<p>The mean deviation about the median of the following distribution is</p><table border='1'><tr><th>Marks obtained</th><td>10</td><td>11</td><td>12</td><td>14</td><td>15</td></tr><tr><th>Number of students</th><td>2</td><td>3</td><td>8</td><td>3</td><td>4</td></tr></table>
Step-by-Step Solution
Key Concept: Calculate median using cumulative frequencies, then find mean deviation as the average of absolute deviations of each observation from the median, weighted by frequencies.
<p><strong>Step 1:</strong> Organize the data: Marks (10, 11, 12, 14, 15) with frequencies (2, 3, 8, 3, 4) respectively.</p><p><strong>Step 2:</strong> Calculate cumulative frequencies: 2, 5, 13, 16, 20. Total frequency N = 20.</p><p><strong>Step 3:</strong> Find median position = N/2 = 10. Since cumulative frequency reaches 13 at marks = 12, the median = 12.</p><p><strong>Step 4:</strong> Calculate absolute deviations from median (12):<br/>|10-12| = 2, |11-12| = 1, |12-12| = 0, |14-12| = 2, |15-12| = 3</p><p><strong>Step 5:</strong> Calculate mean deviation = Σ(f·|d|)/N = [2(2) + 3(1) + 8(0) + 3(2) + 4(3)]/20 = [4 + 3 + 0 + 6 + 12]/20 = 25/20 = 1.25</p><p>∴ Answer: B</p>
Correct Answer: B