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Question
Calculate the mean deviation from the median of the following data:
| Class interval | 0 – 6 | 6 – 12 | 12 – 18 | 18 – 24 | 24 – 30 |
| Frequency | 4 | 5 | 3 | 6 | 2 |
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Solution
| Class-interval | `f_i` | `x_i` | `c.f.` | `d_i = |x_i - Med|` | `f_i d_i` |
| 0 – 6 | 4 | 3 | 4 | 11 | 44 |
| 6 – 12 | 5 | 9 | 9 | 5 | 25 |
| 12 – 18 | 3 | 15 | 12 | 1 | 3 |
| 18 – 24 | 6 | 21 | 18 | 7 | 42 |
| 24 – 30 | 2 | 27 | 20 | 13 | 26 |
| N = 20 | `sumf_i d_i` = 140 |
Median class = `(N/2)^"th"` term
= `(20/2)^"th"` term
= 10th term
i.e. 12 – 18
∴ Median = `l + (N/2 - c.f.)/f xx h`
= `12 + (10 - 9)/3 xx 6`
= `12 + 1/3 xx 6`
= 12 + 2
= 14
and M.D. = `(sumf_i d_i)/N`
= `140/20`
= 7
Hence, the required M.D. = 7
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