The weights in kilograms of 60 workers in a factory are given in the following frequency table. Find the mean weight of a worker.
Weight (in kg) x: 60 61 62 63 64 65
No of workers f: 5 8 14 16 10 7

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Solution

Let the assumed mean be A= 63
Calculation of Mean
Weight (in kg) No of workers $d_{i} = x_{i} - 63$ $f_{i} d_{i}$
60 5 -3 -15
61 8 -2 -16
62 14 -1 -14
63 16 0 0
64 10 1 10
65 7 2 14
$N = \sum f_{i} = 60$ $\sum f_{i} d_{i} = - 21$
We have,
N= 60, A= 63 and $\sum f_{i} d_{i} = - 21$
$∴ M e a n = A + [\frac{1}{N} \sum f_{i} d_{i}]$
$∴ M e a n = 63 + (\frac{- 21}{60}) = 63 - \frac{7}{20} = 63 - 0.35 = 62.65$
Hence, mean weight of a worker= 62.65 kg.

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Weight (in kg)	$60$	$64$	$68$	$70$	$72$
Number of workers	$3$	$4$	$2$	$2$	$1$

The following table shows the weights of $12$ workers in a factory:

$\begin{matrix} Weight (in kg) & 60 & 63 & 66 & 69 & 72 No. of workers & 4 & 3 & 2 & 2 & 1 \end{matrix}$

Find the mean weight of the workers.

Weight (in kg)	60	63	66	69	72
No. of workers	4	3	2	2	1

Weight (in kg)	60	63	66	72	75
Number of workers	4	5	3	1	2

Weight (in kg):	60	63	66	72	75
Numbers of workers:	4	5	3	1	2

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