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.

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Solution

From the data given above, we observe that maximum class frequency is 61 of class interval 60 - 80.

So, modal class = 60 - 80

Lower class limit $l$ of modal class = 60

Frequency $(f_{1})$ of modal class = 61

Frequency $(f_{0})$ of class preceding the modal class = 52

Frequency $(f_{2})$ of class succeeding the modal class = 38

Class size $h$ = 20

$Mode = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h = 60 + (\frac{61 - 52}{2 (61) - 52 - 38}) (20) = 60 + (\frac{9}{122 - 90}) (20) = 60 + (\frac{9 \times 20}{32}) = 60 + \frac{90}{16} = 60 + 5.625 = 65.625$

So, modal lifetime of electrical components is 65.625 hours.

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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.

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
No. of components: 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.

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.

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Question 2 The following data gives the information on the observed lifetimes (in hours) of 225 electrical components: Lifetimes(in hours)0−2020−4040−6060−8080−100100−120Frequency103552613829 Determine the modal lifetimes of the components.