Find the mean, median and mode of the following data:
Classes: $0 - 20$ $20 - 40$ $40 - 60$ $60 - 80$ $80 - 100$ $100 - 120$ $120 - 140$
Frequency: $6$ $8$ $10$ $12$ $6$ $5$ $3$

Question

Find the mean, median and mode of the following data:Classes:0−2020−4040−6060−8080−100100−120120−140Frequency:681012653

Filo · Accepted Answer

Classesxi​ fi​ fi​xi​ c.f  0−20106 60  6 20−40308 240  14 40−605010 500 24 60−807012840 36 80−10090 6 540  42 100−1201105 550  47 120−140130 3 390  50   ∑fi​=50∑fi​xi​=3120  ⇒  Mean=∑fi​∑fi​xi​​=503120​=62.4⇒  N=50 and 2N​=25∴  Median class =60−80l= 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.⇒  Here, l=60,f=12,cf=24,h=20Median=l+f2N​−cf​×h⇒  Median=60+1225−24​×20⇒  Median=60+1220​=61.66⇒  Modalclass=60−80⇒  l=30,f=12,f1​=10,f2​=6,h=20Mode=l+2f−f1​−f2​f−f1​​×h⇒  Mode=60+2×12−10−612−10​×20⇒  Mode=60+5=65

$Cl a sses$	$x_{i}$	$f_{i}$	$f_{i} x_{i}$	$c . f$
$0 - 20$	$10$	$6$	$60$	$6$
$20 - 40$	$30$	$8$	$240$	$14$
$40 - 60$	$50$	$10$	$500$	$24$
$60 - 80$	$70$	$12$	$840$	$36$
$80 - 100$	$90$	$6$	$540$	$42$
$100 - 120$	$110$	$5$	$550$	$47$
$120 - 140$	$130$	$3$	$390$	$50$
		$\sum f_{i} = 50$	$\sum f_{i} x_{i} = 3120$

Question Text	Find the mean, median and mode of the following data:
Answer Type	Text solution:1
Upvotes	150

Find the mean, median and mode of the following data:
Classes: $0 - 20$ $20 - 40$ $40 - 60$ $60 - 80$ $80 - 100$ $100 - 120$ $120 - 140$
Frequency: $6$ $8$ $10$ $12$ $6$ $5$ $3$

Text solutionVerified

Practice questions from similar books

Classes:	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$	$120 - 140$
Frequency:	$6$	$8$	$10$	$12$	$6$	$5$	$3$