Ex 14.2, 2 - Information on the observed lifetimes (in hours) - Mode

  1. Chapter 14 Class 10 Statistics
  2. Serial order wise
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Ex 14.2, 2 The following data gives the information on the observed lifetimes (in hours) of 225 electrical components . Determine the modal lifetimes of the components. Lifetimes (in hours) 0 − 20 20 − 40 40 − 60 60 − 80 80 − 100 100 − 120 Frequency 10 35 52 61 38 29 Lifetimes (in hours) Frequency 0 – 20 10 20 – 40 35 40 – 60 52 60 – 80 61 80 – 100 38 100 – 120 29 Mode = l + (𝑓1 −𝑓0)/(2𝑓1 −𝑓0 −𝑓2) × h Modal class = Interval with highest frequency = 60 – 80 where l = lower limit of modal class= 60 h = class-interval = 20 − 0 = 20 f1 = frequency of the modal class=61 f0 = frequency of the class before modal class=52 f2 = frequency of the class after modal class=38 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

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