The team said upper corner seats for Sunday games will cost $5 and upper box and reserved seats will be sold for $10, the Chicago Sun-Times reported Friday.
Bleacher, outfield reserved, lower corner and premium upper box seats will be available for $15, the team said.
The "family Sundays" events will feature autograph sessions and the opportunity for children to run the bases after games.
The White Sox drew 1,965,955 fans during the 2012 season, the first time the number has dipped below 2 million since 2004.
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