given: 0

Re: PS - Standard Deviation (GMATPrep) [#permalink]  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.
VP
Joined: 21 Sep 2003
Posts: 1069
Location: USA
Followers: 3

Kudos [?]: 38 [0], given: 0

[#permalink]  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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Manager
Joined: 10 Jun 2004
Posts: 84
Followers: 1

Kudos [?]: 0 [0], given: 0

[#permalink]  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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-Genius is one percent inspiration, and ninety-nine percent perspiration.

[#permalink] 23 May 2006, 18:50
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# A certain list of 100 data has an average (arithmetic mean)

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