Statistic Question

If a postive number k is added to each number in a set of numbers , which of the following will increase by k

Median , Range , Inter-quartile range
ANSWER
Without loss of generality, assume that n is a multiple of 4
Let the set of numbers are x1,x2,x3,....,xn
where x1<=x2<=x3,....,<=xn
Then the new sequence is x1+k,x2+k,x3+k,....,xn+k
where x1+k<=x2+k<=x3+k,....<=xn +k
Now we can compare the Median , Range , Inter-quartile range of two sequences
1 Median
Original sequence xn/2
New sequence xn/2+k
2 Range
Original sequence xn-x1
New sequence (xn+k)-(x1+k)=xn-x1
3 Inter-quartile range
Original sequence x3n/4-xn/4
New sequence (x3n/4+k)-(xn/4+k)=x3n/4-xn/4
So only Median will increase by k