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How is historical data for forex collected or computed?

I'm looking at four sources of forex data, as compiled in the question, What data sources are available online? And I think I must be misunderstanding something, perhaps something fundamental, but I'm ...
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How To Account For Inflation Over Historical Data

I believe inflation is greatly affecting my sample data, even when using percent-changes for movements. I have read this post, which recommends the formula ((Current-Base Year CPI) * Price) / ...