Gate 2021 Q50. The grade of copper(in wt%) of an ore body determined at locations 1,2 and 3 are indicated below. The grade of copper at an unknown location x calculated using Inverse-Square Distance weighting (IDW) is _________ wt% .

Solution - Topic - Inverse Distance Weighted Method

\[W(x) = \frac{\Sigma (\frac{Wi}{Zi}) }{\Sigma (\frac{1}{Zi}) }\]

where,

W(x) - Ore grade at unknown point x

Wi - Ore grade at a known point i.

Zi - Distance of the known point i from the unknown point x.

But, they ask for - Using Inverse-Square distance weighting

so now, formula become 

\[W(x) = \frac{\Sigma (\frac{Wi}{Zi^{2}}) }{\Sigma (\frac{1}{Zi^{2}}) }\]

\[\large W(x) = \frac{\frac{1.5}{2^{2}}+\frac{1.8}{3^{2}}+\frac{2.5}{5^{2}}}{\frac{1}{2^{2}}+\frac{1}{3^{2}}+\frac{1}{5^{2}}}\]

\[\large W(x) = \frac{\frac{1.5}{4}+\frac{1.8}{9}+\frac{2.5}{25}}{\frac{1}{4}+\frac{1}{9}+\frac{1}{25}}\]

\[\large W(x) = \frac{0.375+0.2+0.1}{0.25+0.11+0.04}\]

\[W(x) = \frac{0.675}{0.4}\]

\[W(x) = 1.68 %\]