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

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Byju's Answer

Standard XI

Statistics

Mode of Continuous Series

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, given that the modal class is 60-80.

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

Given that the modal class is 60-80.

Here,
$L = 60, D_{1} = 61 - 52 = 9$
$D_{2} = 61 - 38 = 23, h = 20$
$M o d e = L + \frac{D_{1}}{D_{1} + D_{2}} \times h = 60 + \frac{9}{9 + 23} \times 20 = 65.62 hours$

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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 lifetime of the components.

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.

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.

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.

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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, given that the modal class is 60-80.

The correct option is B 65.62 Given that the modal class is 60-80. Here, L=60,D1=61−52=9 D2=61−38=23,h=20 Mode=L+D1D1+D2×h=60+99+23×20=65.62 hours

The correct option is B
65.62

Given that the modal class is 60-80.

Here,
$L = 60, D_{1} = 61 - 52 = 9$
$D_{2} = 61 - 38 = 23, h = 20$
$M o d e = L + \frac{D_{1}}{D_{1} + D_{2}} \times h = 60 + \frac{9}{9 + 23} \times 20 = 65.62 hours$