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The coefficient of variation of the rainfall for six rain gauge stations in catchments was found to be 29.54%. The optimum number of stations in the catchments for an admissible 10% error in the estimation of the mean rainfall will be
Correct answer is '9'. Can you explain this answer?
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Solution:
Coefficient of variation (CV) is given by:
CV = (Standard deviation/Mean) x 100%
Given, CV = 29.54%
Let the number of stations be 'n'
The standard error of the mean is given by:
Standard error = Standard deviation/√n
For an admissible error of 10%, the standard error of the mean should be 10% of the mean rainfall.
Therefore, we have:
Standard error = 0.1 x Mean rainfall
0.1 x Mean rainfall = Standard deviation/√n
Mean rainfall = Standard deviation/√n x 10
n = (Standard deviation/Mean rainfall)^2 x 100
Substituting the given values, we get:
n = (29.54/10)^2 x 100
n = 87.05
Rounding off to the nearest integer, we get:
n = 9
Therefore, the optimum number of stations in the catchments for an admissible 10% error in the estimation of the mean rainfall is 9.
Coefficient of variation (CV) is given by:
CV = (Standard deviation/Mean) x 100%
Given, CV = 29.54%
Let the number of stations be 'n'
The standard error of the mean is given by:
Standard error = Standard deviation/√n
For an admissible error of 10%, the standard error of the mean should be 10% of the mean rainfall.
Therefore, we have:
Standard error = 0.1 x Mean rainfall
0.1 x Mean rainfall = Standard deviation/√n
Mean rainfall = Standard deviation/√n x 10
n = (Standard deviation/Mean rainfall)^2 x 100
Substituting the given values, we get:
n = (29.54/10)^2 x 100
n = 87.05
Rounding off to the nearest integer, we get:
n = 9
Therefore, the optimum number of stations in the catchments for an admissible 10% error in the estimation of the mean rainfall is 9.
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The coefficient of variation of the rainfall for six rain gauge stations in catchments was found to be 29.54%. The optimum number of stations in the catchments for an admissible 10% error in the estimation of the mean rainfall will beCorrect answer is '9'. Can you explain this answer?
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