A store like Walmart knows the price of every item in every store and usually similar things for competitors. They use this information to adjust their prices locally.

A shopper might know a few prices from personal experience, but not in depth. So the store features a low price on items that shoppers use as an index ("loss leaders") and then makes it up on other items.

The internet is putting an end to this game, at least for more expensive items like electronics. Online merchants can offer nothing special except price so many sites now provide price comparison databases. This is partly manipulated by the merchants who must agree to provide the data, but is much more transparent than before. Since the comparison sites usually get a referral fee it is sometimes cheaper to go to various merchants directly and look for a deal. This is especially true with airline tickets. The tradeoff is spending more time online.

As to measuring inflation, the issue is so politically sensitive that it is impossible to get real data from government departments. In the US, for example, the annual adjustment to Social Security depends on the inflation data, so a small change can amount to billions of additional payouts. There is also the issue of how to price improvements in the quality of an item.
If a new computer is 2GHz instead of 1GHz and costs the same is it really "cheaper"?

Policies not Politics
---- Daily Landscape