The following data gives the information on the observed lifetimes (in hours) of $225$ electrical components:
Lifetimes (in hours)
$0 - 20$
$20 - 40$
$40 - 60$
$60 - 80$
$80 - 100$
$100 - 120$
Frequency
$10$
$35$
$52$
$61$
$38$
$29$
Determine the modal lifetimes of the components.

Question

The following data gives the information on the observed lifetimes (in hours) of

225

electrical components:

Lifetimes (in hours)	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$
Frequency	$10$	$35$	$52$	$61$	$38$	$29$

Determine the modal lifetimes of the components.

Filo · Accepted Answer

Here , frequency of class interval 60−80 is maximum.So, it is the modal classNow, l= Lower limit of modal class =60f1​= Frequency of modal class =61f0​= Frequency of class preceding the modal class =52f2​ = Frequency of class succeeding the modal class =38h= Class interval width = 20So, Mode =l+(2f1​−f0​−f2​f1​−f0​​)×h=60+(2(61)−52−3861−52​)×20=60+(122−909​)×20=60+(329​)×20=60+5.625Mode =65.625Therefore, modal lifetime of electrical components is 65.625 hours

Question Text	The following data gives the information on the observed lifetimes (in hours) of $225$ electrical components: Determine the modal lifetimes of the components.
Answer Type	Text solution:1
Upvotes	150

The following data gives the information on the observed lifetimes (in hours) of $225$ electrical components:
Lifetimes (in hours)
$0 - 20$
$20 - 40$
$40 - 60$
$60 - 80$
$80 - 100$
$100 - 120$
Frequency
$10$
$35$
$52$
$61$
$38$
$29$
Determine the modal lifetimes of the components.

Text solutionVerified

Practice questions from similar books

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:Lifetimes (in hours)0−2020−4040−6060−8080−100100−120Frequency103552613829Determine the modal lifetimes of the components.

Text solutionVerified

Practice questions from similar books

The following data gives the information on the observed lifetimes (in hours) of $225$ electrical components:
Lifetimes (in hours)
$0 - 20$
$20 - 40$
$40 - 60$
$60 - 80$
$80 - 100$
$100 - 120$
Frequency
$10$
$35$
$52$
$61$
$38$
$29$
Determine the modal lifetimes of the components.