What is the mean deviation about the mean?
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. 10.15
- B. 10.65 ✓
- C. 11.15
- D. 11.65
Correct Answer: B. 10.65
Explanation
The mean is \bar{x} = \frac{\sum f_ix_i}{N} = \frac{690}{20} = 34.5. The absolute deviations |x_i - \bar{x}| are 29.5, 19.5, 9.5, 0.5, 10.5, 20.5. Multiplying by frequencies yields 29.5, 39, 38, 3, 42, 61.5. The sum is 213. The mean deviation about the mean is \frac{213}{20} = 10.65.
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