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The following data gives the information on the observed lifetimes (in hours) of 225 electrical components :

2. The following data gives the information on the observed lifetimes (in hours) of 225 electrical components :

        2.2

 Determine the modal lifetimes of the components.

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The class having maximum frequency is the modal class.

The maximum frequency is 61 and hence the modal class = 60-80

Lower limit (l) of modal class = 60, class size (h) = 20

Frequency ( f_1 ) of the modal class = 61 frequency ( f_0 ) of class preceding the modal class = 52, frequency ( f_2 ) of class succeeding the modal class = 38.

Mode = l + \left(\frac{f_1-f_0}{2f_1 - f_0 - f_2} \right).h

\\ = 60 + \left(\frac{61-52}{2(61)-52-38} \right).20 \\ \\ = 60 + \frac{9}{32}.20

= 65.62

Thus, the modal lifetime of 225 electrical components is 65.62 hours

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