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Question
The lengths (in cm) of 10 rods in a shop are given below:
40.0, 52.3, 55.2, 72.9, 52.8, 79.0, 32.5, 15.2, 27.9, 30.2
Find mean deviation from the mean also.
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Solution
Let
\[\bar{x}\] be the mean of the given data set.
\[\bar{x} = \frac{40 + 52 . 3 + 55 . 2 + 72 . 9 + 52 . 8 + 79 + 32 . 5 + 15 . 2 + 27 . 9 + 30 . 2}{10} = 45 . 98\]
|
\[x_i\]
|
\[\left| d_i \right| = \left| x_i - 45 . 98 \right|\]
|
| 40 | 5.98 |
| 52.3 | 6.32 |
| 55.2 | 9.22 |
| 72.9 | 26.92 |
| 52.8 | 6.82 |
| 79 | 33.02 |
| 32.5 | 13.48 |
| 15.2 | 30.78 |
| 27.9 | 18.08 |
| 32 | 13.98 |
| Total | 164.6 |
\[MD = \frac{1}{10} \times 164 . 6 = 16 . 46\]
Mean deviation from the mean is 16.4 cm.
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