Last updated at May 12, 2021 by Teachoo

Transcript

Ex 14.3, 1 The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them. Finding Mode Mode = l + (ππ β ππ)/(πππ β ππ β ππ) Γ h Modal class = Interval with highest frequency = 125 β 145 where l = lower limit of modal class h = class-interval f1 = frequency of the modal class f0 = frequency of class before modal class f2 = frequency of class after modal class Putting values in formula Mode = l + (π1 βπ0)/(2π1 βπ0 βπ2) Γ h = 125 + (20 β 13)/(2(20) β 13 β 14) Γ 20 = 125 + 7/(40 β 27) Γ 20 = 125 + 7/13 Γ 20 = 125 + 10.77 = 135.77 Finding Median Median = l + (π/2 βππ)/π Γ h Here, π΅/π β΄ 125 β 145 is the median class And, l = lower limit of median class h = class-interval cf = cumulative frequency of the class before median class f = frequency of the median class Putting values in formula Median = l + (π/2 βππ)/π Γ h = 125 + (34 β 22)/20 Γ 20 = 125 + 12/20 Γ 20 = 125 + 12 = 137 Now, letβs find Mean Mean(π₯ Μ ) = a + h Γ (ββππππ)/(ββππ) Where a = assumed mean h = Class interval = 85 β 65 = 20 Also, ββππ = 68 ββππππ = 7 Putting values in formula Mean(π Μ ) = a + h Γ (ββππππ)/(ββππ) π₯ Μ = 135 + 20 Γ 7/68 π₯ Μ = 135 + 2.05 π Μ = 137.05 Therefore, Mean is 137.05 So, Mean = 137.05 , Median = 137, Mode = 135.77 β΄ Mean, Median, Mode are approximately the same

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.