The CPI is actually IMO a lousy indicator of "inflation". The commonly used CPI-U measures the change in cost for an urban living renter who works full time and doesnt pay for their own health care, but receives it as a free benefit from their job.
It uses a number of adjustments and 'basket substitutions'. For example, if steak becomes too expensive, the index substitutes hamburger, with the argument that this is what a regular person would do. In my opinion, thats pricing behavioral changes, not true cost of living.
We had a huge spike in the CPI a couple of years ago, principally from the jump in oil and gasoline prices and when those plunged, it weighed down the other increases in the CPI.
So if you're an urban worker and renter, chances are the CPI-U is somewhat representative of your experienced rate of inflation, although if you tend to drive a little or a lot, eat certain foods frequently or otherwise step out of the 'norm' then the index wont track your spending changes very well.
I suspect quite a few of us arent young and live in an apartment in the city, and many may be retired or working part time and may be paying for some or all of our own health care. That means we're experiencing a lot more inflation than the CPI would let on.