Say you made three different mass measurements of a sugar cube. You know the mass is 1.0g. how would you know whether or not the measurements were accurate? Precise?

Suppose you weighed the cube and obtained the following:

0.50 g; 1.0 g; 1.50 g
The average is 1.00 g; therefore, the accuracy is very good but the precision is lousy.

Suppose you weighed the cube and obtained the following:
0.50 g; 0.51 g; 0.49 g.
The average is 0.50 g which is far from the actual value of 1.0 g; therefore, the accuracy is lousy but the precision is good.

Suppose the weighings were as follows:
0.50 g; 0.60 g; 0.70 g.
The accuracy is not good (its a long way to 1.0 g) AND the precision is not good either.

The fourth case is the last possibility.
0.99 g; 1.0 g; 1.1 g.
The average is 1.0 g; therefore, the accuracy is very good and the precision is very good.

To determine if the measurements were accurate and precise, you would need to compare them to the accepted value or true value, which in this case is known to be 1.0g.

Accuracy refers to how close the measurements are to the true value. To check for accuracy, calculate the average of the three measurements. If the average mass is very close to 1.0g, then the measurements are accurate. If the average mass is significantly different from 1.0g, then the measurements are not accurate.

Precision refers to the consistency or reproducibility of the measurements. To check for precision, calculate the range or the difference between the largest and smallest measurement. If the range is relatively small, then the measurements are precise. If the range is large, then the measurements are not precise.

Here's a step-by-step process on how to determine accuracy and precision given the three mass measurements:

1. Add up the three measured masses.
2. Divide the sum by 3 to calculate the average.
3. Compare the average mass to the true value of 1.0g. If they are close, the measurements are accurate.
4. Determine the range by subtracting the smallest mass measurement from the largest.
5. Compare the range to a reasonable value. If it is small, the measurements are precise.

Remember, accuracy and precision are two different concepts. Measurements can be accurate but not precise, precise but not accurate, both accurate and precise, or neither accurate nor precise.