S and T are sets of numbers. The standard deviation of the

Question

S and T are sets of numbers. The standard deviation of the elements of set S is q. Is the standard deviation of S U T greater than q? 

(1) The range of S U T is different from the range of S. 
(2) There is only one element in T, and it is twice the arithmetic mean of the elements in S.

I know it is posted before but if you please help me with the concept here.

* from the question stem i thought that in sets we are not allowed for repetition.  Please clarify 

if repetiton is allowed then

s U t could be s if this is the case then we have one of two scenarios

1) every element in s is in t and visa versa .... therfore the range , the mean and the median remain as is and thus the variance is the same.

2) t is only a subset of s ......therfore the range stay as is ( , the median and the mean might or might not change depending on whether repetition is or is not allowed. and the variance may inc or decrease depending on the the values of T and their location from the mean.

 Am i right ? please explain 

from st one :

The range changed : therfore my conclusion is 

The range must have increased . and thus the mean of the new set changed and the median changed too.

regarding the variance : sure it has changed but we can never know whether with an inc or dec.

 Is this because of , it could be a case where only one extreme values is introduced, but as long as we have no idea about the rest of elements in T WE CAN NEVER KNOW THE OVERALL EFFECT of T on the variance of the new set? 

St two we are gain introducing relatively one extreme value if compared to the mean ......

 Is this because the mean of S will change ( increase) and thus still we can never know the effect of this change on the distance of each value in the newly formed set unless we know each element ??( s U t) 

I will highly appreciate if any one can clarfiy the concepts.

Thanks in advance

kevincan · Answer

Why isn't repetition allowed? S={1,2,3,4,4,5}is a valid set.

yezz · Answer

Thanks for your reply Kevin ,

I know you posted this extremely exciting problem??

Can you please explain the rest of my inquiries....i will highly appreciate it and i promise i will try the ( Beach combers) :lol:

Thanks

Thanks

kevincan · Answer

Right! Adding elements to a set and increasing its range will not necessarily increase standard deviation. Consider {0,0,0,0,10} as S and {-0.1} as T. SD can even fall in (2), as long as the mean is a very small number

yezz · Answer

Thanks ya basha

I WILL KEEP MY PROMISE

S and T are sets of numbers. The standard deviation of the

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