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I'm working on a report which needs to explain in non-technical terms the effects of a cumulative error, and why it is of importance to use absolute calculations.

Definition of 'cumulative error' from dictionary.com:

an error that gradually increases in degree or significance during a series of measurements or calculations; an error that grows during observation

Ideally I could give a real world example so they grasp the concept of it without knowing about the specifics.

The first one I though of is 'Chinese whispers' which is pretty well known, but I wouldn't exactly classify it as 'real world'. Does anybody know of better examples?

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The "Telephone game" is precisely the concept. What more "fully" are you asking for? Why "concept of it without knowing about the specifics."? What's wrong with specifics? –  S.Lott Feb 20 '12 at 16:34
My marriage. I'm kidding, I love my wife. Good night, folks! –  jiggy Feb 20 '12 at 16:34
@S.Lott: I updated the question to indicate I'd prefer a 'real world' example. I realized my problem with Chinese Whispers is it isn't exactly real world, it's just a game. –  Steven Jeuris Feb 20 '12 at 16:37
It's as real-world as it gets. When you report to your manager, it gets filtered and simplified. They report to their manager and on up the food chain. At the top of the organization, none of what you said has been received. It can't be any more real world than this. And it's non-technical. –  S.Lott Feb 20 '12 at 16:41
Most real world examples I know about are a result of systematic error in measurement devices, which are not helped by absolute calculations. Are you interested in these types of examples? –  Jay Elston Feb 20 '12 at 16:52
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6 Answers

up vote 11 down vote accepted

Real world? Try carpentry. Most people have played around in a workshop a little.

You measure a piece of lumber and cut it. You need 20 of these. But to save time you take the previous one you cut, lay it flush with the next piece of lumber, and mark where you need to cut.

After 20 times you'll notice that your saw has a non-zero width and/or your pencil doesn't mark exactly where you want to cut. Errors build up and the first piece of lumber won't match the last piece of lumber.

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Do you know why we use the Gregorian calendar today in most of the western parts of the world? It is because its predecessor, the Julian calendar, made a cumulative error over the years. Read this Wikipedia article for the details:


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This is brilliant! Thanks. –  Steven Jeuris Feb 20 '12 at 17:42
"made a cumulative error". A matter of opinion. The Orthodox church doesn't agree that this is an "error". They celebrate their holidays under the old Julian calendar. And. It can be called the result of a flawed approximation, instead of a measurement error. It's possible for this example to dissolve into dispute. –  S.Lott Feb 20 '12 at 18:30
@S.Lott: A 'matter of opinion' isn't relevant to the question. All I am looking for is an easy to grasp example to get the concept across easily. –  Steven Jeuris Feb 20 '12 at 22:04
If some folks don't think it's an error, then it may not be "easy to grasp". It's not a great example because the presence of the error is disputable in the first place. –  S.Lott Feb 20 '12 at 22:10
@S.Lott: I believe we should at least credit managers with the ability to imagine an error exists, disputable or not. :) If they want to dispute anything they can attempt to dispute the actual facts I mention later on. I do see how 'whispering' conveys that aspect more, but that isn't my main concern. I just want a concise example, and this answer is exactly that. –  Steven Jeuris Feb 20 '12 at 22:17
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If you want something that shows accretion of errors and appears technical, then measure small things. This is not as good as the whisper game (sometimes called the telephone game). The whisper game is the best illustration.

Bring in a dozen small dice -- different sizes preferred.

Everyone measure 1 die.

Everyone accepts a measurement from the person on their left, adds the size of their dice and reports it to the person on their right.

The last person reports the accumulated length.

As a quality check, line the dice up and measure the entire span of dice. See how close you are.

The problem with any measurement-based demonstration is that everyone argues that more accuracy is possible with some kind of more stringent quality controls. Non-scientists have a false belief in repeatability of measurements and the idea that you can "somehow" control all the error-inducing degrees of freedom.

Whispering shows that there are something which cannot be controlled.

Measuring merely opens you up for discussion of how to measure even more accurately. It reduces the range of the accumulated error, but doesn't eliminate the error itself.

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"For want of a nail, a shoe was lost"...


For Want of a Nail

For want of a nail the shoe was lost.
For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of a rider the message was lost.
For want of a message the battle was lost.
For want of a battle the kingdom was lost.
And all for the want of a horseshoe nail.

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Always a great thing to remember, but more "pay attention to the little things" than "cumulative error". –  Ross Patterson Feb 22 '12 at 2:32
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Take a value like 0.335. Consider this value to be the selling price of an item in your store. Sell this item to 50 customers. When you sum the total without rounding you get this value: $16.75 but when your computer rounds the value to 2 digits after the point before storing each sale in memory (to become 0.34), your total will be $17. The gap between the two numbers will keep growing as you sell more and more.

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Few years ago we had a customer that wanted to use existing surveillance cameras to keep track of how many people are in the building at any given time.

Our company had object counting video analytics algorithm but it was only 98% accurate. Generally, it would be used to estimate traffic flow patterns, not keep track of precise counts.

So this customer had an acceptance test to run the algorithm for one day. At the beginning of the day, the building is almost empty (few security guards, some night people). 24 hours later it is also supposed to be almost empty. During the day several thousand people enter and exit. They came back and said that our algorithm had astronomical percent error because whatever counting error accumulated during the day, they simply divided that by expected number of people which was very low.

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