Statistics
Mean Deviation from Median
Grade 11
Question:
<p>Following are the marks obtained by 9 students in a mathematics test: 50, 69, 20, 33, 53, 39, 40, 65, 59. The mean deviation from the median is</p>
<p>9</p>
<p>10.5</p>
<p>12.67</p>
<p>14.76</p>
Step-by-Step Solution
Key Concept: First arrange data in ascending order to find the median, then calculate the sum of absolute deviations from the median and divide by the number of observations. Mean deviation = Σ|xᵢ - median|/n
<p><strong>Step 1:</strong> Arrange the 9 marks in ascending order:</p><p>20, 33, 39, 40, 50, 53, 59, 65, 69</p><p><strong>Step 2:</strong> Find the median. Since n = 9 (odd), median is the 5th value:</p><p>Median = 50</p><p><strong>Step 3:</strong> Calculate absolute deviations from median:</p><p>|20 - 50| = 30</p><p>|33 - 50| = 17</p><p>|39 - 50| = 11</p><p>|40 - 50| = 10</p><p>|50 - 50| = 0</p><p>|53 - 50| = 3</p><p>|59 - 50| = 9</p><p>|65 - 50| = 15</p><p>|69 - 50| = 19</p><p><strong>Step 4:</strong> Sum of deviations = 30 + 17 + 11 + 10 + 0 + 3 + 9 + 15 + 19 = 114</p><p><strong>Step 5:</strong> Mean Deviation = 114/9 = 12.67 (or 114/9)</p><p>∴ Answer: C</p>
Correct Answer: C