<p>Median of 9 distinct observations is the \(\left(\dfrac{9+1}{2}\right)\)th term, that is, 5th term = 20.5. If each of the largest 4 observations are increased by 2, then the median will:</p>
Step-by-Step Solution
Key Concept: The median of 9 observations is the 5th term when arranged in ascending order. When we modify only the largest 4 observations (6th, 7th, 8th, 9th terms), the 5th term position and value remain unchanged since it's not among the modified terms.
<p><strong>Step 1:</strong> For 9 distinct observations arranged in ascending order, the median is the (9+1)/2 = 5th term = 20.5</p><p><strong>Step 2:</strong> The observations in order are: a₁ < a₂ < a₃ < a₄ < a₅ < a₆ < a₇ < a₈ < a₉, where a₅ = 20.5 is the median.</p><p><strong>Step 3:</strong> When we increase the largest 4 observations (a₆, a₇, a₈, a₉) by 2, we get a new arrangement: a₁ < a₂ < a₃ < a₄ < a₅ < (a₆+2) < (a₇+2) < (a₈+2) < (a₉+2)</p><p><strong>Step 4:</strong> The 5th term in the new arrangement is still a₅ = 20.5, since the first 5 terms are unchanged. The median position remains the same (5th term), and its value remains 20.5.</p><p>∴ The median remains unchanged at 20.5. (Answer: C)</p>
Correct Answer: C