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A catchment may be idealised as a rectangle. There are three rain gauges located inside the catchment at arbitrary locations. The average precipitation over the catchment is estimated by two methods:

  1. Arithmetic mean $(P_A)$
  2. Thiessen polygon $(P_T)$

Which one of the following statements is correct?

  1. $P_A$ is always smaller than $P_T$
  2. $P_A$ is always greater than $P_T$
  3. $P_A$ is always equal to $P_T$
  4. There is no definite relationship between $P_A$ and $P_T$
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