Green2k1 wrote:
Data set \(S\) consists of positive numbers. If -1 is added as an element to set \(S\), which of the following is
NOT possible?
A. The mean will decrease but median will not change.
B. The median will decrease but mean will not change.
C. The range will increase but median will not change.
D. The range will increase but mean will decrease.
E. The standard deviation will increase but mean will decrease.
BunuelHow can we justify option C The range will increase but median will not change. This case is also not possible.
if i am not mistaken -
addition and subtraction does not has impact on Range or Standard deviation- also the option C says that median will not change - Median will change??
S = {1, 1} --> the range = 0 and the median = 1.
S' = {-1, 1, 1} --> the range = 2 (increased) and the median =1 (the same).
As you can see C (The range will increase but median will not change) is possible.
I think you are mixing adding a constant to ALL elements of a set with adding a number AS AN ADDITIONAL element TO a set.
Yes i faltered at reading the question stem. "If -1 is added
an element to set SS" - i considered, adding -1 to each element of set S.