The following data gives the information on the observed lifetime -in hours- of 225 electrical components- - Life-time-in-hours- amp- 0-20 amp- 20-40 amp- 40-60 amp- 60-80 amp- 80-100 amp- 100-120- Number -of- components amp- 10 amp- 35 amp- 52 amp- 61 amp- 38 amp- 29- - Determine the modal lifetime of the components-60-02-65-69-66-21-65-62-

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Finding mode for Grouped Data when class intervals are given

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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 lifetime 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
$M o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h \Rightarrow 60 + (\frac{61 - 52}{(2 \times 61) - 52 - 38}) \times 20 \Rightarrow 60 + (\frac{9}{32} \times 20) = 65.62$

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Similar questions

The following data gives the information on the observed 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 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 gives the information on the life - time (in hours) of 75 electrical instruments.

Lifetime (in hours)	0-20	20-40	40-60	60-80	80-100	100-120
Frequency	10	15	12	21	8	9

find the mean lifetime of the instruments.

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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 lifetime 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
$M o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h \Rightarrow 60 + (\frac{61 - 52}{(2 \times 61) - 52 - 38}) \times 20 \Rightarrow 60 + (\frac{9}{32} \times 20) = 65.62$