Problem 13

Explanation

Properties of Average and Range

• Average: Its value changes if each data point is added, subtracted, multiplied, or divided.
• Range: Its value only changes if each data point is multiplied or divided (it does not change if added or subtracted).

Finding the Value of $b$

The initial range is $12$. Then, each data value is subtracted by $a$ and divided by $b$. Since the range only changes when multiplied or divided, the new range becomes:

Finding the Value of $a$

The initial average is $24$. Then, each data value is subtracted by $a$ and divided by $b$, so the new average becomes:

Substitute the value $b = 2$:

Thus, the values are $a = 4$ and $b = 2$.