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A student measures the length of a rod five times: 10.2, 10.4, 10.1, 10.3 and 10.5 cm.
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A student measures the length of a rod five times: 10.2, 10.4, 10.1, 10.3 and 10.5 cm. Find the mean, the standard deviation with ddof=0 and with ddof=1, and the standard error of the mean, which is the sample standard deviation divided by . Which standard deviation should the student report, and why?
The worked solution
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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. The mean is the centre. The five measurements are a sample of all the measurements that could be made, so the sample standard deviation (ddof=1) is the right one.
Check. The mean is 10.3. The deviations from the mean are -0.1, 0.1, -0.2, 0 and 0.2. Their squares add up to 0.01 + 0.01 + 0.04 + 0 + 0.04 = 0.10. Divided by it is 0.02, and the square root is 0.1414. Divided by it is 0.025, and the square root is 0.1581. The standard error is .
Answer: mean 10.30 cm, ddof=0 gives 0.1414, ddof=1 gives 0.1581, and the standard error is 0.0707 cm. Report the sample standard deviation, 0.158 cm, because the five measurements are a sample.
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