A certain list of 100 data

[Capthan]

A certain list of 100 data has an average 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 a SD less than d?

a) -6 and 0
b) 0 and 0
c) 0 and 6
d) 0 and 12
e) 6 and 6

please explain your answer.

[Kunal]

In order to decrease the Std Dev we need to add the 2 new # which are as close to the avg 6 as possible. So I would select the option E. Whats the OA?

[RonPurewal]

ok, so "standard deviation" measures the SPREAD of the data around the average. in other words, the farther the data are from the average, the greater the s.d.

in other words:
* if you ADD data that are FARTHER FROM THE AVERAGE than are the existing data, then the s.d. will INCREASE.
* if you ADD data that are CLOSER TO THE AVERAGE than are the existing data, then the s.d. will DECREASE.

this means that you have to add data that are CLOSER to the average (i.e., 6).

the only way to ensure this is to add actual 6's, because you have no idea how far the existing points are from 6; for all you know, the entire set could be a bunch of 5.9999's and 6.0001's. (all you know is that at least some of the data points are non-6's, because otherwise the standard deviation would be 0 and couldn't be decreased.)

therefore, (e).

[anoo.anand]

thanks RON ..for the explanation...

just one morw query... in this case shud we consider that what ever value we add...the average should remain same ??

if so then we only hav 2 options left 0 & 12 ; and ; 6 & 6


Thanks ...

[RonPurewal]

thanks RON ..for the explanation...

just one morw query... in this case shud we consider that what ever value we add...the average should remain same ??

if so then we only hav 2 options left 0 & 12 ; and ; 6 & 6


Thanks ...

no, this is just a question about the standard deviation.

adding, for instance, 6 and 7 would create a smaller standard deviation than would adding 0 and 12, even though 6 and 7 don't have an average of 6.

all that matters, as stated in the posts above, is how close the numbers are to the average.

--

side note: please do not write abbreviations such as "shud" (or "+ve" or "-ve"). they make posts extremely hard to read.
thanks in advance.