What is mean deviation about the median ?
Consider the following for the next three (03) items that follow : Consider the following grouped frequency distribution: <table> <thead><tr><th>Class</th><th>0-10</th><th>10-20</th><th>20-30</th><th>30-40</th><th>40-50</th><th>50-60</th></tr></thead> <tbody> <tr><td>Frequency</td><td>1</td><td>2</td><td>4</td><td>6</td><td>4</td><td>3</td></tr> </tbody> </table>
- A. 11.4
- B. 11.1
- C. 10.8
- D. 10.5 ✓
Correct Answer: D. 10.5
Explanation
The median is M = 35. The midpoints (x_i) are 5, 15, 25, 35, 45, 55. The absolute deviations |x_i - M| are 30, 20, 10, 0, 10, 20. Multiplying by frequencies gives 30, 40, 40, 0, 40, 60. The sum is 210. The mean deviation about the median is \frac{\sum f_i|x_i - M|}{N} = \frac{210}{20} = 10.5.
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