To find the correct range and median for the set of numbers [tex]\(\{4, 7, 12\}\)[/tex], let's go through the step-by-step process.
### Step 1: Calculate the Range
The range of a set of numbers is the difference between the maximum and minimum values in the set.
1. Identify the minimum value in the set: [tex]\( \min(4, 7, 12) = 4 \)[/tex]
2. Identify the maximum value in the set: [tex]\( \max(4, 7, 12) = 12 \)[/tex]
3. Calculate the range:
[tex]\[
\text{Range} = \max - \min = 12 - 4 = 8
\][/tex]
### Step 2: Calculate the Median
The median is the middle number in a sorted list of numbers.
1. First, sort the set of numbers: [tex]\(\{4, 7, 12\}\)[/tex] (it is already sorted in this case).
2. Since there are 3 numbers, the median is the second number in the sorted list (the middle one):
[tex]\[
\text{Median} = 7
\][/tex]
### Conclusion
Based on these calculations, the range of the set [tex]\(\{4, 7, 12\}\)[/tex] is [tex]\(8\)[/tex], and the median is [tex]\(7\)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{2) \text{ a range of 8 and a median of 7}}
\][/tex]
