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  • Find the mean deviation about the mean. (6) xi 10 30 50 70 90 fi 4 24 28 16 8

6.   Find the mean deviation about the mean.

   \small \\x_i\hspace{1cm}10\hspace{1cm}30\hspace{1cm}50\hspace{1cm}70\hspace{1cm}90\\\small f_i\hspace{1cm}4\hspace{1.1cm}24\hspace{1.1cm}28\hspace{1.1cm}16\hspace{1.2cm}8

               

Answers (1)

best_answer
x_i f_i f_ix_i |x_i - \overline{x}| f_i|x_i - \overline{x}|
10 4 40 40 160
30 24 720 20 480
50 28 1400 0 0
70 16 1120 20 320
90 8 720 40 320
 

\sum{f_i}

= 80

\sum f_ix_i

= 4000

  

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

=1280

N = \sum_{i=1}^{5}{f_i} = 80 ; \sum_{i=1}^{5}{f_ix_i} = 4000

\overline{x} = \frac{1}{N}\sum_{i=1}^{n}f_ix_i = \frac{4000}{80} = 50

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

\sum f_i|x_i - \overline{x}| = 1280

\therefore M.D.(\overline{x}) = \frac{1}{80}\sum_{i=1}^{5}f_i|x_i - \overline{x}|

= \frac{1280}{80} = 16

Hence, the mean deviation about the mean is 16

Posted by

HARSH KANKARIA

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