Weight of 15 persons is as follows:

Weight (kg) 20 28 34 39 42 50 53 54 59 64 72 74 74 78 79

Find out mean weight, using Direct Method as well as Short-cut Method.

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Solution

S. No. Weight
(X) d = X − A

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15 20
28
34
39
42
50 = A
53
54
59
64
72
74
74
78
79 −30
−22
−16
−11
−8
0
3
4
9
14
22
24
24
28
29

∑X = 820 ∑d = 70

Direct Method:
$A . M . = X = \frac{Σ X}{N} = \frac{820}{15} = 54.67$

Shortcut Method:
$A . M . = X = A + \frac{Σ d}{N} Here, A represents the assumed mean d represents the deviations of the values from the assumed mean .$

Here, we take 50 as assumed mean. Thus, we take deviations of the values from 50.
$X = 50 + \frac{70}{15} = 50 + 4.67 = 54.67$

Thus, the mean weight is 54.67 kg.

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S. No.	Weight (X)	d = X − A
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15	20 28 34 39 42 50 = A 53 54 59 64 72 74 74 78 79	−30 −22 −16 −11 −8 0 3 4 9 14 22 24 24 28 29














	∑X = 820	∑d = 70

70	55	51	42	57	45	60	47	63	53
33	65	39	82	55	64	58	61	65	42
50	52	53	45	45	25	36	59	63	39
65	54	49	54	64	75	42	41	52	35
30	35	15	48	26	20	40	55	46	18

70	55	51	42	57	45	60	47	63	53
33	65	39	82	55	64	58	61	65	42
50	52	53	45	45	25	36	59	63	39
65	54	49	54	64	75	42	41	52	35
30	35	15	48	26	20	40	55	46	18

Weight of 15 persons is as follows: Weight (kg) 20 28 34 39 42 50 53 54 59 64 72 74 74 78 79 Find out mean weight, using Direct Method as well as Short-cut Method.

Weight of 15 persons is as follows:

Weight (kg) 20 28 34 39 42 50 53 54 59 64 72 74 74 78 79

Find out mean weight, using Direct Method as well as Short-cut Method.

70	55	51	42	57	45	60	47	63	53
33	65	39	82	55	64	58	61	65	42
50	52	53	45	45	25	36	59	63	39
65	54	49	54	64	75	42	41	52	35
30	35	15	48	26	20	40	55	46	18