Question

The coefficient of variation of the rainfall for existing six rain gauge stations in the catchment was found to be 29.54%. The optimum number of stations in the catchment for an admissible 10% error in the estimation of mean rainfall will be:

• A. 3
• B. 6
• C. 9
• D. 12

Hint:

The optimum number of stations for estimating mean rainfall is based on the coefficient of variation and the desired error margin.

Answer 1

The Correct Option is C

Step 1: Formula for Optimum Number of Stations.
The optimum number of rain gauge stations (\(n\)) in the catchment can be calculated using the formula: \[ n = \left( \frac{C}{E} \right)^2 \] Where: - \(C\) is the coefficient of variation (29.54% or 0.2954) - \(E\) is the allowable error (10% or 0.1)
Step 2: Substituting the Values.
Substitute the values into the formula: \[ n = \left( \frac{0.2954}{0.1} \right)^2 = (2.954)^2 \approx 8.74 \approx 9 \]
Step 3: Conclusion.
Thus, the optimum number of stations is approximately 9, making option (3) the correct answer.

Final Answer: \[ \boxed{9} \]