Suppose that a data set $X$ had a range $=45$ and interquartile range $=12$.
a) A new data set $Z$ was created by adding ten to every data value of $X$. What is the range and interquartile range for the new data set?
- The new range =
- The new interquartile range $=$
b) How does adding every data value by a constant affect the range and interquartile range?
The new range and IQR will also be increased by the constant.
Only the new range will be increased by the constant.
Only the new IQR will be increased by the constant.
The new range and IQR will be unchanged.

Step 1 ：Given a data set $X$ with a range of 45 and an interquartile range of 12.

Step 2 ：A new data set $Z$ is created by adding 10 to every data value of $X$.

Step 3 ：Adding a constant to every data value in a set shifts the entire set by that constant. This means that the minimum and maximum values of the set will each increase by the constant, but the range (the difference between the maximum and minimum) will remain the same.

Step 4 ：Similarly, the first quartile (Q1) and third quartile (Q3) will each increase by the constant, but the interquartile range (the difference between Q3 and Q1) will also remain the same.

Step 5 ：Therefore, the range and interquartile range of the new data set will be the same as those of the original data set.

Step 6 ：So, the new range is \(\boxed{45}\) and the new interquartile range is \(\boxed{12}\).

Step 7 ：Adding a constant to every data value in a set does not change the range or the interquartile range.