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Question
Find the mean deviation about the mean of the distribution:
| Size | 20 | 21 | 22 | 23 | 24 |
| Frequency | 6 | 4 | 5 | 1 | 4 |
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Solution
| Size `(x_i)` | Frequency `(f_i)` | `f_ix_i` | `d_i = |x_i - barx_i|` | `f_i d_i` |
| 20 | 6 | 120 | 1.65 | 9.90 |
| 21 | 4 | 84 | 0.65 | 2.60 |
| 22 | 5 | 110 | 0.35 | 1.75 |
| 23 | 1 | 23 | 1.35 | 1.35 |
| 24 | 4 | 96 | 2.35 | 9.40 |
| Total | 20 | 433 | 6.35 | 25.00 |
Mean `barx = (sumf_ix_i)/(sumf_i)`
= `433/20`
= 21.65
Mean deviation MD = `(sumf_i d_i)/(sumf_i)`
= `25/20`
= 1.25
Here, the required MD = 1.25
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