Is there a short version to this problem without listing numbers for the sets and trying out different numbers?
S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
A) The mean of S is equal to the mean of T
B) the median of S is equal to the median of T
C) the range of S is equal to the range of T
D) The mean of S is greater than the mean of T
E) The range of S is less than the range of T
i wouldn't even think of trying out numbers....
this kind of question test the understanding
of the concept of mean,range and median and their behavior. so basic understanding is enough here. here are the explanations:
we should remember that S is exactly like T plus one number which is different.
a) is there a possibility to add a number to a set that will keep the mean unchanged? of course there is... you can add the mean itself.
b) is it possible to add a number to a set of 8 numbers so that the median will remain the same? yes of course... the median of an even number of data points is half the sum of the middle points. adding this "half the sum of middle points" to the set creates another set with the same median.
c) is there a possibility to to add a number to a set without changing the range? sure there is, just add a number which is between the minimum and the maximum.
d) is there a possibility to add a number to a set so that the average increase? sure there is, just add a big number.
e) can you add a number to a set so that the range will decrease? oh no... if you add a number, either the range remains the same if you added something that is between the min and the max, or increase if you add something above the max or below the min.
E is your answer.