9. Find the mean deviation about the mean.

Income per day in Rs \small 0-100 \small 100-200 \small 200-300 \small 300-400 \small 400-500 \small 500-600 \small 600-700 \small 700-800
Number of persons \small 4 \small 8 \small 9 \small 10 \small 7 \small 5 \small 4 \small 3

 

Answers (1)

Income

per day

Number of 

Persons f_i

Mid

Points x_i

f_ix_i |x_i - \overline{x}| f_i|x_i - \overline{x}|
0 -100 4 50 200 308 1232
100 -200 8 150 1200 208 1664
200-300 9 250 2250 108 972
300-400 10 350 3500 8 80
400-500 7 450 3150 92 644
500-600 5 550 2750 192 960
600-700 4 650 2600 292 1168
700-800 3 750 2250 392 1176
 

\sum{f_i}

=50

 

\sum f_ix_i

=17900

 

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

=7896

 

N = \sum_{i=1}^{8}{f_i} = 50 ; \sum_{i=1}^{8}{f_ix_i} = 17900

\overline{x} = \frac{1}{N}\sum_{i=1}^{8}f_ix_i = \frac{17900}{50} = 358

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

\sum f_i|x_i - \overline{x}| = 7896

\therefore M.D.(\overline{x}) = \frac{1}{50}\sum_{i=1}^{8}f_i|x_i - \overline{x}|

= \frac{7896}{50} = 157.92

Hence, the mean deviation about the mean is 157.92

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