The best replacement for categorical data is numerical data.

The best alternatives to categorical data are rated as following:
★★★★★  numerical data
★★  quantitative data
★★  continuous
★★  nominal data
★  continuous data
★  discrete data
★  measurement data
  ordinal
  quantitative
  numerical

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No companions for categorical data have been suggested so far.
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Google Trends

Scale is based on the average worldwide traffic of categorical data in all years. Click on graph for more.
categorical data
numerical data
quantitative data