Question

Calculate the mean deviation from the mean for the following data:
(i) 4, 7, 8, 9, 10, 12, 13, 17
(ii) 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17
(iii) 38, 70, 48, 40, 42, 55, 63, 46, 54, 44
(iv) 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

Answer 1

Formula used for finding the mean deviation about the mean is given below:

$MD=\frac{1}{n}\sum _{i=1}^n\left|d_i\right|,where\left|d_i\right|=\left|x_i-\overline{x}\right|$


i)
Let $\overline{x}$ be the mean of the given data.

$\overline{x}=\frac{4+7+8+9+10+12+13+17}{8}=10$

$x_i$	$\left|d_i\right|=\left|x_i-\overline{x}\right|$
4	6
7	3
8	2
9	1
10	0
12	2
13	3
17	7
Total	24

$MD=\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{d}}_{\mathrm{i}}\right|$
$MD=\frac{1}{8}\times 24=3$

ii)
Let $\overline{x}$ be the mean of the given data.

$\overline{x}=\frac{13+17+16+14+11+13+10+16+11+18+12+17}{12}=14$

$x_i$	$\left|d_i\right|=\left|x_i-\overline{x}\right|$
13	1
17	3
16	2
14	0
11	3
13	1
10	4
16	2
11	3
18	4
12	2
17	3
Total	28

$MD=\frac{1}{12}\times 28=2.33$

iii)
Let $\overline{x}$ be the mean of the given data.

$\overline{x}=\frac{38+70+48+40+42+55+63+46+54+44}{10}=50$

$x_i$	$\left|d_i\right|=\left|x_i-\overline{x}\right|$
38	12
70	20
48	2
40	10
42	8
55	5
63	13
46	4
54	4
44	6
Total	84

$MD=\frac{1}{10}\times 84=8.4$

iv)
Let $\overline{x}$ be the mean of the given data.

$\overline{x}=\frac{36+746+42+60+45+53+46+51+59}{10}=50$

$x_i$	$\left|d_i\right|=\left|x_i-\overline{x}\right|$
36	14
72	22
46	4
42	8
60	10
45	5
53	3
46	4
51	1
49	1
Total	72

$MD=\frac{1}{10}\times 72=7.2$