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The population of a town as per census records were 200000,210000 and 230000 forcthe years 1981,1991,2001 respectively.the population of the town as per geometric mean method in the year 2011?
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The population of a town as per census records were 200000,210000 and ...
Geometric Mean Method to Find Population
The geometric mean method is a statistical technique used to calculate the average growth rate of a variable over a period of time. It is commonly used in finance and economics to measure the average annual growth rate of investments, stock prices, and other financial indicators. In this case, we will use it to find out the population of the town in 2011 based on the population figures for the years 1981, 1991, and 2001.
Formula for Geometric Mean
The formula for geometric mean is:
GM = (n√x1 * x2 * ... * xn)
Where GM is the geometric mean, n is the number of observations, and x1, x2, ..., xn are the values of the variable.
Calculating the Geometric Mean of Population Growth
To apply the geometric mean method to find the population of the town in 2011, we need to calculate the geometric mean of the population growth over the three decades from 1981 to 2001:
GM = (3√200000 * 210000 * 230000) = 216360
Therefore, the geometric mean of the population growth over the three decades from 1981 to 2001 is 216360.
Using Geometric Mean to Find the Population in 2011
Now that we have calculated the geometric mean of the population growth, we can use it to find the population of the town in 2011. To do this, we need to use the following formula:
P2011 = P2001 * (GM / P2001) ^ 10
Where P2011 is the population in 2011, P2001 is the population in 2001, GM is the geometric mean, and ^ denotes exponentiation. By substituting the values, we get:
P2011 = 230000 * (216360 / 230000) ^ 10 = 340313
Therefore, the population of the town in 2011 is 340313.
Conclusion
The geometric mean method is a useful statistical tool for calculating the average growth rate of a variable over a period of time. In this case, we used it to find the population of a town in 2011 based on the population figures for the years 1981, 1991, and 2001. By calculating the geometric mean of the population growth over the three decades from 1981 to 2001, we were able to use it to calculate the population in 2011. The result we got was 340313, which was the population of the town in 2011.
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The population of a town as per census records were 200000,210000 and 230000 forcthe years 1981,1991,2001 respectively.the population of the town as per geometric mean method in the year 2011?
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The population of a town as per census records were 200000,210000 and 230000 forcthe years 1981,1991,2001 respectively.the population of the town as per geometric mean method in the year 2011? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The population of a town as per census records were 200000,210000 and 230000 forcthe years 1981,1991,2001 respectively.the population of the town as per geometric mean method in the year 2011? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The population of a town as per census records were 200000,210000 and 230000 forcthe years 1981,1991,2001 respectively.the population of the town as per geometric mean method in the year 2011?.
The population of a town as per census records were 200000,210000 and 230000 forcthe years 1981,1991,2001 respectively.the population of the town as per geometric mean method in the year 2011? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The population of a town as per census records were 200000,210000 and 230000 forcthe years 1981,1991,2001 respectively.the population of the town as per geometric mean method in the year 2011? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The population of a town as per census records were 200000,210000 and 230000 forcthe years 1981,1991,2001 respectively.the population of the town as per geometric mean method in the year 2011?.
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