Set S consists of positive numbers. If -1 is added

Thanks a Lot Zarrolou and Ron

BTW seems like GMAT is a playground for all RONs ( Previously It was Manhattan Ron , Now Vertisas Ron) ...I am definitely going give my son's name RON..hehehhehe( i m still unmarried )

Jokes apart can someone tell me when are the below conditions become false.... (these changes in mean , median really bug me up)

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.

m17 q33

Set S consists of positive numbers. If -1 is added as an element to set S, which of the following is impossible ?

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.

The mean of set S is \(\frac{sum}{n}\), where \(n\) is the number of terms in set S.

Since set S consist of positive numbers, then when we add -1 to the set the sum of the numbers in the new set will decrease. So, the new mean will be \(\frac{less \ sum}{more \ terms}=\frac{less \ sum}{n+1}\), which will be less than \(\frac{sum}{n}\). Hence the mean must decrease.

Answer: B.

Hey sujit2k7, thanks for the compliment about the Rons! I'll pass it on to my parents. I tell them it stands for "Really Outstanding Name"

As for your question about when these changes become false, Zarrolou's post gives a good example of how these conditions can change with the set 2,2. All four other options (A, C, D, E) could occur in that situation. In general terms, the introduction of a new term will change the mean of a set unless the new term is exactly that mean. However a median can remain the same even if scores of new numbers are introduced.

Consider a set consisting of ten 5's {5,5,5,5,5,5,5,5,5,5}. You could add -1's until the number of terms in this set went from 10 to 19 and the set would then be {-1,-1,-1,-1,-1,-1,-1,-1,-1, 5,5,5,5,5,5,5,5,5,5}, in which case the middle term would still be 5, so the mean would remain unchanged. However as soon as you add a single -1 the mean will drop from 5 to 4.5 or so. It helps when looking at these abstract questions to try real numbers and then draw logical conclusions from your observations.

Hope this helps!
-Ron

The question becomes a simple one because of one word : Positive.

So, in case the set consists of only positive number, the mean will be positive.
Now, when we add a negative number, the mean HAS to go down.
Any option that tells you ' mean does not change' or 'mean will increase' are impossible.

Only B stands.

But let us work on each of the cases.

Mean: Will decrease always.

Median: Will decrease or remain the same. It will NEVER increase.
{2,2,2,3} and {-1,2,2,2,3}....Median is 2 in each case
{1,2,3} and {-1,1,2,3}....Median is 2 and 1.5 respectively

Range: Will increase always.(by at least 1)
{2,2,2,3} and {-1,2,2,2,3}....Range is 1 and 4 respectively

SD: Should increase almost always as the spread increases.



A. The mean will decrease but median will not change.
Possible

B. The median will decrease but mean will not change.
Impossible

C. The range will increase but median will not change.
Possible

D. The range will increase but mean will decrease.
Possible

E. The standard deviation will increase but mean will decrease.
Possible


B

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