Determine the modal lifetimes of the components.
NCERT Class 10 Math’s Chapter 14 Statistics
NCERT Textbook Page No. 275
Exercise 14.2
Question No. 2
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:
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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 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 + ((f₁ – f₀)/(2f₁ – f₀ – f₂)) × h = 60 + ((61 – 52)/(2 × 61 – 52 – 38)) × 20 = 60 + 9/32 × 20 = 60 + 5.625 = 65.625
Therefore, modal lifeline of electrical components is 65.625 hours.