Xn are the items of the given series to simplify

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: on. Symbolically, GM = n x 1.x 2 ...x n Where x1, x2. ..xn are the items of the given series. To simplify calculations, logarithms are used. Sikkim Manipal University Page No. 173 Research Methodology Unit 11 Accordingly, GM = Anti log of (log x /n) In discrete series GM = Anti log of f . log x / f Illustration 1. Find Geometric mean for the following data. 25 279 112 3675 84 Values (x) 9 18 54 73 648 Log x 25 1.3979 279 2.4456 112 2.0492 3675 3.5652 84 1.9242 9 0.9542 18 1.2552 54 1.7323 73 1.8633 648 2.8116 19.9986 = Anti log of (log x /n) = Anti log of (19.9986 / 10) = Anti log of 1.9986 = GM 99.967 Geometric mean for discrete series Calculate geometric mean of the following data given below:- Sikkim Manipal University Page No. 174 Research Methodology Unit 11 Class No. of families Income Landlords 1 100 Cultivators 50 80 Landless labourers 25 40 Money lenders 2 750 Scholl teachers 3 100 Shop keepers 4 150 Carpenters 3 120 Weavers 5 60 Income Frequency Log x f. Log x 1000 1 3.0000 3.0000 80 50 1.9031 95.1550 40 25 1.6021 40.0525 750 2 2.8751 5.7502 100 3 2.0000 6.0000 150 4 2.1761 8.7044 120 3 2.0792 6.2376 60 5 1.7782 8.8910 93 = Anti log of f. log x / f = Anti log of 173.7907 / 93 = Anti log 1. 86871 = GM 173.7907 73.91 Harmonic Mean In individual series HM = N / (1/x) In discrete series HM = N / f (1/m) N = Total frequency M = Mi values of the class Sikkim Manipal University Page No. 175 Research Methodology Unit 11 Illustration For individual series 1. Find harmonic mean of the following data 5 10 3 7 125 Values x 5 10 3 7 125 58 47 80 45 26 HM = = 80 45 26 Factorial 1/x .2 .1 .33 .14 .008 .017 .021 .014 .022 .038 ( 1/x) =.89 10 / .89 = 47 N / (1/x) HM 58 11.235 Harmonic mean for discrete series Compute harmonic mean for the following data Marks : 10 20 25 30 40 50 Frequency : 20 10 15 25 10 20 Marks Frequency 1/x f. 1/x 10 20 .1 2.0 20 10 .05 .5 25 15 .04 .6 30 25 .033 .83 40 10 .025 .25 50 20 .02 .4 f = 100 Sikkim Manipal University f (1/x) = 4.58 Page No. 176 Research Methodology Unit 11 HM = N / f (1/x) HM...
View Full Document

Ask a homework question - tutors are online