- #1

KDPhysics

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- Homework Statement
- Error analysis for standard introductory physics experiment.

- Relevant Equations
- Arithmetic mean, standard deviation, half range.

Suppose I measure the distance between two objects for three trials. The two objects then get farther away, and I measure the distance between them again for three trials. I repeat this for 3 more different distances, getting a total of 15 measurements (3 trials for 5 distances).

I then compute the average and the half-range (approximates the uncertainty) for each distance. For example, the first distance will have average 3.3m and uncertainty 0.15m . In this, case, since the uncertainty is fairly small, I have been told to keep the two significant figures and simply make the number of digits after the comma in the average to coincide with the number of digits after the comma of the uncertainty. So, i would write 3.30±0.15. That is clear to me.

The problem is, what if the second distance is 5.3±0.7. In this case, I only keep one significant figure for the uncertainty. But then, the measurements will have a different number of significant figures. Is this ok? Or should I report the first measurement as 3.3±0.2?

Also, to compute the uncertainty, should I use the half range or the standard deviation (i'm in high school)?

I then compute the average and the half-range (approximates the uncertainty) for each distance. For example, the first distance will have average 3.3m and uncertainty 0.15m . In this, case, since the uncertainty is fairly small, I have been told to keep the two significant figures and simply make the number of digits after the comma in the average to coincide with the number of digits after the comma of the uncertainty. So, i would write 3.30±0.15. That is clear to me.

The problem is, what if the second distance is 5.3±0.7. In this case, I only keep one significant figure for the uncertainty. But then, the measurements will have a different number of significant figures. Is this ok? Or should I report the first measurement as 3.3±0.2?

Also, to compute the uncertainty, should I use the half range or the standard deviation (i'm in high school)?