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Question
In 38, 70, 48, 34, 63, 42, 55, 44, 53, 47 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.
\[\bar{ x } = \frac{38 + 70 + 48 + 34 + 63 + 42 + 55 + 44 + 53 + 47}{10} = 49 . 4\]
|
\[x_i\]
|
|
| 38 | 11.4 |
| 70 | 20.6 |
| 48 | 1.4 |
| 34 | 15.4 |
| 63 | 13.6 |
| 42 | 7.4 |
| 55 | 5.6 |
| 44 | 5.4 |
| 53 | 3.6 |
| 47 | 2.4 |
| Total | 86.8 |
\[MD = \frac{1}{10} \times 86 . 6 = 8 . 68\]
\[\bar{ x } - MD = 49 . 4 - 8 . 68 = 40 . 72\]
\[\text{ and } \bar { x } + MD = 49 . 4 + 8 . 68 = 58 . 08\]
There are 6 observations between 40.72 and 58.08.
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