# Explain why a systematic error canβt be corrected for by taking the mean of many readings.?

Asked by Siblinings (136) February 19th, 2010

http://i170.photobucket.com/albums/u276/saenbateman/cir.jpg?t=1266576368

Is it because if one is wrong they’ll all be wrong so by getting the mean will make no difference?

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I don’t understand the relevance of the image to the question. However, your basic idea seems to be close to the correct idea. A “systematic” error is in contrast to “random” error, in that a systematic error will always trend in one direction.

For instance, to take a very simple example, let’s say you’re measuring something with a ruler. Systematic error would occur if your ruler was inherently flawed. Let’s say it got melted on a hot day, and ended up longer than it should be. An “inch” on your ruler is now 1.1 inches. You’re measure the same object 5 times , and get the following information from your flawed ruler:

10.7 inches
11.1 inches
11.0 inches
11.3 inches
10.9 inches

The mean of these five measurements is 11. However, due to the systematic error from the stretched ruler, you would be off, but have no way of knowing this (in this example, of course, the object would “actually” be 10 inches long.)

With random error, taking the mean can help narrow in on the correct answer within a data set. Random error occurs equally in all directions from the “true” value that you are trying to measure. If you measured the same object 5 times with a ruler that had no inherent systematic error (a good ruler), you could get the following data:

9.9
10.2
10.1
9.8
10.1

Taking the mean of these results gets you 10.02, an answer very close to the “true” value of 10.0.

note: i deliberately did not allow the fake data set to result in a perfectly “true” answer. In any experiment, you are likely to end up slightly “off” of what the actual value should be. This is why scientists must account for their estimated error using various statistical tools

hannahsugs (3238)

I’m guessing the image is related to the homework question this is regarding.

What @hannahsugs said

It is possible to calibrate for a systemic answer if you can calibrate your long ruler, you can then compensate for it. E.g., http://en.wikipedia.org/wiki/Hubble_Space_Telescope#Flawed_mirror

grumpyfish (6615)

@grumpyfish: agreed, and I usually steer away from answering homework questions, but since it’s a conceptual question, I felt safe giving @Siblinings a conceptual, generalized answer.

hannahsugs (3238)

Yes, what he said