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Calculate the Mean Deviation from the Mean for the Data: 4, 7, 8, 9, 10, 12, 13, 17 - Mathematics

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Question

Calculate the mean deviation from the mean for the data: 

 4, 7, 8, 9, 10, 12, 13, 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.

\[x = \frac{4 + 7 + 8 + 9 + 10 + 12 + 13 + 17}{8} = 10\]

 
\[x_i\]
 
\[\left| d_i \right| = \left| x_i - \bar{x} \right|\]
4 6
7 3
8 2
9 1
10 0
12 2
13 3
17 7
Total 24

 

\[MD = \frac{1}{n} \sum^n_{i = 1} \left| d_i \right|\]

\[MD = \frac{1}{8} \times 24 = 3\]

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Chapter 32: Statistics - Exercise 32.1 [Page 6]

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RD Sharma Mathematics [English] Class 11
Chapter 32 Statistics
Exercise 32.1 | Q 2.1 | Page 6

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