Question

Two sets of numbers having medians \( p \) and \( q \) respectively are combined to form a new set. If \( p>q \), then the median \( m \) of the new set satisfies \( q<m<p \).

• A. Always
• B. Sometimes
• C. Never
  % Correct answer
• D.
• E.

Hint:

When combining two sets, always check how the elements from each set interact in the combined set to determine the correct median.

Answer 1

The Correct Option is B

When combining two sets with medians \( p \) and \( q \) where \( p>q \), the median of the combined set depends on how the two sets are ordered. In general, the median of the combined set will lie between \( p \) and \( q \), but this is not always guaranteed. The median could fall outside this range if the sets are highly unbalanced or contain large numbers of extreme values. Thus, the correct answer is "Sometimes".