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The following data gives the information on the observed lifetimes (in hours) of 225 electrical components - CBSE Class 10 - Mathematics

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Question

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.

Solution

From the data given above, it can be observed that the maximum class frequency is 61, belonging to class interval 60 − 80.

Therefore, modal class = 60 − 80

Lower class limit (l) of modal class = 60

Frequency (f1) of modal class = 61

Frequency (f0) of class preceding the modal class = 52

Frequency (f2) of class succeeding the modal class = 38

Class size (h) = 20

`"Mode" = l+((f_1-f_0)/(2f_1-f_0-f_2))xh`

=`60+((61-52)/(2(61)-52-38))(20)`

=`60+(9/(122-90))(20)`

=60+90/16=  60+5.625

= 65.625

Therefore, modal lifetime of electrical components is 65.625 hours.

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 14: Statistics
Ex. 14.20 | Q: 2 | Page no. 275
 NCERT Solution for Mathematics Textbook for Class 10 (2018 to Current)
Chapter 14: Statistics
Ex. 14.20 | Q: 2 | Page no. 275
Solution The following data gives the information on the observed lifetimes (in hours) of 225 electrical components Concept: Mode of Grouped Data.
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