1. Find Mean deviation about MEAN;MEDIAN from the following data
`3,23,13,11,15,5,4,2`

Solution:
Mean `bar x=(sum x)/n`

`=(3+23+13+11+15+5+4+2)/8`

`=76/8`

`=9.5`

Median :
Observations in the ascending order are :
`2,3,4,5,11,13,15,23`

Here, `n=8` is even.

`M=(text{Value of } (n/2)^(th) text{ observation} + text{Value of } (n/2 + 1)^(th) text{ observation})/2`

`=(text{Value of } (8/2)^(th) text{ observation} + text{Value of } (8/2 + 1)^(th) text{ observation})/2`

`=(text{Value of }4^(th) text{ observation} + text{Value of }5^(th) text{ observation})/2`

`=(5 + 11)/2`

`=8`

`x`	`|x - bar x| = |x - 9.5|`	`|x - M| = |x - 8|`
3	6.5	5
23	13.5	15
13	3.5	5
11	1.5	3
15	5.5	7
5	4.5	3
4	5.5	4
2	7.5	6
---	---	---
76	48	48

Mean deviation of Mean
`delta bar x = (sum |x - bar x|)/n`

`delta bar x = 48/8`

`delta bar x = 6`


Coefficient of Mean deviation `=(delta bar x)/(bar x)`

`=6/9.5`

`=0.6316`


Mean deviation of Median
`delta bar x = (sum |x - M|)/n`

`delta bar x = 48/8`

`delta bar x = 6`


Coefficient of Mean deviation `=(delta bar x)/(bar x)`

`=6/8`

`=0.75`

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2. Find Mean deviation about MEAN;MEDIAN;MODE from the following data
`69,66,67,69,64,63,65,68,72`

Solution:
Mean `bar x=(sum x)/n`

`=(69+66+67+69+64+63+65+68+72)/9`

`=603/9`

`=67`

Median :
Observations in the ascending order are :
`63,64,65,66,67,68,69,69,72`

Here, `n=9` is odd.

`M=` value of `((n+1)/2)^(th)` observation

`=` value of `((9+1)/2)^(th)` observation

`=` value of `5^(th)` observation

`=67`

Mode :
In the given data, the observation `69` occurs maximum number of times (`2`)

`:. Z = 69`

`x`	`|x - bar x| = |x - 67|`	`|x - M| = |x - 67|`	`|x - Z| = |x - 69|`
69	2	2	0
66	1	1	3
67	0	0	2
69	2	2	0
64	3	3	5
63	4	4	6
65	2	2	4
68	1	1	1
72	5	5	3
---	---	---	---
603	20	20	24

Mean deviation of Mean
`delta bar x = (sum |x - bar x|)/n`

`delta bar x = 20/9`

`delta bar x = 2.2222`


Coefficient of Mean deviation `=(delta bar x)/(bar x)`

`=2.2222/67`

`=0.0332`


Mean deviation of Median
`delta bar x = (sum |x - M|)/n`

`delta bar x = 20/9`

`delta bar x = 2.2222`


Coefficient of Mean deviation `=(delta bar x)/(bar x)`

`=2.2222/67`

`=0.0332`


Mean deviation of Mode
`delta bar x = (sum |x - Z|)/n`

`delta bar x = 24/9`

`delta bar x = 2.6667`


Coefficient of Mean deviation `=(delta bar x)/(bar x)`

`=2.6667/69`

`=0.0386`

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