The following data gives the information on the observed lifetimes (in hours) of 225 electric components:
Determine the modal lifetimes of the components.
Solution:
Modal Class is the class with the highest frequency.
Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)] × h
Here, Class size, h
The lower limit of modal class, l
The frequency of modal class, f₁
The frequency of class preceding modal class, f₀
The frequency of class succeeding the modal class, f₂
From the table, it can be observed that the maximum class frequency is 61, belonging to class interval 60 − 80
Therefore, modal class = 60 − 80
Class size, h = 20
Lower limit of modal class, l = 60
Frequency of modal class, f₁ = 61
Frequency of class preceding modal class, f₀ = 52
Frequency of class succeeding the modal class, f₂ = 38
Mode = l + [(f₁ - f₀) / (2f₁ - f₀ - f₂)] × h
= 60 + [(61 - 52)/(2 × 61 - 52 - 38)] × 20
= 60 + [9/(122 - 90)] × 20
= 60 + (9/32) × 20
= 60 + 5.625
= 65.625
Hence, the modal lifetimes of the components are 65.625 hours.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 14
Video Solution:
The following data gives information on the observed lifetimes (in hours) of 225 electric components. Determine the modal lifetimes of the components.
NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.2 Question 2
Summary:
The following data gives information on the observed lifetimes (in hours) of 225 electric components. The modal lifetimes of the components are 65.62 hours.
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