Santa Barbara’s median home prices jumped higher and faster than any of the 40 counties in which the California Association of Realtors tracks sales. The median home sale price in S.B. jumped from $600,000 last April to $1.1 million this April, an increase of 83 percent. Statewide, the average jumped by 34 percent. According to the statewide Realtors association, the number of homes selling for more than the asking price has achieved new record levels, and the length of time inventory remains on the market has been cut in half.