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The Mean Deviation of the Data 3, 10, 10, 4, 7, 10, 5 from the Mean is (A) 2 (B) 2.57 (C) 3 (D) 3.57 - Mathematics

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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 

MCQ
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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

\[= \frac{\sum_{} \left| x_i - 7 \right|}{7}\]

\[= \frac{\left| 3 - 7 \right| + \left| 10 - 7 \right| + \left| 10 - 7 \right| + \left| 4 - 7 \right| + \left| 7 - 7 \right| + \left| 10 - 7 \right| + \left| 5 - 7 \right|}{7}\]
\[ = \frac{4 + 3 + 3 + 3 + 0 + 3 + 2}{7}\]
\[ = \frac{18}{7}\]
\[ = 2 . 57\]

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Chapter 32: Statistics - Exercise 32.9 [Page 51]

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RD Sharma Mathematics [English] Class 11
Chapter 32 Statistics
Exercise 32.9 | Q 22 | Page 51

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