B.False✓ Correct
The range of a data set is the difference between the maximum value and the minimum value.
Let's take an example data set: `S = {1, 3, 6, 8, 9}`.
The maximum value is 9 and the minimum value is 1.
The range = 9 - 1 = 8.
Now, let's increase each number in the list by 10 to create a new set, `S`.
`S = {11, 13, 16, 18, 19}`.
In the new set, the maximum value is 19 and the minimum value is 11.
The new range = 19 - 11 = 8.
The range has not changed.
Algebraically, if the original max is `M` and the original min is `m`, the range is `M - m`.
After adding 10 to every number, the new max is `M + 10` and the new min is `m + 10`.
The new range is `(M + 10) - (m + 10) = M + 10 - m - 10 = M - m`.
The range is unchanged. Therefore, the statement "The range is increased by 10" is **False**.
Expert