Let's determine whether the statement about the median of the given numbers is true or false.
### Step-by-Step Solution:
1. List of Given Numbers:
The given numbers are 3 and 12.
2. Sorting the Numbers:
First, we sort the list of numbers:
- Sorted List: [3, 12]
3. Finding the Median:
- To determine the median, we need to consider the number of elements in the list.
- The list has an even number of elements (two elements).
- For an even number of elements, the median is the average of the two middle numbers.
[tex]\[
\text{Median} = \frac{\text{First Middle Number} + \text{Second Middle Number}}{2}
\][/tex]
- Here, the first middle number is [tex]\(3\)[/tex] and the second middle number is [tex]\(12\)[/tex].
Therefore,
[tex]\[
\text{Median} = \frac{3 + 12}{2} = \frac{15}{2} = 7.5
\][/tex]
4. Comparison with the Given Median:
- The given median is [tex]\(16\)[/tex].
- The calculated median is [tex]\(7.5\)[/tex].
5. Conclusion:
The calculated median ([tex]\(7.5\)[/tex]) does not match the given median ([tex]\(16\)[/tex]). Therefore, the statement is false.
### Final Answer:
The statement "The median of this distribution is 16" is false. The correct median of the distribution is [tex]\(7.5\)[/tex].
