Four measurements of the mass of a block are recorded as 2.01 ~g , 2.02 ~g , 2.03 ~g , and 2.05 ~g . The final reported mass of the block, expressed in the standard form (mean mean absolute error) with appropriate significant figures, is:

Step-by-step solution

First, calculate the mean of the mass measurements: Sum = 2.01 + 2.02 + 2.03 + 2.05 = 8.11 ~g Mean = 8.11 4 = 2.0275 ~g Since the original measurements have two decimal places, the mean must be rounded to two decimal places. Rounding 2.0275 ~g gives 2.03 ~g . Next, calculate the absolute errors for each measurement using the rounded mean ( 2.03 ~g ): |2.01 - 2.03| = 0.02 ~g |2.02 - 2.03| = 0.01 ~g |2.03 - 2.03| = 0.00 ~g |2.05 - 2.03| = 0.02 ~g Sum of absolute errors = 0.02 + 0.01 + 0.00 + 0.02 = 0.05 ~g Mean absol