Explanation:
The exact question is as follows :
Given - The student who traveled to 3 states visited 6 new states during a vacation.
To find - Does increasing the 3 to 6 change the median? If so, how?
Proof -
Yes,
If we increase the 3 states to 6 states, it changes the median
Because
The median of the first 3 states is the middle state.
For example -
If we have 3 states X, Y, Z
Then the median is the state Y
Now,
The median of 6 states is the average of the 2 middle states.
For example -
If we have 6 states
X, Y, Z, U, V, W
Then
The median is not explicit.
Median is the average of the two middle states, Z and U.
And
Average of Z and U = half of the sum of Z and U.
i.e. (Z + U)/2.
And we can see that,
Median of 3 States is not equal to Median of 6 states
i.e. Y is not equal to (Z + U)/2.
So,
We can say that,
Increasing the state 3 to 6 changes the median.