Inflation is one of the economy's most important vital signs and one of the subtlest to measure. The CPI inflation rate -- the 12-month change in the consumer-price index -- gets most of the attention. But there are multiple ways to measure price changes that influence how investors and the Federal Reserve track inflation.

Here's a look at how inflation statistics work.

What is the CPI?

Prices on specific items rise and fall all the time. Inflation refers to a broader pattern in which prices rise across the economy as a whole. Over time, this gradually erodes the purchasing power of a dollar.

The consumer-price index, or CPI, aims to measure this phenomenon. Published monthly by the Bureau of Labor Statistics, part of the Labor Department, it tracks a basket of goods and services purchased by the typical consumer, from furniture to automobiles and insurance, distilling thousands of prices into one monthly number.

Like a stock index, it isn't measured in dollars. Instead, the CPI is set so that 100 equals average prices from 1982-84. Every month, the BLS updates the index to rise or fall in line with how prices have moved since the previous month.

The inflation rate is simply how much, in percentage terms, the CPI has increased. The Labor Department reported Wednesday that prices rose by 3.4% in July from a year earlier. That is based on the CPI reaching an index level of 333.918, and comparing it with the index level 12 months earlier of 323.048.

If the inflation rate falls, for example from 4% to 3%, that doesn't mean that prices have fallen, only that they are rising more slowly.

Falling prices -- when the price index decreases instead of increases -- is called deflation. Persistent deflation is extremely rare.

How is inflation measured?

Much of the price data comes from hundreds of BLS employees who fan out across the country every month to check prices at supermarkets, doctors' offices, clothing stores and the like. The BLS also collects some prices digitally. Prices for cellphone plans and gasoline arrive from analytics companies that track those industries, for example.

To blend all these prices into the index, the BLS must determine how much weight each category should get. It does this by surveying Americans once a year on how much of their spending goes to food, rent, entertainment and other categories.

The resulting index represents how prices are changing for the average American. But it is only an average; it doesn't apply equally to everyone. For example, rising gasoline prices push up the inflation rate, but a person who doesn't drive wouldn't feel the blow.

The BLS also adjusts the data to remove regular seasonal patterns (for example, higher airfares during prime travel months) to identify the underlying trend. When analysts cite monthly changes, they are almost always citing seasonally adjusted figures.

Annual vs. monthly numbers

The 12-month change is what most people think of as the inflation rate. But it is of limited use to analysts interested in the most timely, granular trends, because 11 of the 12 months in that change had previously been published. Professional investors and business economists focus on the month-to-month change in the CPI. In July, the CPI rose 0.1% from June.

But there are reasons to convert from monthly to annual, for example to figure out whether the annual rate is running above the Federal Reserve's 2% target. Monthly price increases of 0.17% -- sustained for a full year -- would yield roughly 2% annual inflation.

Core and PCE

Economists also look at different subsets of the CPI for a more nuanced picture of inflation. One of the most important is the core rate, which examines CPI without food and energy prices. Though those categories make up about 20% of the index, they often bounce around because of weather, geopolitical events and other one-offs that might not reflect underlying economic trends.

Most recently, the Iran conflict has been pushing up energy prices, so core inflation is running cooler than the full index. In July, the core CPI rose by 0.2%, contributing to a 2.5% rise over the past 12 months.

The Federal Reserve, which aims to keep inflation at 2%, focuses on another inflation measure entirely: the personal-consumption expenditures price index, which is published by the Commerce Department. The PCE treats categories differently, for example including all spending on healthcare on behalf of consumers, such as by employers and the government, not just what consumers pay out of pocket. PCE numbers take a couple of weeks longer to arrive, but Fed officials believe they better reflect how costs throughout the economy are changing.