The following data gives the information on the observed lifetime in hours of 225 electrical components-Wline Life time in hours - 0-20 - 20-40 - 40-60 - 60-80 - 80-100 - 100-120 1WlineNumber of components - 10 - 35 - 52 - 61 - 38 - 29 1 Wline array Determine the modal lifetimes of the components-A- 65-69B- 66-21C- 60-02D- 65-62

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Byju's Answer

Standard VI

Mathematics

Finding mode for Grouped Data when class intervals are givenÂ

The following...

Question

The following data gives the information on the observed lifetime (in hours) of 225 electrical components:

$\begin{matrix} L i f e t i m e (i n h o u r s) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 & 100 - 120 N u m b e r o f c o m p o n e n t s & 10 & 35 & 52 & 61 & 38 & 29 \end{matrix}$

Determine the modal lifetimes of the components.

60.02

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65.62

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65.69

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66.21

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Solution

The correct option is B 65.62
Modal class = 60-80, $l$ = 60, $f_{1}$ = 61, $f_{0}$ = 52, $f_{2}$ = 38 and h = 20
$M o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h \Rightarrow 60 + (\frac{61 - 52}{(2 \times 61) - 52 - 38}) \times 20 \Rightarrow 60 + (\frac{9}{32} \times 20) = 65.62$

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Similar questions

The following data gives the information on the observed lifetime (in hours) of 225 electrical components:

$\begin{matrix} L i f e t i m e (i n h o u r s) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 & 100 - 120 N u m b e r o f c o m p o n e n t s & 10 & 35 & 52 & 61 & 38 & 29 \end{matrix}$

Determine the modal lifetimes of the components, given that the modal class is 60-80.

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
No. of components: 10 35 52 61 38 29
Determine the modal lifetimes of the components.

Q. 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.

Q. The following data gives the information on the observed lifetime (in hours) of 225 electrical components:

\begin{matrix} L i f e t i m e (i n h o u r s) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 & 100 - 120 N u m b e r o f c o m p o n e n t s & 10 & 35 & 52 & 61 & 38 & 29 \end{matrix}

Determine the modal lifetimes of the components.

Question 2
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:

$\begin{matrix} Lifetimes(in hours) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 & 100 - 120 Frequency & 10 & 35 & 52 & 61 & 38 & 29 \end{matrix}$

Determine the modal lifetimes of the components.

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The following data gives the information on the observed lifetime (in hours) of 225 electrical components: Life time (in hours)0−2020−4040−6060−8080−100100−120Number of components103552613829 Determine the modal lifetimes of the components.

The correct option is B 65.62Modal class = 60-80, l = 60, f1 = 61, f0 = 52, f2 = 38 and h = 20 Mode=l+(f1−f02f1−f0−f2)×h⇒60+(61−52(2×61)−52−38)×20⇒60+(932×20)=65.62