Medina was the location of a fatal shootout between tax protestor Gordon Kahl and U.S. Marshalls.
According to the United States Census Bureau, the city has a total area of 1.0 square miles (2.6 km²), of which, 1.0 square miles (2.6 km²) of it is land and 0.98% is water.
There were 165 households out of which 19.4% had children under the age of 18 living with them, 52.1% were married couples living together, 3.6% had a female householder with no husband present, and 39.4% were non-families. 37.6% of all households were made up of individuals and 26.1% had someone living alone who was 65 years of age or older. The average household size was 2.03 and the average family size was 2.62.
In the city the population was spread out with 20.0% under the age of 18, 2.1% from 18 to 24, 20.6% from 25 to 44, 23.6% from 45 to 64, and 33.7% who were 65 years of age or older. The median age was 50 years. For every 100 females there were 79.1 males. For every 100 females age 18 and over, there were 78.7 males.
The median income for a household in the city was $22,059, and the median income for a family was $31,500. Males had a median income of $31,458 versus $17,500 for females. The per capita income for the city was $16,860. About 4.8% of families and 14.1% of the population were below the poverty line, including 15.4% of those under age 18 and 15.0% of those age 65 or over.