Statistics
Median
Grade None
Question:
<p>The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set</p>
<p>is increased by 2.</p>
<p>is decreased by 2.</p>
<p>is two times the original median.</p>
<p>remains the same as that of the original set.</p>
Step-by-Step Solution
Key Concept: The median of 9 observations is the 5th element when arranged in order. Since we're only modifying the largest 4 observations (positions 6-9), the 5th position remains unchanged, so the median stays the same.
<p><strong>Step 1:</strong> For a set of 9 distinct observations arranged in ascending order, the median is the 5th observation (middle value).</p><p><strong>Step 2:</strong> The largest 4 observations are in positions 6, 7, 8, and 9 of the ordered set.</p><p><strong>Step 3:</strong> Increasing each of these 4 observations by 2 does not affect their relative order or the position of the 5th observation.</p><p><strong>Step 4:</strong> The 5th observation (median) remains at position 5 and retains its original value of 20.5.</p><p><strong>Step 5:</strong> The new set will have median = 20.5 (unchanged).</p><p>∴ Answer: D (The median remains 20.5)</p>
Correct Answer: D