Question at position 9 Rather than using a stopwatch, suppose you measured the pendulum's period 10 times using a metronome. Your measurements are as follows: {3 s, 3 s, 3 s, 3 s, 3s, 3 s, 3 s, 3 s, 3 s, 3s}. The mean measurement is 3 s. In your lab notebook, how should you report the uncertainty in your mean measurement? 0 s1 s0.75 s3s1.3s0.7 s0.5 sClear my selection

Question

Question at position 9  Rather than using a stopwatch, suppose you measured the pendulum's period 10 times using a metronome. Your measurements are as follows: {3 s, 3 s, 3 s, 3 s, 3s, 3 s, 3 s, 3 s, 3 s, 3s}. The mean measurement is 3 s. In your lab notebook, how should you report the uncertainty in your mean measurement? 0 s1 s0.75 s3s1.3s0.7 s0.5 sClear my selection

BlackTom AI · Accepted Answer

Starting with the core idea: the uncertainty in the mean is derived from the spread of your measurements, not just the value of the mean itself.
Option 1: 0 s. Since every one of the ten measurements is exactly 3 s, the data show no spread at all. The standard deviation of identical values is 0, and the standard error of the mean (SEM = s/√n) would also be 0. Therefore, reporting the uncertainty as 0 s reflects your data precisely.
Option 2: 1 s. This would imply substantial spread among the measurements, which is contradicted by the identical values reported. There is no basis for a 1 s uncertainty here.
Option 3: 0.75 s. This is another way of expressing a nonzero spread, but with perfectly identical measurements the computed uncertainty should be zero; 0.75 s would overstate the precision implied by the data.
Option 4: 3 s. Presenting the mean as 3 s with a 3 s uncertainty would indicate a huge uncertainty equal to the mean itself, which does not align with the observed data where all trials matched exactly.
Option 5: 1.3 s. Similar to 1 s or 0.75 s, it suggests notable scatter in the measurements, which is not present here.
Option 6: 0.7 s. This is a small, nonzero uncertainty, incompatible with the fact that all ten measurements are identical; the sample has zero spread, so the SEM cannot be nonzero.
Option 7: 0.5 s. Again, nonzero and not supported by the data, since there is no variation to justify any uncertainty.
In summary, since every measurement equals 3 s, the spread is zero, leading to an uncertainty of 0 s for the mean. The other options imply some spread or instrument limitations that are not reflected by the given data.

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