Is the standard deviation of the scores of Class A’s students greater

Question: Is \(SD_A > SD_B\)?

CONCEPT: Standard deviation depends on the following two measures
1) The number of terms in the set
2) Separation between the terms when terms arranged in increasing order

Standard Deviation does NOT depend on
1) How big/small the terms are

Statement 1: The average (arithmetic mean) score of Class A’s students is greater than the average score of Class B’s students.
Greater Average of one set than the other set doesn't predict which set will have larger/smaller standard deviation hence
NOT SUFFICIENT

Statement 2: The median score of Class A’s students is greater than the median score of Class B’s students
Greater Median of one set than the other set doesn't predict which set will have larger/smaller standard deviation hence
NOT SUFFICIENT

Combining the two statements

Case 1:
Set A = {10, 11, 12, 13, 14}
Set B = {0, 1, 2, 3, 4}

Set A has higher mean and median than that of set B but the standard deviation of both sets are same

Case 2:
Set A = {10, 11, 12, 13, 14}
Set B = {0, 1, 2, 3, 5}

Set A has higher mean and median than that of set B but the standard deviation of Set A is smaller than Standard deviation of set B

Case 3:
Set A = {10, 11, 12, 13, 15}
Set B = {0, 1, 2, 3, 4}

Set A has higher mean and median than that of set B and the standard deviation of Set A is bigger than Standard deviation of set B

NOT SUFFICIENT

Answer: Option E