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Question
Find the mean deviation about the median of the following distribution:
| Marks obtained | 10 | 11 | 12 | 14 | 15 |
| No. of students | 2 | 3 | 8 | 3 | 4 |
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Solution
| Marks obtained |
`f_i` | `c.f.` | `d_i = |x_i - Med|` | `f_i d_i` |
| 10 | 2 | 2 | 2 | 4 |
| 11 | 3 | 5 | 1 | 3 |
| 12 | 8 | 13 | 0 | 0 |
| 14 | 3 | 16 | 2 | 6 |
| 15 | 4 | 20 | 3 | 12 |
| Total | 20 | 25 |
Here `sumf_i` = N = 20 and `sumf_i d_i` = 25
Median = `1/2[(N/2)^"th" "observation" + (N/2 + 1)^"th" "observation"]`
= `1/2[(20/2)^"th" "observation" + (20/2 + 1)^"th" "observation"]`
= `1/2[10^"th" "observation" + 11^"th" "observation"]`
= `1/2[12 + 12]`
∴ Median = 12
∴ M.D. = `(sumf_i d_i)/(sum f_i)`
= `25/50`
= 1.25
Hence, the required M.D. = 1.25
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