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Calculate the Mean Deviation from the Mean for The Data:(Ii) 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

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Question

Calculate the mean deviation from the mean for the  data:

 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

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Solution

Formula used for finding the mean deviation about the mean is given below: 

\[MD = \frac{1}{n} \sum^n_{i = 1} \left| d_i \right| , \text{ where } \left| d_i \right| = \left| x_i - x \right|\]

Let x  be the mean of the given data. 

\[x = \frac{13 + 17 + 16 + 14 + 11 + 13 + 10 + 16 + 11 + 18 + 12 + 17}{12} = 14\]

 
\[x_i\]
 
\[\left| d_i \right| = \left| x_i - \bar{x} \right|\]
13 1
17 3
16 2
14 0
11 3
13 1
10 4
16 2
11 3
18 4
12 2
17 3
Total 28

 

\[MD = \frac{1}{12} \times 28 = 2.33\]

 

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Chapter 32: Statistics - Exercise 32.1 [Page 6]

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R.D. Sharma Mathematics [English] Class 11
Chapter 32 Statistics
Exercise 32.1 | Q 2.2 | Page 6

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