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

Q. 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: (i) Arithmetic mean (PA), and (ii) Thiessen polygon (PT). Which one of the following statements is correct?
(A) PA is always smaller than PT
(B) PA is always greater than PT
(C) PA is always equal to PT
(D) There is no definite relationship between PA and PT
Ans: There is no definite relationship between PA and PT
Solution:  The correct option is  There is no definite relationship between PA and PT There is no definite relationship between arithmetic mean and Thiessen polygon method. Only it can be said that in Thiessen polygon method , average value is more uniformly distributed as compared to arithmetic mean.
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