GATE 2024 AG – Question 56

Soil and Water Conservation Engineering · Hydrology · 2 marks · Numerical answer

Five rain gauges record annual rainfall90,100,80,120,110 cm. For5% permissible error in the mean, find the number of additional stations as an integer.

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Correct answer: 5 to 5

Explanation

Mean rainfall is 100 cm. The sample squared deviations total1000 cm²,so sample standard deviation is $\sqrt{1000/(5-1)}=15.81139$ cm. Coefficient of variation is 15.81139%. Required total stations $N=(CV/e)^2=(15.81139/5)^2=10$. Subtract the existing5 to obtain **5 additional stations**.

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