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Find the Mean Deviation from the Mean for the Data:Xi510152025fi74635 - Mathematics

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Question

Find the mean deviation from the mean for the data:

xi 5 10 15 20 25
fi 7 4 6 3 5
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Solution

xi fi fixi
 

\[\left| x_i - \bar{x} \right|\]
 

\[f_i \left| x_i - 14 \right|\]
5 7 35 9 63
10 4 40 4 16
15 6 90 1 6
20 3 60 6 18
25 5 125 11 55
 
 

\[N = 25\]
 

\[\sum^n_{i = 1} f_i x_i = 350\]
 
 

\[\sum^n_{i = 1} f_i \left| x_i - 14 \right| = 158\]
\[\bar { x  } = \frac{\sum^{n} _{i=l} f_i x_i}{N} = \frac{350}{25} = 14\]
\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| x_i - x \right| = \frac{1}{25} \times 158 = 6 . 32\]

 

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Chapter 32: Statistics - Exercise 32.2 [Page 11]

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RD Sharma Mathematics [English] Class 11
Chapter 32 Statistics
Exercise 32.2 | Q 4.2 | Page 11

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