The name of the town was originally spelled "Norwhich", but the additional 'h' was dropped shortly after the town was chartered. The town was named after Norwich, Connecticut[?], the state from which the first settlers originated. Norwich was the original home of Norwich University[?], which later moved to Northfield[?].
Norwich maintains one of the only interstate public school systems, the Dresden School District, which is shared by the towns of Norwich and Hanover, New Hampshire.
There are 1,367 households out of which 41.1% have children under the age of 18 living with them, 58.1% are married couples living together, 8.7% have a female householder with no husband present, and 30.9% are non-families. 24.2% of all households are made up of individuals and 8.6% have someone living alone who is 65 years of age or older. The average household size is 2.59 and the average family size is 3.10.
In the town the population is spread out with 29.3% under the age of 18, 4.9% from 18 to 24, 23.6% from 25 to 44, 31.3% from 45 to 64, and 11.0% who are 65 years of age or older. The median age is 41 years. For every 100 females there are 95.7 males. For every 100 females age 18 and over, there are 90.1 males.
The median income for a household in the town is $66,000, and the median income for a family is $78,178. Males have a median income of $49,350 versus $33,871 for females. The per capita income for the town is $35,285. 3.8% of the population and 1.5% of families are below the poverty line. Out of the total people living in poverty, 1.1% are under the age of 18 and 6.2% are 65 or older.
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