Question

The student who traveled to 3 states visited 3 new states during a vacation. Does increasing the 3 to 6 change the median? If so, how?

Answer 1

Yes, changing from 3 states to 6 states changes the median because:

- The median of the first 3 states is simply the middle-placed state of the 3 states.

- The median of 6 states is the average of the 2 middle states.

Explanation:

Suppose the first 3 states in order are:

A, B, C.

The median of these states is simply the middle state, B.

Adding 3 new states to have:

A, B, C, D, E, F.

The median is not explicit. It is the average of the two middle states, C and D.

Average of C and D is half of the sum of C and D.

That is (C + D)/2.

Which is different from B.