The following data gives the information on the observed lifetime in hours of 225 electrical components- Life time in hours 0-20 20-40 40-60 60-80 80-100 100-120- Number of components 10 35 52 61 38 29- -Determine the modal lifetimes of the components-

Modal class = 60 80, l = 60, f_1 = 61, f_0 = 52, f_2 = 38 and h = 20 Mode = l + ( f_1 f_0/2f_1 f_0 f_2 ) × h ⇒ 60 + ( 61 52/(2 × 61) 52 38 ) × 20 ...

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Byju's Answer

Standard VIII

Mathematics

Finding Mode for Grouped Data When Class Intervals Are Given

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

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.

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.

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

$\begin{matrix} Lifetimes(in hours) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 & 100 - 120 No.of components & 10 & 35 & 52 & 61 & 38 & 29 \end{matrix}$

Determine the modal lifetimes 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
Frequency	10	35	52	61	38	29

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