The following data gives the information on the observed lifetimes -in hours- of - 225- electrical components-Lifetimes -in hours-0-2020-4040-6060-8080-100100-120No- of components- 10- 35- 52- 61- 38- 29-Determine the modal lifetimes of the components-

Lifetime(in hours) #160;No. of components #160;0 20 #160;10 #160;20 40 #160;35 #160;40 60 #160;52 #160;60 80 #160;61 #160;80 100 #160;38 ...

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Byju's Answer

Standard X

Mathematics

Finding Mode for Grouped Data When Class Intervals Are Given

The following...

Question

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.

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Solution

$\begin{matrix} Lifetimes(in hours) & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 & 100 - 120 No.of components & 10 & 35 & 52 & 61 & 38 & 29 \end{matrix}$
Mode $= l + \frac{f_{1} - f_{0}}{2 f_{1} - (f_{0} + f_{2})} \times h$
As frequency is maximum for the class $60 - 80,$ modal class is $60 - 80.$
where,
$l$ = lower limit of modal class $= 60$
$f_{1}$ = frequency of modal class $= 61$
$f_{0}$ = frequency of class preceding the modal class $= 52$
$f_{2}$ = frequency of class succeding the modal class $= 38$
$h$ = higher limit - lower limit $= 80 - 60 = 20$

Mode $= 60 + \frac{61 - 52}{2 \times 61 - (52 + 38)} \times 20$

$\Rightarrow$ Mode $= 60 + \frac{9}{32} \times 20 = 60 + 5.625 = 65.625$

Hence, the modal lifetimes of the components are $65.625$ hrs.

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The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:Lifetimes(in hours)0−2020−4040−6060−8080−100100−120No.of components103552613829Determine the modal lifetimes of the components.