Looking at a sample of 8000 entries from the 2MASS catalog
On average stars were 1.18 magnitudes brighter in red than blue (SD was 0.46) with a range from 4.2 magnitudes brighter to 0.5 magnitudes fainter.
On average stars were 3.65 magnitudes brighter in K than blue (SD was 0.82) with a range from 11.9 magnitudes brighter to 0.8 magnitudes fainter.
On average stars were 0.77 magnitudes brighter in K than J (SD was 0.33) with a range from 3.4 magnitudes brighter to 1.5 magnitudes fainter.
On average stars were 1.70 magnitudes brighter in J than Red (SD was 0.61) with a range from 7.0 magnitudes brighter to 4.2 magnitudes fainter.
This mass of data must be useful for something. Perhaps looking for very red stars many of which are known to be variable.