Question

Given a set A with median \( m_1 = 2 \) and set B with median \( m_2 = 4 \). What can we say about the median of the combined set?

• A. at most 1
• B. at most 2
• C. at least 1
• D. at least 2

Hint:

When combining sets, the median of the combined set typically lies between the medians of the individual sets, depending on their sizes.

Answer 1

The Correct Option is D

Step 1: Understand the problem. We are given two sets:
Set \( A \) with median \( m_1 = 2 \),
Set \( B \) with median \( m_2 = 4 \).
When combining sets A and B, the median of the combined set will depend on the values of \( m_1 \) and \( m_2 \), and the total number of elements in the two sets. 
Step 2: Median of Combined Sets.
If the total number of elements in the combined set is even, the median lies between the medians of the two sets.
Since \( m_1 = 2 \) and \( m_2 = 4 \), the combined median will be at least 2 because the smallest median is 2, and no value smaller than 2 can lie between the two medians.
Step 3: Conclusion. Thus, we can say that the median of the combined set is at least 2. The correct answer is: \[ \boxed{{at least 2}}. \]