Inflation is measured by a weaighted average of goods and services and there is no particularly big problem of corruption in the measurement.
OK, I was a bit facetious about the inflation measurement.
The problem with it, though, is that the standard deviation between what people spend their money on based on age, occupation, where they live…..etc., make the national average kind of useless.
If I am 63 and live in a Houston suburb (which I do), then the mix of expeditures that I typically make is radically different from the 26 year old living in Brooklyn. Which is why (at least from my perspective) I look at the national medians and say “that must be some good shit those people are smoking.” :-)