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  • Find the mean deviation about the mean. (5) xi : 5 10 15 20 25 fi : 7 4 6 3 5

5. Find the mean deviation about the mean.

    \small \\x_i\hspace{1cm}5\hspace{1cm}10\hspace{1cm}15\hspace{1cm}20\hspace{1cm}25\\\small f_i\hspace{1cm}7\hspace{1cm}4\hspace{1.15cm}6\hspace{1.22cm}3\hspace{1.3cm}5

    

            

Answers (1)

best_answer
x_i f_i f_ix_i |x_i - \overline{x}| f_i|x_i - \overline{x}|
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
 

\sum{f_i}

= 25

\sum f_ix_i

= 350

  

\sum f_i|x_i - \overline{x}|

=158

N = \sum_{i=1}^{5}{f_i} = 25 ; \sum_{i=1}^{5}{f_ix_i} = 350

\overline{x} = \frac{1}{N}\sum_{i=1}^{n}f_ix_i = \frac{350}{12} = 14

Now, we calculate the absolute values of the deviations from mean, |x_i - \overline{x}|  and

\sum f_i|x_i - \overline{x}| = 158

\therefore M.D.(\overline{x}) = \frac{1}{25}\sum_{i=1}^{n}f_i|x_i - \overline{x}|

= \frac{158}{25} = 6.32

Hence, the mean deviation about the mean is 6.32

 

Posted by

HARSH KANKARIA

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