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Question
In 22, 24, 30, 27, 29, 31, 25, 28, 41, 42 find the number of observations lying between
\[\bar { X } \] − M.D. and
\[\bar { X } \] + M.D, where M.D. is the mean deviation from the mean.
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Solution
Let \[\bar{x}\] be the mean of the data set.
\[\bar{ x } = \frac{22 + 24 + 30 + 27 + 29 + 31 + 25 + 28 + 41 + 42}{10} = 29 . 9\]
|
\[x_i\]
|
\[\left| d_i \right| = \left| x_i - 29 . 9 \right|\]
|
| 22 | 7.9 |
| 24 | 5.9 |
| 30 | 0.1 |
| 27 | 2.9 |
| 29 | 0.9 |
| 31 | 1.1 |
| 25 | 4.9 |
| 28 | 1.9 |
| 41 | 11.9 |
| 42 | 12.1 |
| Total | 48.8 |
\[MD = \frac{1}{10} \times 48 . 8 = 4 . 88\]
\[\bar{ x } - M . D . = 29 . 9 - 4 . 88 = 25 . 02, \]
\[\text{ and } \bar { x } + M . D . = 29 . 9 + 4 . 88 = 34 . 78\]
There are 5 observations between 25.02 and 34.78.
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