For a data set the mean is 3.17 and the range is 1.4. the data set is transformed by adding 0.5 tp each data value. what are the mean and range of the new data set

The range will NOT be affected since all we're doing is shifting everything up by 0.5, which visually means the distribution curve is shifted 0.5 units to the right. The difference between the largest and smallest value will stay the same. So that's why the range stays the same at 1.4

The mean will shift by 0.5 units if we add 0.5 to each data value, so,
New mean = (old mean) + 0.5
New mean = 3.17 + 0.5
New mean = 3.67