The following data gives the information on the observed lifetime in hours of 225 electrical components-WineWline t e x t N u m b e r o f c o m p o n e n t s - 10 - 35 - 52 - 61 - 38 - 29 - Wline array Determine the modal lifetimes of the components-A- 60-02B- 65-62C- 65-69D- 66-21

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Standard VI

Mathematics

Mode for Grouped Data

The following...

Question

The following data gives the information on the observed lifetime (in hours) of 225 electrical components:
$\begin{matrix} Life time (in hours) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 & 100 - 120 Number of components & 10 & 35 & 52 & 61 & 38 & 29 \end{matrix}$

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, f1 = 61, f0 = 52, f2 = 38 and h = 20
Mode = $l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h \Rightarrow 60 + (\frac{61 - 52}{(2 \times 61) - 52 - 38}) \times 20 \Rightarrow 60 + (\frac{9}{32} \times 20) = 65.62$

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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 lifetime of the components.

Q. The following data is 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.

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.

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 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.

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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 65.62 Modal 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

The correct option is B
65.62

Modal class = 60-80, l = 60, f1 = 61, f0 = 52, f2 = 38 and h = 20
Mode = $l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h \Rightarrow 60 + (\frac{61 - 52}{(2 \times 61) - 52 - 38}) \times 20 \Rightarrow 60 + (\frac{9}{32} \times 20) = 65.62$