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In this video tutorial for R programming, the narrator demonstrates how to sum duplicate rows in a data frame. Two examples are shown based on a data frame created with lines two and three of the code. By running these lines, a new data frame object named "data" appears in the RStudio. This data frame contains six rows and two columns (x1 and x2). To sum values in column x2 based on duplicates in column x1, the aggregate function is used. Line 5 of the code shows how to specify the column for summing values within the aggregate function.