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The mean rainfall over a catchment has to be estimated. The data for four rain gauges located in and around the catchment is listed in the table. Which one of the following statements is correct: Rain gauge station: P, Q, R, S Whether located inside the catchment: Yes, Yes, Yes, No Thiessen weightage factor: 0.25, 0.50, 0.10, 0.15 Rainfall (mm): 100, 110, 100, 125

1. The estimate obtained from the Thiessen-mean method is greater than that obtained using the arithmetic-mean method
2. The estimate obtained from the Thiessen-mean method is equal to that obtained using the arithmetic-mean method
3. The estimate obtained from the Thiessen-mean method is less than that obtained using the arithmetic-mean method
4. The Thiessen-mean method cannot be applied in this case

Correct answer: The estimate obtained from the Thiessen-mean method is equal to that obtained using the arithmetic-mean method

Solution

Thiessen mean = 0.25*100 + 0.50*110 + 0.10*100 + 0.15*125 = 25+55+10+18.75 = 108.75 mm. Arithmetic mean = (100+110+100+125)/4 = 435/4 = 108.75 mm. The two estimates are exactly equal.

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