I didn't use the word "exact." But regardless, the way CPI measures are used by policymakers and others assume they are highly accurate. Otherwise a 2% increase in the CPI would be meaningless, since there could either be inflation or deflation.
Everyone should keep in mind that inflation for each individual is different because we all consume different things. The BLS calculation is a weighted average of prices. It’s their best guess and they don’t hide how they make the guess.
What is wrong with their methodology? How should it change? Have you read about the different measure they use and how they make their calculations? Do you think they shouldn’t measure it at all?
We’ve all experienced a general rise in prices the past year and have a sense that something abnormal is occurring. BLS’s calculation confirms this. Our sense of abnormality is confirmed by the data.