# Communicating losses and imprecision in liquid measurement by analogy

I'm writing a presentation for people and I need an analogy to convey the following problem:

Person A wants to sell a liquid, so he fills a tank, measures volume and sends to Person B. Now Person B receives the liquid and wants to know if he received the volume he bought from Person A, so since this liquid is now stored in his tank, Person B measures the liquid volume. Person B measures won't match exactly Person A measures - due to losses and imprecisions in both measures.

These are oil tanks and I need to explain this to really varied audience that contains people unskilled in metrology. Also, Person A and B can be the same person in different places - which is actually the case that I'm studying.

I think an analogy for the tanks would be good, but I can't think anything! How can I explain this problem in a way that a lay audience will understand?

• I'm going to guess there will be more instincts to close this, but the existence of uncertainty and inconsistency in measurements is a reality of engineering, and conveying engineering concepts is critical, especially since some of the things engineers deal with are very complex and need to be understood by people with vastly different backgrounds. – Trevor Archibald Feb 11 '15 at 4:16
• I don't think that it hits all of the points, but I'm reminded of measuring cooking oil for a recipe. Fill the measuring cup, pour into a bowl and you've still got a good bit of oil on the surface of the measuring cup, so clearly not all of the oil measured made it into the food (let's say it's waffles, people like waffles). – Dan Feb 11 '15 at 4:56
• For what its worth I think that most of metrology should fall under Engineering. I think your example is reasonably simple, just keep out any extra complications at least until the end. If you really need an analogy beer is always good :). I'm not quite sure what your actual question is. – nivag Feb 11 '15 at 10:01
• I read your story about tanks, but I am not sure what point you want to teach, or how you want your audience to change its behaviour. Is it "losses", "imprecision", both, or something else? Can you edit your question to make your goal clearer? – dcorking Feb 11 '15 at 12:22
• I can edit for achieving purposes. I can't right now because I'm not on a computer. I just discovered I could add comments. Also just noted people really like to downvote things. – eri0o Feb 11 '15 at 13:39

I'm not sure of the specifics of your problem, it seems to be relatively straightforward to me. I have previoulsy considered addressing the subject of measurement errors with schoolchildren in the following manner - it may be of help to you and your audience or change in subject may confuse and distract them from your topic, that's up to you to decide.

Step 1 - give all the students and length of string (considerably longer than a metre) and ask them to put two knots in the string exactly a metre apart, based on their own estimation. The smart ones will use a length they already know as a guide - most common is their own height.

Step 2 - measure the lengths achieved against a ruler and see who got closest. A leaderboard of some kind can make this more fun. This can lead into a discussion of estimation in general. Plotting a scatter plot of the measurements might also be interesting and lead into a discussion about distributions (with enough students I think I'd expect a roughly normal distribution?)

Step 3 - now change the ruler for a tape measure and get everyone to remeasure someone elses string - they will inevitably get slightly different results. Write these down and look at the differences. Perhaps now also draw out a scatter plot of the differences. The change in results should bring up all sorts of questions to prompt your discussions on metrology. Examples could be:

• Are the metre ruler and the tape measure the same length? Which of these is the most accurate measure of a metre? How can we test them?
• Why do two measures of the same thing come out different? Was there an element of judgement by eye on the part of the measurer? Did the string stretch? Did the tape measure stretch? Were the conditions in the room the same? Have the knots tightened or slipped?
• Was the level of precision used in recording the measurements the same? What is the right level of precision? Did we agree on what part of the knots we were measuring to?
• Is there a general trend in the difference results? Are they dominated by bias or random errors?

I've done steps 1 and 2 with students, along with similar experiments on time and mass. (Generally they are roughly ok at estimating a metre, largely underestimate how long a second is, and are wildly inaccurate at estimating a kilogram). Step 3 is an extension that I've planned but not yet gotten round to trying out.

I think you could also carry out similar experiments/demonstrations with your exact problem of liquids in containers as well.

• My presentation already happened, but I like your idea to address the problem of conveying an idea with an experiment. I haven't thought about that previously, but already plan to use it on a second presentation I have to make. So I'm choosing your answer. Right now I followed @nivag and kept complications hidden to simplify and introduced those slowly - and just the main ones. – eri0o Feb 11 '15 at 13:21