The following table gives the daily income of $50$ workers of a factory:
Daily income (in Rs.) $100 - 120$ $120 - 140$ $140 - 160$ $160 - 180$ $180 - 200$
Number of workers: $12$ $14$ $8$ $6$ $10$
Find the mean, mode and median of the above data

Question

The following table gives the daily income of

50

workers of a factory:

Daily income (in Rs.)	$100 - 120$	$120 - 140$	$140 - 160$	$160 - 180$	$180 - 200$
Number of workers:	$12$	$14$	$8$	$6$	$10$

Find the mean, mode and median of the above data

Filo · Accepted Answer

ClassFrequencyfi​ Midvaluexi​ fi​xi​ cf  100−20012 110 1320 12 120−140 14 130 1820 26 140−160 8 150 1200 34 160−1806 170 102040 180−200 10 190 1900 50  ∑fi​=50 ∑fi​xi​=7260 ⇒  Mean=fi​∑fi​xi​​=507260​=145.2⇒  We have, N=50. Then, 2N​=25.⇒  Median class is 120−140l= lower limit of the modal classh= size of the class intervalsf= frequency of the modal classf1​= frequency of the class preceding the modal classf2​= frequency of the class succeed in the modal class.⇒  So, l=120,h=20,N=50cf=12,f=14.Median=l+f2N​−cf​×h⇒  Median=120+1425−12​×20⇒  Median=120+7130​∴   Median=120+18.6=138.6⇒  Modal class =120−140⇒  l=120,f=14f1​=12,f2​=8,h=20⇒  Mode=l+2f−f1​−f2​f−f1​​×h⇒  Mode=120+2×14−12−814−12​×20⇒  Mode=120+840​∴  Mode=125

$Cl a ss$	$F re q u e n cy$ $f_{i}$	$M i d v a l u e$ $x_{i}$	$f_{i} x_{i}$	$c f$
$100 - 200$	$12$	$110$	$1320$	$12$
$120 - 140$	$14$	$130$	$1820$	$26$
$140 - 160$	$8$	$150$	$1200$	$34$
$160 - 180$	$6$	$170$	$1020$	$40$
$180 - 200$	$10$	$190$	$1900$	$50$
	$\sum f_{i} = 50$		$\sum f_{i} x_{i} = 7260$

Question Text	The following table gives the daily income of $50$ workers of a factory: Find the mean, mode and median of the above data
Answer Type	Text solution:1
Upvotes	150

The following table gives the daily income of $50$ workers of a factory:
Daily income (in Rs.) $100 - 120$ $120 - 140$ $140 - 160$ $160 - 180$ $180 - 200$
Number of workers: $12$ $14$ $8$ $6$ $10$
Find the mean, mode and median of the above data

Text solutionVerified

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The following table gives the daily income of 50 workers of a factory:Daily income (in Rs.)100−120120−140140−160160−180180−200Number of workers:12148610Find the mean, mode and median of the above data

Text solutionVerified

Practice questions from similar books

The following table gives the daily income of $50$ workers of a factory:
Daily income (in Rs.) $100 - 120$ $120 - 140$ $140 - 160$ $160 - 180$ $180 - 200$
Number of workers: $12$ $14$ $8$ $6$ $10$
Find the mean, mode and median of the above data