# errors, random and approximations

Hello good evening all!

If a reading is reported as R = 200.045 + 0.001 or 200.045 - 0.001 Ohm. Does +0.001 or -0.001 Ohm represents a systematic or random error?

Thanking you.

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It represents random error. Random error is a bit of 'spreading out', but systematic error means the data is centered around the wrong spot. Put another way:

Say your wife asks you your anniversary. If you guess the date slightly wrong, that's random error. You know roughly what's going on, but the data isn't exact.

If you give the correct date of her birthday instead, that's systematic error. Accurate, but at the same time completely off the mark.

Having both is either awful science or grounds for divorce.

Random error can be calculated through standard deviation, which you can learn more about here. The wiki page on variance gives a good sense of where this formula comes from.

Systematic error is different. Say I measure your height and get a bunch of values within a few millimetres of each other. These are just numbers, and so I can compute how spread out they are just fine. However, nothing about the numbers can tell me that you didn't take your shoes off. Systematic error is when the value you get is wrong. What makes it wrong can't be determined mathematically, and can only be ensured by being very careful about how you run your experiment.

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! what a wonderful example you have given. Ok fine. can you show the random error in mathematical way. I mean take some small data and classify the random and systematic error. for more and better understanding. please... – KRRG-BITS Jun 27 '12 at 19:02
edited with an explanation of how we think about these types of errors. – Robert Mastragostino Jun 27 '12 at 19:19
! is there any other kind of errors? then how we generalize such errors exists? could you answer please. Your answer is more effective and interesting... – KRRG-BITS Jun 27 '12 at 19:41
Systematic error is what statisticians call bias. It indicates that the estimate has its distribution centered around the wrong point. Random error comes about because of sampling variability. Each time you take an observation you have the true value plus some random noise (e.g. measurement error) Model parameters can be estimated from noisy data. The estimate should be close to the true parameter but due to the random error which generally is symmetrically distributed around 0. – Michael Chernick Jun 27 '12 at 19:52
The estimate has a resulting standard eror a the + or- 0.001 in your example indicates that the standard error of your estimate is 0.001. – Michael Chernick Jun 27 '12 at 19:52