[mlyle]

Housing is a component of the consumer price index used to measure inflation. The proportion matches the proportion of household spending that most USians spend on housing.

Of course, not every household is the average household. Some households spend more of their spending on things that have increased more than the average household. Some spend less of their spending on such things.

And, of course, even if the average wage has risen quicker than inflation, that doesn't mean any specific household's wages have.

[gjsman-1000]

How about, instead of looking at the average, you look at the median.

[mlyle]

I said "average" not "mean". The median is a form of average.

BLS looks at mostly median households in the survey dataset, but also considers means of some aggregates, when choosing weightings of goods in the basket.

I suspect in the specific case you're talking about -- housing -- using the mean would overweight housing in the basket.