Question

Colleen has the following data:

14 14 10 9 b
If the range is 6, which number could b be?

Answer 1

To find the possible values for \( b \), we first need to understand how the range is calculated. The range of a set of numbers is defined as the difference between the maximum and minimum values.

Given the numbers: \( 14, 14, 10, 9, b \), we need to determine values for \( b \) such that the range is equal to 6.

1. **Identifying the Maximum and Minimum:**
In the data set, the current maximum is \( 14 \) (since \( 14 \) appears twice) and the current minimum is \( 9 \).

2. **Expressing the Range:**
The formula for the range is:
\[
\text{Range} = \text{Max} - \text{Min}
\]
We want this range to equal \( 6 \):
\[
14 - 9 = 5
\]

3. **Considering the Value of \( b \):**
- If \( b < 9 \): The minimum would be \( b \) and the maximum would still be \( 14 \), giving a range of \( 14 - b \).
- If \( b > 14 \): The maximum would be \( b \) and the minimum would still be \( 9 \), giving a range of \( b - 9 \).
- If \( 9 \leq b \leq 14 \): The minimum remains \( 9 \), and the maximum is \( 14 \), so the range remains \( 14 - 9 = 5\).

To make the range equal to \( 6 \), we consider the following two scenarios:
- **If \( b < 9 \):**
\[
14 - b = 6 \implies b = 8
\]
- **If \( b > 14 \):**
\[
b - 9 = 6 \implies b = 15
\]

Thus, \( b \) can either be \( 8 \) or \( 15 \).

**Conclusion:**
The values that \( b \) could take in order for the range to equal \( 6 \) are \( b = 8 \) or \( b = 15 \).