<p>The median of a set of nine distinct observations is 20.5. If each of the last four observations of the set is increased by 2, then the median of the new set</p>
<p>(1) Is increased by 2</p>
<p>(2) Is decreased by 2</p>
<p>(3) Is two times the original median</p>
<p>(4) 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. Increasing only the last four observations (positions 6-9) does not affect the 5th position, so the median remains unchanged.
<p><strong>Step 1:</strong> For 9 distinct observations arranged in ascending order, the median is the 5th observation (middle value).</p><p><strong>Step 2:</strong> Initially: observations are at positions 1, 2, 3, 4, 5, 6, 7, 8, 9 where position 5 = 20.5</p><p><strong>Step 3:</strong> When the last four observations (positions 6, 7, 8, 9) are increased by 2, only these positions change.</p><p><strong>Step 4:</strong> The 5th observation (median) remains at 20.5 since it is not modified. The set remains in ascending order (positions 6-9 increase but stay ≥ position 5).</p><p><strong>Step 5:</strong> Therefore, the median of the new set = 20.5 (unchanged)</p><p>∴ Answer: D</p>
Correct Answer: D