If a balance consistently measures a standard weight as 10.01 g, 10.02 g, and 10.03 g, how should the final result be presented, assuming a calculated standard deviation of 0.01g?
Understand the Problem
The question is asking how to properly report a series of measurements given their mean and standard deviation. The key concepts here are mean, standard deviation, and how to represent uncertainty in a measurement.
Answer
10.02 ± 0.01 g
The final result should be presented as 10.02 ± 0.01 g, where 10.02 g is the mean of the measurements and 0.01 g is the standard deviation.
Answer for screen readers
The final result should be presented as 10.02 ± 0.01 g, where 10.02 g is the mean of the measurements and 0.01 g is the standard deviation.
More Information
The measurements are 10.01 g, 10.02 g, and 10.03 g. The average of these measurements is (10.01 + 10.02 + 10.03) / 3 = 10.02 g. Given a calculated standard deviation of 0.01 g, the final result is presented with the uncertainty.
Tips
When reporting measurements, always include the uncertainty (standard deviation) to indicate the precision of the measurement. The uncertainty provides information about the spread or variability of the data around the mean.
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