Impact on Range

The range measures how spread out a data set is, from lowest to highest.
It is simply the maximum value minus the minimum value.

Because only the two extremes matter, a new data point changes the range only when it sits outside them.
If a set runs from $2$ to $26$, its range is $26 - 2 = 24$; adding a value of $45$ makes $45$ the new maximum, so the range grows to $45 - 2 = 43$.

A new value that lands between the current minimum and maximum has no effect on the range.
Adding $15$ to that same set does not change the highest or lowest value, so the range stays $24$.

Removing a data point can also change the range, but only if you remove one of the extremes.
Taking out the maximum lowers the highest value, so the range shrinks; removing a middle value leaves the range the same.

A data set has a minimum of $5$ and a maximum of $30$. A new value of $50$ is added. What is the new range? \ Since $50$ is larger than the old maximum, it becomes the new maximum. \ So the range is $50 - 5 = 45$.

A data set ranges from $10$ to $40$, and a new value of $25$ is added. What happens to the range?
The value $25$ falls between the current minimum $10$ and maximum $40$, so it changes neither extreme.
So the range stays $40 - 10 = 30$.

A data set is $5, 8, 12, 19, 30$. The value $30$ is removed. What is the new range?
Removing $30$, the maximum, leaves $19$ as the new highest value.
So the new range is $19 - 5 = 14$.