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प्रश्न
In 34, 66, 30, 38, 44, 50, 40, 60, 42, 51 find the number of observations lying between
\[\bar{ X } \] + M.D, where M.D. is the mean deviation from the mean.
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उत्तर
Let \[ \bar {x} \] be the mean of the data set.
\[\bar{ x } = \frac{34 + 66 + 30 + 38 + 44 + 50 + 40 + 60 + 42 + 51}{10} = 45 . 5\]
\[MD = \frac{1}{n} \sum^n_{i = 1} \left| d_i \right|, \text{ where} \left| d_i \right| = \left| x_i - x \right|\]
|
\[x_i\]
|
|
| 34 | 11.5 |
| 66 | 20.5 |
| 30 | 15.5 |
| 38 | 7.5 |
| 44 | 1.5 |
| 50 | 4.5 |
| 40 | 5.5 |
| 60 | 14.5 |
| 42 | 3.5 |
| 51 | 5.5 |
| Total | 90 |
\[MD = \frac{1}{10} \times 90 = 9\]
\[\bar{ x } - M . D . = 45 . 5 - 9 = 36 . 5\]
\[Also, \bar { x } + M . D . = 45 . 5 + 9 = 54 . 5\]
Hence, there are 6 observations between 36.5 and 54.5.
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