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?
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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.