Ex 14.2, 4 - State-wise teacher-student ratio in higher - Ex 14.2

Ex 14.2, 4 - Chapter 14 Class 10 Statistics - Part 2
Ex 14.2, 4 - Chapter 14 Class 10 Statistics - Part 3
Ex 14.2, 4 - Chapter 14 Class 10 Statistics - Part 4
Ex 14.2, 4 - Chapter 14 Class 10 Statistics - Part 5

  1. Chapter 14 Class 10 Statistics (Term 2)
  2. Serial order wise

Transcript

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. Finding Mode 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 Putting Values in formula 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 Now, Finding Mean Mean(๐‘ฅ ฬ…) = a + h ร— (โˆ‘โ–’๐’‡๐’Š๐’–๐’Š)/(โˆ‘โ–’๐’‡๐’Š) Where a = assumed mean h = Class interval = 20 โ€“ 15 = 5 Also, โˆ‘โ–’๐’‡๐’Š = 35 โˆ‘โ–’๐’‡๐’Š๐’–๐’Š = โˆ’58 Putting values in formula Mean(๐’™ ฬ…) = a + h ร— (โˆ‘โ–’๐’‡๐’Š๐’–๐’Š)/(โˆ‘โ–’๐’‡๐’Š) ๐‘ฅ ฬ… = 37.5 + 5 ร— (โˆ’58)/35 ๐‘ฅ ฬ… = 37.5 โ€“ 8.286 ๐’™ 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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