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# A certain list of 100 data has a mean of 6 and a standard

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SVP
Joined: 21 Jul 2006
Posts: 1510
A certain list of 100 data has a mean of 6 and a standard [#permalink]

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16 Jul 2008, 06:07
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A certain list 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 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

thanks
Director
Joined: 14 Aug 2007
Posts: 727

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16 Jul 2008, 06:45
tarek99 wrote:
A certain list 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 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

thanks

I think E 6,6 should be the answer.

sum of 100 numbers = 100 * 6 = 600

D = SQRT( 1/100 * summation of [(x[i] - 6) ^2 ]

with addition of 2 terms the total number of terms will be 102, so the bracketed part of SQRT above is already smaller,

My approach involves not increasing the summation part, and 6, 6 is ideal option for this

adding 6 + 6 to 600 = 612

mean will be 612/102 = 6..unchanged
since the added terms are 6,6 , the difference (6-6) = 0 and wont add to the summation part of SQRT above

thus SD will be smaller.
CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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16 Jul 2008, 08:38
My fast approach to SD. (10-20sec)

Think of SD as average deviations of data from a mean.
the less deviations we add the more we reduce SD. 6 and 6 add the least deviations: 0=(6-6) and 0=(6-6). So, E
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Senior Manager
Joined: 07 Jan 2008
Posts: 289

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16 Jul 2008, 08:47
Mindful that, mean=6 and also keep formula for SD in mind.

Without adding anything in numerator, 6 & 6 add +2 in the denominator; So E.
SVP
Joined: 21 Jul 2006
Posts: 1510

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16 Jul 2008, 13:34
OA is E.

According to the OE, it says that when you add at least 2 numbers that are the same as the average, then the standard deviation becomes smaller. My question here is that aren't you reducing the standard deviation anyways when you add just one number that is the same as the average? do you really need at least 2 numbers??
SVP
Joined: 17 Jun 2008
Posts: 1547

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16 Jul 2008, 15:45
tarek99,

Re: PS: Standard Deviation   [#permalink] 16 Jul 2008, 15:45
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