Question

How will adding the value 50 affect the mean and median of the data set 8, 10, 12, 18, 22?














A.

The mean will increase more than the median.











B.

The median will increase more than the mean.











C.

The mean and median will increase by the same amount.











D.

The mean and median will both stay the same.

Answer 1

I will give medal

Answer 2

Original mean mu = (a1 + a2 + ... + an)/n. New mean mu' = [(50 + a1) + ... + (50 + an)]/n = (50n+a1+...+an)/n = 50+mu.

Two cases for the median:

If n is odd, original median is a_k, where k is the middle and a1 < a2 < ... < an. New median is still a_k, but it has been increased by 50.

If n is even, original median is (a_k+a_[k+1])/2. New median is (a_k+50+a_[k+1]+50)/2 = (a_k+a_[k+1])/2 + 50.

So, both the mean and median increase by 50.

Answer 3

wow why don't you have a medal
thx

Answer 4

Thank you. Glad I could help.