To determine what whole number the missing piece of data must be to have a range of 15, we can follow these steps:
1. List the given data points:
The given data points are:
[tex]\[
14, 9, 12, 2, 2, 8, 2, 1
\][/tex]
2. Identify the current maximum and minimum values:
- Maximum value: [tex]\(14\)[/tex]
- Minimum value: [tex]\(1\)[/tex]
3. Calculate the current range:
[tex]\[
\text{Current range} = 14 - 1 = 13
\][/tex]
4. Determine the target range:
The target range is [tex]\(15\)[/tex].
5. Calculate the potential missing value to achieve the target range:
To achieve a range of 15, the missing piece could either:
- Decrease the minimum value, or
- Increase the maximum value.
6. Calculate the missing value to decrease the minimum value:
To find such a value, subtract 15 from the current maximum value:
[tex]\[
\text{Missing value (lower)} = 14 - 15 = -1
\][/tex]
Since we need a whole number, and typically a positive integer for data, [tex]\(-1\)[/tex] is not a valid choice.
7. Calculate the missing value to increase the maximum value:
To find such a value, add 15 to the current minimum value:
[tex]\[
\text{Missing value (upper)} = 1 + 15 = 16
\][/tex]
This is a valid whole number.
So, to achieve a range of 15, the missing piece of data must be [tex]\(16\)[/tex].
