In ALL STATES, not just Kansas, 100% of homes Sold Through A Realtor are homes owned (legal title) by THE OWNER (FSBO)...think about it. Now for homes sold without a Realtor, that percentage is tracked by the NAR (National Association of Realtors). Direct your questions to them. Are you writting a term paper or selling a house?

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On average about 10% of homes in the US are sold without a Realtor.
The National Association of Realtors (NAR) reports that 5% of the time the seller knew the buyer, 5% of the time they did not know the buyer, and 86% of the time they eventually listed with a Realtor.

When a home is sold without professional representation, it sells on average for 16% LESS.

Homes are bought by a buyer represented by a Realtor about 90% of the time.

I do not know that ratio of homes sold without professional assistance for given geographic areas.