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Arithmetic mean and Thiessen average precipitation

Short answer

Arithmetic mean = (30.8+34.6+32.0+24.6)/4 = 30.50 mm. Thiessen polygon mean = (Σ P_i A_i)/Σ A_i = 4664.8/153 = 30.49 mm.

Calculate the average precipitation using the arithmetic mean method and the Thiessen polygon method based on the following data.

Station No.Precipitation (mm)Area (km²)
130.845
234.640
332.030
424.638

Arithmetic mean method

Pˉ=30.8+34.6+32.0+24.64=122.04=30.50 mm\bar{P} = \frac{30.8 + 34.6 + 32.0 + 24.6}{4} = \frac{122.0}{4} = 30.50\ \text{mm}

Thiessen polygon method

Each station's rainfall is weighted by its polygon area.

StationPiP_i (mm)AiA_i (km²)PiAiP_iA_i (mm·km²)
130.8451386.0
234.6401384.0
332.030960.0
424.638934.8
Total1534664.8
Pˉ=∑PiAi∑Ai=4664.8153=30.49 mm\bar{P} = \frac{\sum P_iA_i}{\sum A_i} = \frac{4664.8}{153} = 30.49\ \text{mm}

Answer: Arithmetic mean = 30.50 mm; Thiessen mean = 30.49 mm. The two are nearly equal here because the station areas are fairly similar; the Thiessen value is slightly lower mainly because station 3 (32.0 mm) has the smallest area and so gets less weight.

✓ Answer checked by Claude Opus 5.5 (high effort)

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