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A water quality index converts individual parameters into 0-100 sub-indices and combines them with weights reflecting their importance. The weighted arithmetic form is simple but can mask a single very poor parameter; the geometric form penalises poor sub-indices more heavily, which is why both are usually reported.
Weighted index
WQI = sum of sub-index x weight
Geometric index
WQI = product of sub-index^weight
A single catastrophic parameter can be masked by good scores elsewhere in an arithmetic index. Geometric or minimum-operator forms avoid it, which matters when the failing parameter is a pathogen indicator.
No. Compliance is assessed parameter by parameter against standards. An index is a communication and trend tool, not a regulatory test.