Is the standard deviation of set S greater than the standard deviation

Case 1-

S = {1,11} and T={1,10}

SD of S > SD of T

Case 2-

S = {1,6,11} and T={1,10}

SD of S < SD of T

Both cases satisfy both statements and give different answer.

Insufficient

E

IMO A,

Statement 1: The range of set S is greater than the range of set T:

The range rule tells us that the standard deviation of a sample is approximately equal to one-fourth of the range of the data. In other words s = (Maximum – Minimum)/4.
Therefore if the range of Set S is 10 and Range if set T is 5
The approximate Standard deviation of set S = 10/4 = 2.5
Whereas standard deviation of set T = 5/4 = 1.25
Therefore,
Set S Standard Deviation > Set T Standard Deviation
(Sufficient)

Statement 2: The mean of set S is greater than the mean of set T

Case 1: Let say mean of set S is 8 where Set S is (6,7,8,9,10)
And Set T mean is 6 where set T is (2,4,6,8,10)
Using the range method.
Set T range is higher than Set S making standard deviation of set T is higher than Set S.
Set T SD > Set S SD

Case 2: Let say mean of set S is 8 where Set S is (4,6,8,10,12)
And Set T mean is 6 where set T is (4,5,6,7,8)
Using the range method.
Set T range is lower than Set S making standard deviation of set T is lower than Set S.
Set T SD < Set S SD
(Insufficient)

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sd measures the dispersion of a dataset relative to its mean
without knowing the terms, we cannot know the sd

(1) insufic
no info about the terms

(2) insufic
no info about the terms;
also, sets with different means can have the same sd

(1/2) insufic
no info about the terms

Ans (E)

Is the standard deviation of set S greater than the standard deviation of set T ?

Statement 1: The range of set S is greater than the range of set T
Clearly Insufficient. As mean is not known, the no, of elements in the sets are not known, it could be anything.

Statement 2: The mean of set S is greater than the mean of set T.
Clearly Insufficient. The no. of elements in the set is unknown. The spread of the set is also unknown.

Combining the 2 statements also doesn't help much.
In my opinion.

Answer is E.

(1) The range of set S is greater than the range of set T


Range = highest -lowest

Standard deviation is square root of average the square of the distance from mean .

If Set T has more number of terms that is some distance from mean it will have more standard deviation irrespective of the range .

Insufficient .

(2) The mean of set S is greater than the mean of set T

Standard deviation is square root of average the square of the distance from mean .

If a set has more no of terms then at some distance from mean then it's standard deviation will be more.
Insufficient .

Combining 1 and 2 also
Insufficient .

Hence E is the ans .

Is the standard deviation of set S greater than the standard deviation of set T ?

(1) The range of set S is greater than the range of set T
(2) The mean of set S is greater than the mean of set T

1) Relative range is given, but not individual values to find the spread
insufficient

2) Relative Mean is given, but not the individual values
insufficient

1+2)
we cant say anything about the spread of values in each of the set
insufficient

Ans E

Bunuel Sir kindly explain why range rule is not valid here?
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Solution:

Statement One Alone:

The range of set S is greater than the range of set T.

Despite knowing the range of set S is greater than the range of set T, we can’t determine whether the standard deviation of set S is greater than the standard deviation of set T. We have no information about the individual data values in either set, nor do we know the number of elements in either set.

Statement Two Alone:

The mean of set S is greater than the mean of set T.

Despite knowing the mean of set S is greater than the mean of set T, we can’t determine whether the standard deviation of set S is greater than the standard deviation of set T. Again, we have insufficient information about the individual data values in either set and the number of elements in either set.


Statements One and Two Together:

Despite knowing both the range and the mean of set S is greater than the corresponding measures of set T, we still can’t determine whether the standard deviation of set S is greater than the standard deviation of set T. Without knowing any data values in either set, it’s impossible to determine which set has a larger standard deviation.

Answer: E

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