Question

- Why is important to include uncertainty in a measurement in a lab setting?

- Suppose you want to measure how fast your friend can run a race. To do this, you set up a straight track with a starting line and a finishing line and have your friend run from one end to the other. To calculate their speed, you need to know how far they ran and the time it took, so you measure the length of the track with a measuring tape, and you time your friend’s run using a stop watch. Describe at least one possible source of random uncertainty and one possible source of systematic uncertainty that might exist in this type of experiment. Uncertainty does not include making a mistake

- Give two examples of scenarios where it is crucial that the level of uncertainty in an experiment must be as small as possible.

- Does a small standard deviation signify more or less uncertainty in the data? Explain.

- Does a wider normal distribution plot indicate more or less uncertainty in the data? Explain.

Answer 1

Any measurements we make will have some uncertainty associated. This uncertainty some measurement is limited to so called 'accuracy' and 'precision' of the instrument which is used in order to carry out the measurements. If these uncertainties are not included it is not likely that the experimenter will obtain a fairly good result at the end of his measurements. Therefore it is necessary to include uncertainty in measurement in a lab setting.

There could be uncertainty whenever there is some distance between the scale used for measuring and indicator used for measurement. It is important to note that, this can be occasionally a source of significant amount of error. In the given situation, Random errors could arise as a result of precision limitation of the measuring device which can be the timer we use to measure the time taken to cover a particular distance. Systematic errors can also be present due to inaccuracies that are present in the same direction. Random errors can be compensated for by increasing the number of observations whereas systematic errors cannot.

Suppose that we have a sensor which we want to use for a measurement by knowing the uncertainty of the sensor it is possible for us to trust the measurements. In such situations if we neglect uncertainty the consequence could be expensive, waste of energy and materials. Secondly for measurements such as the radius vod deuteron, to get a correct estimate we can analyse theoretical uncertainties of nuclear structure corrections.

We know that a large value of standard deviation indicates that the observation points are spread from the mean position, whereas a small value of standard deviation means that the observation points are pretty much close to the mean. Therefore smaller standard deviation means less uncertainty.

If the value of standard deviation is large we see that we will obtain a normal distribution plot which is wider and flatter. Therefore wider normal distribution plot implies there exist a larger amount of uncertainty.