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

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.

Concept: Mode of Grouped Data
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#### APPEARS IN

NCERT Class 10 Maths
Chapter 14 Statistics
Exercise 14.2 | Q 2 | Page 275
RD Sharma Class 10 Maths
Chapter 15 Statistics
Exercise 15.5 | Q 8 | Page 46