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11 Oct 2023, 03:42
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E
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Difficulty:
55%
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Question Stats:
56% (01:06) correct
44%
(01:13)
wrong
based on 208
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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
(1) Range of set X is greater than that of set Y
(2) Mean of set X is greater than that of set Y
11 Oct 2023, 22:47
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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.
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.
exam_explorer
12 Oct 2023, 07:22
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exam_explorer
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
