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  1. Chapter 14 Class 10 Statistics
  2. Serial order wise
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Ex 14.2, 4 The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures. Mode = l + (๐‘“1 โˆ’๐‘“0)/(2๐‘“1 โˆ’๐‘“0 โˆ’๐‘“2) ร— h Modal class = Interval with highest frequency = 30 โ€“ 35 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 Mode = l + (๐‘“1 โˆ’๐‘“0)/(2๐‘“1 โˆ’๐‘“0 โˆ’๐‘“2) ร— h = 30 + (10 โˆ’9)/(2(10) โˆ’ 9 โˆ’ 3) ร— 5 = 30 + 1/(20 โˆ’12) ร— 5 = 30 + 5/8 = 30 + 0.625 = 30.625 Number of students / teacher Number of States/ U.T. 15 โ€“ 20 3 20 โ€“ 25 8 25 โ€“ 30 9 30 โ€“ 35 10 35 โ€“ 40 3 40 โ€“ 45 0 45 โ€“ 50 0 50 โ€“ 55 2 Mean(๐‘ฅ ฬ…) = a + h ร— (โˆ‘โ–’๐‘“๐‘–๐‘ข๐‘–)/(โˆ‘โ–’๐‘“๐‘–) Where a = assumed mean h = Class interval = 20 โˆ’ 15 = 5 & ui = (๐‘ฅ๐‘– โˆ’๐‘Ž)/โ„Ž โˆ‘โ–’๐‘“๐‘– = 35 โˆ‘โ–’๐‘“๐‘–๐‘ข๐‘– = -58 Mean(๐‘ฅ ฬ…) = a + h ร— (โˆ‘โ–’๐‘“๐‘–๐‘ข๐‘–)/(โˆ‘โ–’๐‘“๐‘–) Mean(๐‘ฅ ฬ…) = 37.5 + 5 ร— (โˆ’58)/35 Mean(๐‘ฅ ฬ…) = 37.5 - 58/7 ๐‘ฅ ฬ… = 37.5 โ€“ 8.286 ๐‘ฅ ฬ… = 29.214 โˆด Mean = ๐‘ฅ ฬ… = 29.214 Thus, most states have student-teacher ratio 30.625 (mode), And average student-teacher ratio is 29.214 (mean)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.