Find the mean deviation about the mean for the following data: xi- 5,10,15,20,25; fi- 7,4,6,3,5

Question

Find the mean deviation about the mean for the following data:

1.

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

2. 

xi	10	30	50	70	90
fi	4	24	28	16	8

Answer 1

1.

xi	fi	fixi	|xi-14|	|xi-14|fi
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
	25	350		158

Mean = \(\bar{x}\) = \(\frac{\displaystyle\sum_{i=1}^{n} x_i f_i}{\displaystyle\sum_{i=1}^{n} f_i}\) = \(\frac{350}{25}\) = 14

M.D( \(\bar x\)) = \(\frac{\displaystyle\sum_{i=1}^{n} f_i|x_i - \bar x|}{\displaystyle\sum_{i=1}^{n} f_i}\) =\(\frac{158}{25}\) = 6.32

2. 

xi	fi	fixi	|xi-14|	|xi-14|fi
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
	80	4000		1280

Mean = \(\bar{x}\) = \(\frac{\displaystyle\sum_{i=1}^{n} x_i f_i}{\displaystyle\sum_{i=1}^{n} f_i}\)  = \(\frac{4000}{80} = 50\) 

 M.D( \(\bar x\)) = \(\frac{\displaystyle\sum_{i=1}^{n} f_i|x_i - \bar x|}{\displaystyle\sum_{i=1}^{n} f_i}\)  = \(\frac{1280}{80} = 16\)