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Standard deviation problem

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by vishugogo » Mon Apr 15, 2013 3:45 am
Set X and set Y each contain at least 2 distinct positive integers. Sets X and Y contain the same number of integers. Is the standard deviation of set X greater than the standard deviation of set Y ?

(1) The positive difference between the range of set X and the range of set Y is 12.

(2) Each element of set Y is the square of an element of set X.

Have been able to solve it but just wanted to consider different values from statement 1....

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by srcc25anu » Mon Apr 15, 2013 2:24 pm
St1: positive difference between range of X and Y = 12
I hope I understand this condition correctly.
if set x = {1,13} and set y = {1,25} then SD (x) < SD (y)
if set x = {1,25} and set y = {1,13} then SD (x) > SD (y)
Hence Insufficient

St2: each element of Y is sqaure of an element in X
means the range and therefore the SD of Y has to be greater than SD of X
if set x = {1,2} and set y = {1,4} then SD (x) < SD (y)
if set x = {3,6} and set y = {9,16} then SD (x) < SD (y)
This will be true for any values of elements in set X and Y
hence SUfficient

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by vipulgoyal » Mon Apr 15, 2013 9:14 pm
positive difference between range of X and Y = 12
I hope I understand this condition correctly.
if set x = {1,13} and set y = {1,25} then SD (x) < SD (y) ???
here 12 - 24 = -12

Experts please suggest is there any relation B/w range and SD i mean
range is derectly proptional to SD??
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