Accuracy vs Precision

Mr. Murray's Physics

Why Multiple Samples are Important

Multiple Samples Reduce Measuring Error

In class we used cell phones to measure the period of a pendulum. A cell phone is not a very precise instrument. Taking the period of only one cycle (1 back and forth of the pendulum), we got periods of 1.4, 1.22, and 1.35 seconds. The average gives 1.32 seconds ± 0.18 seconds (though, in reality, it's probably more than that). This error comes from the inaccuracy of our fingers on the cell phone keys. It is exacerbated because we only took the period of one cycle, so the inaccuracy of our measuring method is at the beginning and the end of our sample. Each time you measure something you introduce error.

Next we took the period of 20 cycles. We got times of 27.9, 27.78, and 27.62 seconds. The average period (divided by 20, of course) gives: 1.38 seconds. Because we only took our readings at the beginning and end of our sample, the middle 19 periods have no measuring error. So, our error,too, can be divided by 20, giving: 1.38 ± 0.009 seconds: quite a precise period.

How much do multiple samples help? In one class a student used an analog watch with a second hand: a very imprecise instrument. She was pretty far off from the other periods with only one cycle (by almost 2 seconds), but close over 20 cycles. If we had taken 100 cycles even this student looking at a watch's second hand would have been accurate. A large enough sample increases accuracy for even an imprecise instrument.

This does not mean that we should use imprecise instruments. In the perfect laboratory situation we should use as precise an instrument as we can find, then use multiple sample to reduce the effect of human error and ensure that our numbers are indeed accurate.

Remember - every time you take a measurement you introduce error. So it is always better to take as few measurements as possible. By taking multiple samples, the error is divided by the number of samples.

Multiple Samples Reduce Individual Differences

It should be obvious that multiple samples be taken when performing experiments that include individual occurrences or specimens, such as biology and medical. By studying several individuals the differences within the species or group become less important. Then trends can be determined - norms that can be used for future study or define characteristics.
Example: What is a "normal" size for a human? People come in many heights. Only by averaging the heights of many various people would you be able to determine a normal size. The amount of people you measure matters, as well. Shaquille O' Neal's immense height would skew a small sample, but in a large enough sample, his height would barely change the results. These individuals very far off from the norm do matter in the whole population, of course. The more very tall people (or very short people, of course) there are in the population, the definition of normal height does indeed change.