The lifetimes of 100 light bulbs are tabulated below- Find the modal lifetime-begin array - c-c-c- Whline - Lifetime in ispace hours - Frequency Whline- 0-20 - 7 Whline- 20-40 - 13 Whline- 40-60 - 20 Whline- 60-80 - 18 Whline- 80-100 - 16 Whline- 100-120 - 10 Whline- 120-140 - 7 Whline- 140-160 - 9 Whline- lendarray -

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Mode of Continuous Series

The lifetimes...

Question

The lifetimes of 100 light bulbs are tabulated below. Find the modal lifetime.

$\begin{matrix} L i f e t i m e (i n h o u r s) & F r e q u e n c y 0 - 20 & 7 20 - 40 & 13 40 - 60 & 20 60 - 80 & 18 80 - 100 & 16 100 - 120 & 10 120 - 140 & 7 140 - 160 & 9 \end{matrix}$

70 hours

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72 hours

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58 hours

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84 hours

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Solution

The correct option is A 70 hours
The grouping and analysis table for the distribution is given below

From the analysis table, the class 60-80
has the maximum score. Hence, 60 - 80 is
the modal class.

Here, $L = 60; D_{1} = 20 - 18 = 2$
$D_{2} = 18 - 16 = 2; h = 20$
$M o d e = L + \frac{D_{1}}{D_{1} + D_{2}} \times h = 60 + \frac{2}{2 + 2} \times 20 = 70 h o u r s$

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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. Make a frequency curve of the following data:

Class-interval	20−40	40−60	60−80	80−100	100−120	120−140	140−160
Frequency	3	7	11	15	13	6	2

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.

Q. Compute the mean of the following frequency distribution:

Class	0 − 20	20 − 40	40 − 60	60 − 80	80 − 100	100 – 120	120 – 140
Frequency	6	8	10	12	6	5	3

Q. Find the median of the following data:

Class interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$	$120 - 140$
Frequency	$6$	$8$	$10$	$12$	$6$	$5$	$3$

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The lifetimes of 100 light bulbs are tabulated below. Find the modal lifetime. Lifetime(in hours)Frequency0−20720−401340−602060−801880−10016100−12010120−1407140−1609

The correct option is A 70 hoursThe grouping and analysis table for the distribution is given below From the analysis table, the class 60-80 has the maximum score. Hence, 60 - 80 is the modal class. Here, L=60;D1=20−18=2 D2=18−16=2;h=20 Mode=L+D1D1+D2×h=60+22+2×20=70 hours

The lifetimes of 100 light bulbs are tabulated below. Find the modal lifetime.

$\begin{matrix} L i f e t i m e (i n h o u r s) & F r e q u e n c y 0 - 20 & 7 20 - 40 & 13 40 - 60 & 20 60 - 80 & 18 80 - 100 & 16 100 - 120 & 10 120 - 140 & 7 140 - 160 & 9 \end{matrix}$