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Question
Find the mean deviation about the mean for the data.
| Height in cms | Number of boys |
| 95 - 105 | 9 |
| 105 - 115 | 13 |
| 115 - 125 | 26 |
| 125 - 135 | 30 |
| 135 - 145 | 12 |
| 145 - 155 | 10 |
Solution
| Height in cms | Mid values xi | `d_i (x_i - 130)/10` | Frequency fi | fidi | `|x_i - overline x|` | `f_i|x_i - overline x|` |
| 95 - 105 | 100 | −3 | 9 | −27 | 25.3 | 227.7 |
| 105 - 115 | 110 | −2 | 13 | −26 | 15.3 | 198.9 |
| 115 - 125 | 120 | −1 | 26 | −26 | 5.3 | 137.8 |
| 125 - 135 | 130 | 0 | 30 | 0 | 4.7 | 141.0 |
| 135 - 145 | 140 | 1 | 12 | 12 | 14.7 | 176.4 |
| 145 - 155 | 150 | 2 | 10 | 20 | 24.7 | 247.0 |
| Sum | - | - | 100 | −47 | - | 1128.8 |
Mean `overline x = a +((sumf_i d_i)/(sumf_i)) xx h`
= `130 + ((-47)/100) xx 10`
= 130 − 4.7
= 125.3
Mean Deviation = `(sumf_i |x_i - overline x|)/N`
= `1128.8/100`
= 11.288
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