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problem in standard deviation questions

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by nitin setia » Wed Aug 27, 2008 5:57 am
The average of 100 numbers is 6, and the standard deviation is D, where D is positive. When added which of the following numbers, the new deviation will be less than D?
A. -6 and 0
B. 0 and 0
C. 0 and 6
D. 0 and 12
E. 6 and 6

the answer here is D but can sum1 explain me how do u arrive to this answer.

Thanks
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by hengirl03 » Wed Aug 27, 2008 9:26 am
Should the answer be E: 6 and 6? Standard deviation is how far a number deviates from the mean, right? So if you add 6 and 6, shouldn't the SD become smaller, since 6 is the mean?

Am I missing something?
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by nitin setia » Wed Aug 27, 2008 9:39 am
i appreciate ur response...i guess if u add in 6 & 6 the numerator will not change...while new deviatin will increase by 2...correct me if m wrong & neways the answer tat i hve is D
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by sumithshah » Wed Aug 27, 2008 9:00 pm
Hey Nitin!

Where did you get this question from?
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by hengirl03 » Wed Aug 27, 2008 11:33 pm
Does anyone know how to solve this problem?

Also, what should I know about Standard Deviation for the GMAT? I read about the 34% 14% 2??% tip somewhere, but I not quite sure how to apply it. Thanks!
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Re: problem in standard deviation questions

by x2suresh » Wed Aug 27, 2008 11:54 pm
nitin setia wrote:The average of 100 numbers is 6, and the standard deviation is D, where D is positive. When added which of the following numbers, the new deviation will be less than D?
A. -6 and 0
B. 0 and 0
C. 0 and 6
D. 0 and 12
E. 6 and 6

the answer here is D but can sum1 explain me how do u arrive to this answer.

Thanks
It should be E.

A large standard deviation indicates that the data points are far from the mean and a small standard deviation indicates that they are clustered closely around the mean.
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by Ian Stewart » Thu Aug 28, 2008 6:30 am
The question is from GMATPrep, I believe. The answer here is certainly E, not D, as a few people have pointed out above.
hengirl03 wrote: I read about the 34% 14% 2??% tip somewhere, but I not quite sure how to apply it. Thanks!
When you mention 34% etc, you're referring to details of the 'normal distribution'. That's definitely not something you need to know for the GMAT.
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by GG04 » Wed Sep 10, 2008 7:52 am
can someone please explain this in detail?
Thanks for your help!
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by nikhilagrawal » Fri Sep 26, 2008 4:29 am
can some1 explain the fundamental surrounding ths question ?
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by [email protected] » Fri Sep 26, 2008 4:47 am
Since the average is 6, of the 100 numbers, and we are again adding 6 & 6,it means the deviation will reduce since the numbers are closer to the mean and hence the answer is D
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by bleacherseat » Sat Sep 27, 2008 6:06 am
you dont really need to solve this problem at all.

Think abt it. you are looking for a standard deviation less than D.


Std dev = sq root of [(mean - number)^2 for all numbers / number in that set of number]

so to decrease D , you need to decrease the numerator and increase the denominator.

Denominator is increased to 102 from 100 in all cases.


For numerator to be less, you would need to value of mean to increase. d and e increases the mean most. Between those two answer choices E will decrease the numerator most ,hence is the right answer
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by its time » Tue Dec 22, 2009 4:28 am
Logically, SD of a set will decrease if you add numbers which are equal to its mean. Thus the answer should be E.

I will however provide you with mathematical reasoning to justify the above statement.

S.D. for hundred numbers = d = where 'S' is sum of the squares of the difference between each number and the mean.

Now let the two numbers added be 'x' and 'y'.

S.D after adding the two numbers will be =sq rt ( s/102 + [(x-6)sq+(y-6)sq]/102)

Now it is obvious that will be less than . Also, the minimum value of will be 0 when both 'x' and 'y' are equal to 6.

Thus if the two numbers added are equal to the mean, the SD of the set must decrease. (Unless of course SD of the set was 0 to start with (not in our case) and then in that case SD will remain constant).

Answer : E
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by Lattefah84 » Tue Dec 22, 2009 5:18 am
hengirl03 wrote:Does anyone know how to solve this problem?

Also, what should I know about Standard Deviation for the GMAT? I read about the 34% 14% 2??% tip somewhere, but I not quite sure how to apply it. Thanks!
U used the Official Guide 12nd edition? (& quantitative review) ?
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by hamxa » Thu Dec 24, 2009 11:41 am
@ its time:
thanks for posting sense.
so many ppl here are just spamming !!
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