Question

Background information for the following post lab question: The lab surrounded the hypothesis that the circumference of a circle is directly proportional to the diameter such that C=piD. Our task was to use the provided materials (string, ruler, meter stick, metal rings of various sizes) to devise an experiment to test the stated hypothesis. Our group used the string to measure around the rings, averaging two trials of measuring each ring. We then plotted the circumference and diameter into excel to get a line with slope, 3.1484 (very close to pi)

Why is it more powerful to have two moderatley precise independant measurments of pi than to just have one very precise measurment?

Answer 1

In an experiment we have minimize errors.

Here in this case you have taken multiple readings in order to minimize RANDOM Error

Random Errors in experimental measurements are caused by unknown and unpredictable changes in the experiment. These may be because of the measuring instruments or by environmental conditions.

Here if you say precise means it is the value or measurement, how close a number of measurements of the same quantity agree with each other.

Precision is limited by Random errors. Hence in order to minimize random errors we will measure more number of values and take the to make the measurement more precise.

This is the reason why you have taken two moderately precise independent measurements of Pi than to just have one very precise measurement.