Question

(i) 34, 66, 30, 38, 44, 50, 40, 60, 42, 51

(ii) 22, 24, 30, 27, 29, 31, 25, 28, 41, 42

(iii) 38, 70, 48, 34, 63, 42, 55, 44, 53, 47

find the number of observations lying between bar X –M.D and bar X + M.D, where M.D. is the mean deviation from the mean.

Answer 1

(i) 34, 66, 30, 38, 44, 50, 40, 60, 42, 51

We know that,

MD = 1/n ∑ⁿ_i=1|d_i|

Where, |d_i| = |x_i – x|

So, let ‘x’ be the mean of the given observation.

x = [34 + 66 + 30 + 38 + 44 + 50 + 40 + 60 + 42 + 51]/10

= 455/10

= 45.5

Number of observations, ‘n’ = 10

xi	|di| = |xi – 45.5|
34	11.5
66	20.5
30	15.5
38	7.5
44	1.5
50	4.5
40	5.5
60	14.5
42	3.5
51	5.5
Total	90

MD = 1/n ∑ⁿ_i=1|d_i|

= 1/10 × 90

= 9

Now

bar X – M.D = 45.5 – 9 = 36.5

bar X + M.D = 45.5 + 9 = 54.5

So, There are total 6 observation between bar X – M.D and bar X + M.D

(ii) 22, 24, 30, 27, 29, 31, 25, 28, 41, 42

We know that,

MD = 1/n ∑ⁿ_i=1|d_i|

Where, |d_i| = |x_i – x|

So, let ‘x’ be the mean of the given observation.

x = [22 + 24 + 30 + 27 + 29 + 31 + 25 + 28 + 41 + 42]/10

= 299/10

= 29.9

Number of observations, ‘n’ = 10

xi	|di| = |xi – 29.9|
22	7.9
24	5.9
30	0.1
27	2.9
29	0.9
31	1.1
25	4.9
28	1.9
41	11.1
42	12.1
Total	48.8

MD = 1/n ∑ⁿ_i=1|d_i|

= 1/10 × 48.8

= 4.88

Now

So, There are total 5 observation between 
bar X - MD and bar X + MD

(iii) 38, 70, 48, 34, 63, 42, 55, 44, 53, 47

We know that,

MD = 1/n ∑ⁿ_i=1|d_i|

Where, |d_i| = |x_i – x|

So, let ‘x’ be the mean of the given observation.

x = [38 + 70 + 48 + 34 + 63 + 42 + 55 + 44 + 53 + 47]/10

= 494/10

= 49.4

Number of observations, ‘n’ = 10

xi	|di| = |xi – 49.4|
38	11.4
70	20.6
48	1.4
34	15.4
63	13.6
42	7.4
55	5.6
44	5.4
53	3.6
47	2.4
Total	86.8

MD = 1/n ∑ⁿ_i=1|d_i|

= 1/10 × 86.8

= 8.68

Now