Ex 13.2, 2 - Chapter 13 Class 10 Statistics

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Ex 13.2, 2 The following data gives the information on the observed lifetimes (in hours) of 225 electrical components . Determine the modal lifetimes of the components. Mode = l + (𝑓1 −𝑓0)/(2𝑓1 −𝑓0 −𝑓2) × h Modal class = Interval with highest frequency = 60 – 80 where l = lower limit of modal class h = class-interval f1 = frequency of the modal class f0 = frequency of the class before modal class f2 = frequency of the class after modal class Putting values in formula Mode = 60 + (61 −52)/(2(61)−52 −38) × 20 = 60 + 9/(122 −90) × 2 = 60 + 9/32 × 20 = 60 + 9/8 × 5 = 60 + 5.625 = 65.625 Thus, Modal lifetime of components is 65.625 hours