All that means is that 2014 (January probably) equals 100 in the index. Realistic? Sure, it’s just math. If the index was 100.5 in August, 2017, and 101.0 in August, 2018 (just examples, not actual numbers), those index values are perfectly comparable and generate an inflation rate. No problem.
Then you go on to explain why the basket of goods and services in the index is not the rrr2015 basket. That’s true; it’s very unlikely you personally will be the statistical median consumer across the entire economy. For example, diapers are undoubtedly included in some fashion. But maybe you don’t have a baby, so you don’t buy diapers.
That’s all perfectly OK. The price index is one number, and it necessarily has to collapse a range of experiences down into one number. And this doesn’t really matter over medium and long time horizons. One month to the next, when diapers (in particular) could double in price for some strange reason, but nothing else does, sure, it matters if diapers represent a big share of your household spending. The index won’t capture that particular movement for you and your household. But relative to the whole economy and your life experience over the medium to long term, it’s perfectly fine and a very reasonable aggregation into a single number. After all, if hawker food prices are halved, do you think restaurant food and groceries aren’t correlated? Of course they are. Not perfectly correlated, perhaps, but whether you prefer hawkers more than restaurants or vice versa doesn’t actually matter too much, especially over the medium to long term of the index.
A lot of people (who don’t know much about inflation measures) raise this complaint, that they aren’t the same as the basket. We know that! Practically nobody is! But you’ve got to pick some basket, and the statisticians do a very good job picking a basket of goods and services, and weights, that are economy-wide valid.
Every CPI announcement includes some information on what caused a particular big change, if there is one. The report includes some details on goods and services categories that were big movers, if any were. You can dig into that information if you want to understand whether the “headline” number that particular month is a decent match for you or an excellent match for you that particular month.