Question

The mass of a sample or iron ore is known to be 35.714 grams. You measure the mass of this sample using three different scales and obtain the following masses: 36.2 g, 35 g, 34.9 g and 35.9 g. The accepted tolerance for both error and for accuracy is 2%. With respect to accuracy and precision, how would you best describe these measurements? Hint: Determine the average mass, absolute deviation for each trail, the M.A.D, and Relative Deviation (percent).

Answer 1

1) Determine the average mass = 1/4*(36.2 + 35.0 + 34.9 + 35.9) g = 35.5 g.

2) Determine the relative deviation of each measurement by using the formula

Absolute Dev. = (absolute value of the difference of the actual measurement and the average).

Abs. Dev. for measurement 1 = (36.2 g – 35.5 g) = 1.1097 g.

Abs. Dev. for measurement 2 = (35.5 g – 35.0 g) = 0.5000 g.

Abs. Dev. for measurement 3 = (35.5 g – 34.9 g) = 0.6000 g.

Abs. Dev. for measurement 4 = (35.9 g – 35.5 g) = 0.4000 g.

3) Determine the mean absolute deviation by taking the sum of the absolute deviations obtained above and dividing by the number o measurements.

Mean Abs. Dev. = (1.1097 + 0.5000 + 0.6000 + 0.4000)/4 g = 0.652425 g ≈ 0.6524 g.

4) Determine the relative deviation by dividing the Mean Abs. Dev by the mean of the measurements (average mass) and multiplying by 100.

Rel. Dev. = (0.6524 g)/(35.5 g)*100% = 1.83774% ≈ 1.84% (ans).