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Question
The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is
Options
2
2.57
3
3.57
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Solution
The given observations are 3, 10, 10, 4, 7, 10, 5.
∴ Mean, \[x = \frac{3 + 10 + 10 + 4 + 7 + 10 + 5}{7} = \frac{49}{7} = 7\]
Now,
Mean deviation from mean, MD
\[= \frac{\left| 3 - 7 \right| + \left| 10 - 7 \right| + \left| 10 - 7 \right| + \left| 4 - 7 \right| + \left| 7 - 7 \right| + \left| 10 - 7 \right| + \left| 5 - 7 \right|}{7}\]
\[ = \frac{4 + 3 + 3 + 3 + 0 + 3 + 2}{7}\]
\[ = \frac{18}{7}\]
\[ = 2 . 57\]
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