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.

69.268

hours

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65.625

hours

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62.126

hours

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58.267

hours

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Solution

The correct option is B $65.625$ hours
Modal class of the given data is $60 - 80$ .
Here, $l = 60, f_{m} = 62, f_{1} = 52, f_{1} = 38$ and $h = 20$
$M o d e = l + {\frac{f_{m} - f_{1}}{2 f_{m} - f_{1} - f_{2}}} \times h$
$= 60 + {\frac{61 - 52}{122 - 52 - 38}} \times 20$
$= 60 + \frac{9 \times 20}{32} = 60 + \frac{45}{8} = 60 + 5.625$
$= 65.625$ hours

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Similar questions

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.

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 given the information on the observed life terms (in hours) of

200

electrical components.

Life times (in hours)	40-60	60-80	80-100	100-120	120-140	140-160
Frequency	$25$	$38$	$65$	$24$	$31$	$17$

Determine the modal lifetimes 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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Lifetimes (in hours)	0-20	20-40	40-60	60-80	80-100	100-120
Frequency	10	35	52	61	38	29

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:Lifetimes (in hours)0-2020-4040-6060-8080-100100-120Frequency103552613829Determine the modal lifetimes of the components.

The correct option is B 65.625 hoursModal class of the given data is 60−80.Here, l=60,fm=62,f1=52,f1=38 and h=20Mode=l+{fm−f12fm−f1−f2}×h=60+{61−52122−52−38}×20=60+9×2032=60+458=60+5.625=65.625 hours

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.