Set X and set Y have 10 numbers each. Is standard deviation of set X

Question

Set X and set Y have 10 numbers each. Is standard deviation of set X greater than that of set Y ?

(1) Range of set X is greater than that of set Y
(2) Mean of set X is greater than that of set Y

walterwhite756 · Answer

Given X and Y have 10 nos. each.

Stmt (1):  Range of X > Range of Y
since both X and Y have 10 nos. so even if range of X > range of Y, we do not have information on individual elements of X and Y. 
For example, X = -5,0 (for 8 times), 6 and Y = -5,-5(for 8 times), 5. All conditions satisfy and Std. deviation of X < Std. deviation of Y.
Now reverse the case, X = -5, 5 (for 8 times), 6 and Y = -5, 0(for 8 times), 5. All conditions satisfy but Std. deviation of X > Std. deviation of Y.
Hence  Insufficient .

Stmt (2):  Means of X > Mean of Y
This not at all provides any info on individual elements and their distribution. Hence  Insufficient .

Stmt(1)+Stmt(2) : In both Examples for Stmt(1), Stmt(2) also holds. Therefore together, both statement are  Insufficient .

Hence (E) IMO.

chetan2u · Answer

Standard deviation is the SPREAD of each element from average..
greater the spread more the SD, lesser the spread, smaller the SD

Can we know the spread from the given info?
No, so answer should be E.

Let us check each statement

(1) Range of set X is greater than that of set Y
Set X={1,6,6,6,6,6,6,6,6,11} and set Y={1,2,3,4,6,8,8,9,9,10}
Clearly SD of Y is more than X. 
Set X={1,6,6,6,6,6,6,6,6,11} and set Y={8,8,8,8,8,8,8,8,8,10}
Clearly SD of X is more than Y. 
Insufficient

(2) Mean of set X is greater than that of set Y
Set X={6,6,6,6,6,6,6,6,6,6} and set Y={1,1,1,2,3,4,4,4,4,4}
Clearly SD of Y is more than X. 
Set X={1,6,6,6,6,6,6,6,6,11} and set Y={4,4,4,4,4,4,4,4,4,4}
Clearly SD of X is more than Y. 
Insufficient

Combined
Set X={1,6,6,6,6,6,6,6,6,6} and set Y={2,2,2,2,2,2,2,2,2,2}
Clearly SD of X is more than Y. 
Set X={1,3,3,3,3,3,3,3,3,5} and set Y={1,1,1,1,2,2,4,4,4,4}
Clearly SD of Y is more than X. 
Insufficient

E

ostrick5465 · Answer

(1): the range of a set is not enough to tell about its standard deviation => Insuff
(2): we don't care about the maximum value or minimum value, we do care about the distance from these values to the mean => Insuff

(1)&(2): still cannot compare standard deviation

=> IMO E

Score-Quest · Answer

Even if we know that both the range and mean of set X are greater than those of set Y, it's still not enough information to definitively conclude which set has a greater standard deviation.

For instance, consider the following sets:
Set X: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 (Mean = 55, Range = 90)
Set Y: 1, 2, 3, 4, 5, 6, 7, 8, 9, 50 (Mean = 9.5, Range = 49)
Here, Set X has higher mean and a larger range and also has a higher standard deviation.

But, consider the following sets:
Set X: 10, 50, 50, 50, 50, 50, 50, 50, 50, 100 (Mean = 51, Range = 90)
Set Y: 1, 1, 1, 1, 1, 1, 1, 1, 1, 90 (Mean = 9.9, Range = 89)
Here, Set X has both a higher mean and a larger range than Set Y. However, the standard deviation of Set Y is larger because of the outlier (90), which causes a greater spread of values around the mean compared to Set X.

Thus, even both statements together are not enough to answer the question.

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Set X and set Y have 10 numbers each. Is standard deviation of set X

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Set X and set Y have 10 numbers each. Is standard deviation of set X

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