Norwood was laid out in 1882. The community's name was inspired by the novel Norwood: or, Village Life in New England, by Henry Ward Beecher. A post office called Norwood has been in operation since 1882.
As of the census of 2010, there were 665 people, 241 households, and 167 families living in the city. The population density was. There were 277 housing units at an average density of. The racial makeup of the city was 96.1% White, 0.9% African American, 0.9% Native American, 0.2% from other races, and 2.0% from two or more races. Hispanic or Latino of any race were 1.4% of the population. There were 241 households of which 43.6% had children under the age of 18 living with them, 48.5% were married couplesliving together, 14.9% had a female householder with no husband present, 5.8% had a male householder with no wife present, and 30.7% were non-families. 25.7% of all households were made up of individuals and 10.4% had someone living alone who was 65 years of age or older. The average household size was 2.76 and the average family size was 3.26. The median age in the city was 31.9 years. 31.9% of residents were under the age of 18; 9.2% were between the ages of 18 and 24; 24.8% were from 25 to 44; 24.6% were from 45 to 64; and 9.8% were 65 years of age or older. The gender makeup of the city was 51.7% male and 48.3% female.
2000 census
As of the census of 2000, there were 552 people, 209 households, and 145 families living in the city. The population density was 347.4 people per square mile. There were 245 housing units at an average density of 154.2 per square mile. The racial makeup of the city was 98.01% White, 0.91% Native American, and 1.09% from two or more races. Hispanic or Latino of any race were 0.54% of the population. There were 209 households out of which 38.3% had children under the age of 18 living with them, 53.6% were married couples living together, 11.0% had a female householder with no husband present, and 30.6% were non-families. 27.3% of all households were made up of individuals and 12.4% had someone living alone who was 65 years of age or older. The average household size was 2.64 and the average family size was 3.21. In the city the population was spread out with 30.6% under the age of 18, 11.8% from 18 to 24, 25.7% from 25 to 44, 18.3% from 45 to 64, and 13.6% who were 65 years of age or older. The median age was 32 years. For every 100 females there were 92.3 males. For every 100 females age 18 and over, there were 85.9 males. The median income for a household in the city was $22,614, and the median income for a family was $27,500. Males had a median income of $26,250 versus $24,500 for females. The per capita income for the city was $9,670. About 21.3% of families and 29.5% of the population were below the poverty line, including 39.6% of those under age 18 and 23.6% of those age 65 or over.
