Well of course such a number can. You just calculate average price increases, weighed by their share of spending (a 1% increase in healthcare has more implications than a 1% increase in telephone bills) to the best of your ability.

The question is, how good is the approximation and how meaningful is an average statistic?

The statistic is useful and meaningful, but doesn't say everything. Fortunately we have hundreds of inflation metrics, for different groups (urban, rural), age groups, countries, states, regions and sectors.

Virtually none of these are published in media outside the general CPI measure, but all can be found on government/centralbank/consultants etc websites, typically with methodological sections explaining how they came to their conclusions.

For example: https://www.bls.gov/cpi/home.htm

Here you can find various inflation figures, methodology and data.