The weekly wages of $120$ workers in a factory are shown in the following frequency distribution table. Find the mean of the weekly wages.
Weekly wages (Rupees) $0 - 2000$ $2000 - 4000$ $4000 - 6000$ $6000 - 8000$
No. of workers $15$ $35$ $50$ $20$

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Solution

Class (weekly wages) $X_{i}$ $d_{i} = x_{i} - A$ $U_{i} = \frac{d_{i}}{h}$ frequency $f_{i}$ $f_{1} \times v_{i}$
0-2000 1000 -4000 -2 15 -30
2000-4000 3000 -2000 -1 35 -35
4000-6000 5000(A) 0 0 50 0
6000-8000 7000 +2000 1 20 20
120 -45
$M e a n = A + h (\frac{\sum f_{i} v_{i}}{\sum f_{i}}) = 5000 + 2000 (\frac{- 45}{120})$
$= 5000 - \frac{200 \times 45}{12} = 5000 - 750$
$= R s .4250$
$∴$ Mean of weekly wages is $R s .4250$

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Weekly wages (Rupees)	$0 - 2000$	$2000 - 4000$	$4000 - 6000$	$6000 - 8000$
No. of workers	$15$	$35$	$50$	$20$