Last updated at May 12, 2021 by Teachoo

Transcript

Ex 14.3, 6 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows. Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames Finding Median Median = l + (π/2 βππ)/π Γ h Here, π΅/π β΄ 7 β 10 is median class And, l = h = cf = f = Putting values in formula Median = l + (π/2 βππ)/π Γ h = 7 + (ππ β ππ)/ππ Γ 3 = 7 + 14/40 Γ 3 = 7 + 1.05 = 8.05 So, Median number of letters is 8.05 Now, we will find mode. Finding Mode Mode = l + (π1 βπ0)/(2π1 βπ0 βπ2) Γ h Modal class = Interval highest frequency = 7 β 10 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 = 1500 + (ππ βππ)/(π(ππ)βππβππ) Γ 500 = 7 + (40 β30)/(2(40)β30β16) Γ 3 = 7 + 10/(80β46) Γ 3 = 7 + 10/34 Γ 3 = 7 + 0.88 = 7.88 Thus, Modal number of letters is 7.88 Now, letβs find Mean Mean(π₯ Μ ) = a + h Γ (ββππππ)/(ββππ) Where a = assumed mean h = Class interval = 11.5 Also, ββππ = 100 ββππππ = β106 Putting values in formula Mean(π₯ Μ ) = a + h Γ (ββπππ’π)/(ββππ) π Μ = 11.5 + 3 Γ (βπππ)/πππ π₯ Μ = 11.5 β 3.18 π₯ Μ = 8.32 Therefore, the Mean is 8.32

About the Author

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.