I'm not sure where you are getting the name Catherine. I am sitting here looking at a copy of the 1910 census in Sedgwick County, Kansas, 2WD Wichita Dist 115 and do not see a Catherine. The names are listed as John N. Burger age 42, Maude M age 33, Frank S age 14,Ray F age 12, Maude age 10, William age 9, Ralph age 7, Lillian age 4, and Ruth age?10/12, at any rate an infant.John was working in a packing house.
There is both a Lillian and and William.
On the 1920 census in Fairfax, Osage County, Oklahoma, It lists John Berger, age 52, Maude age 42, Ralph age 17, Lillian age 14, Ruth age 10 , Ivy age 8, and Richard age 4 and ?1/12.
The next family to them is Frank Berger age 24, Callie, age 24, Vera age 2 1/12 and Velma 2/12.