Step 1 :Given the number of TV hours watched per day by each child: [2, 3, 1, 4, 2, 3, 1, 2, 3, 4, 2, 3, 1, 2, 3, 4, 2, 3, 1, 2, 3, 4, 2, 3, 1, 2, 3, 4, 2, 3].
Step 2 :Calculate the average number of hours a day that each child watches television by finding the mean of the 'TVhours' variable. The mean is calculated by summing all the values and dividing by the number of values. In this case, the mean is \(2.5\) hours.
Step 3 :Calculate the range of television hours watched. The range is calculated by subtracting the smallest value from the largest value. In this case, the range is \(3\) hours.
Step 4 :The average number of hours a day that each child watches television is \(\boxed{2.5}\) hours. The range of television hours watched is \(\boxed{3}\) hours.