parkhydel
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.
DS93510.02
Is SD of R < SD of S?
How do we increase the SD of a set? By adding more numbers at the extremes (or removing from the middle)
How do we decrease the SD of a set? By adding more numbers at the middle (or removing from the extreme)
(1) The range of the numbers in R is less than the range of the numbers in S.
Normally, when range is greater, we might expect SD to be greater too
e.g. SD of {0, 1} < SD of {0, 100}
but that will not be the case always.
e.g. SD of {1, 100} > SD of {0, 50, 50, 50, 100}
because the second set has most elements at the mean.
(2) Each number in R occurs once and each number in S is repeated.
SD of {0, 100} > SD {0, 0, 1, 1}
SD of {0, 50, 100} = SD of {0, 0, 50, 50, 100, 100}
SD of {0, 50, 100} < SD of {0, 0, 0, 100, 100}
Not sufficient alone. There is no connection of SD when each number appears once vs when each number is repeated .
Using both,
SD of {0, 1} < SD of {0, 0, 100, 100}
SD of {1, 100} > SD of {0, 0, 50, 50, 50, 50, 50, 50, 100, 100}
Not sufficient.
Answer (E)