Is the standard deviation of the numbers in list R less than the standard deviation of the numbers in list S ?
(1) The range of the numbers in R is less than the range of the numbers in S.
(2) Each number in R occurs once and each number in S is repeated.
nick1816 wrote:
Statement 2 -
Since each number in S is same, SD of S is 0.
nick1816 Thanks for your solution.
This problem has unusual wording, and I believe there is a misunderstanding of the word "repeated". I also read the question this way my first time too, and quickly chose B.
However, after slowing down and retrying and confirming with the
OG, the word "repeated" does not mean ALL the same. It only means that each number is repeated more than once. As a result, we can pick values that make (2) insufficient.
Looking at both statements combined, with some example numbers, to see if we can get both a "Yes" and "No" answer:
Case A: "No", SD of R>S
R = {0,10}
S = {0,0,6,6,6,6,6,6,6,6,6,6,12,12} ---> most of the values are the same as the average of 6, so the standard deviation will be relatively low.
Case B: "Yes", SD of R<S
R = {10} ---> SD = 0
S = {0,0,12,12} ---> SD > 0
Insufficient together --> Answer is E
Note: We do not need the Standard Deviation formula used in the OG. We just need to know the concept that it measures how spread out the data is overall, relative to the mean. A few properties come up more often than others:
1) If we add the same value to each number in a set, the standard deviation doesn't change.
2) If we multiply each value by a constant, the standard deviation is multiplied by that constant.
3) If the range is 0, then the standard deviation is 0
4) As we see in statement 1, just because the range is lower doesn't mean that the standard deviation is lower. Range = Max - Min, whereas standard deviation measures the overall spread of all the values. _________________