Geometric mean
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The document discusses calculating the geometric mean of discrete and continuous data series. For the discrete series, the logarithms of the products of the frequencies and values are summed and divided by the total frequency to calculate the geometric mean. For the continuous series, midpoints are used rather than discrete values, and the geometric mean formula is applied to calculate the overall mean as 17.89. An example is provided for the reader to calculate the geometric mean from given discrete data.
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![GEOMETRIC MEAN
1. Discrete Series
X 8 10 52 25 37
f 5 3 4 2 1
x f Log x f log x
80 0 5 0.9031 4.5155
10 0 3 1.0000 3.0000
52 0 4 1.7160 6.8640
25 0 2 1.3979 2.7958
37 0 1 1.5682 1.5682
N=15 ∑f log x= 18.7435
G= Antilog {∑f log x}
N
= Antilog {18.7435}
15
= Antilog [1.249] 1+1=2
=17.74
2. Continuous series
X 4-8 8-12 12-16 16-20 20-24 24-28 28-32 32-36
f 6 10 18 30 15 12 10 6
x f m Log m f log m
4-8 12/2 6 60 0 0.7782 4.6692
8-12 20/2 10 10 0 1.0000 10.0000
12-16 28/2 18 14 0 1.1461 20.6892
16-20 30 18 0 1.2553 37.6590
20-24 15 22 0 1.3424 20.1360
24-28 12 26 1.4150 16.9800
28-32 10 30 1.4771 14.7710
32-36 6 34 1.5315 9.1890
N= 107 ∑ f log x= 134.034](https://image.slidesharecdn.com/geometricmean-210408070139/85/Geometric-mean-1-320.jpg)
![G= Antilog {∑ f log x}
N
= AL {134.034}
107
=AL[1.2527] 1786+3=17.89 1+1=2
= 17.89
Do it yourself
1.
X 260 120 180 230 220 200
f 7 12 15 11 8 7
2.2571
188.4
2.
C.I. 10-20 20-30 30-40 40-50 50-60
f 5 10 15 7 4
E-notes by
Asst. Prof. Harpreet Kaur
Sri Guru Granth Sahib World University,
Fatehgarh Sahib](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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9
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structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
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- 1. GEOMETRIC MEAN 1. Discrete Series X 8 10 52 25 37 f 5 3 4 2 1 x f Log x f log x 80 0 5 0.9031 4.5155 10 0 3 1.0000 3.0000 52 0 4 1.7160 6.8640 25 0 2 1.3979 2.7958 37 0 1 1.5682 1.5682 N=15 ∑f log x= 18.7435 G= Antilog {∑f log x} N = Antilog {18.7435} 15 = Antilog [1.249] 1+1=2 =17.74 2. Continuous series X 4-8 8-12 12-16 16-20 20-24 24-28 28-32 32-36 f 6 10 18 30 15 12 10 6 x f m Log m f log m 4-8 12/2 6 60 0 0.7782 4.6692 8-12 20/2 10 10 0 1.0000 10.0000 12-16 28/2 18 14 0 1.1461 20.6892 16-20 30 18 0 1.2553 37.6590 20-24 15 22 0 1.3424 20.1360 24-28 12 26 1.4150 16.9800 28-32 10 30 1.4771 14.7710 32-36 6 34 1.5315 9.1890 N= 107 ∑ f log x= 134.034
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