Random error can be inherent to the system being studied or to the instruments being used to measure characteristics of the system. Sometimes it is possible to find or create measuring instruments that produce results with less random error; sometimes not. Statistical methods can often be employed to estimate actual values shorn of random error. If it not too expensive to obtain individual measurements then it's advisable to gather more measurements so that the statistical methods will produce better results.
Systematic errors are often reduced by looking for their sources and eliminating them or by estimating the levels of distortion caused by each of them and correcting measurements accordingly.
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You can overcome or reduce the problem of random error and systematic error while doing an experiment by increasing the sample size, which means averaging over a huge number of observations.
Sampling error leads to random error. Sampling bias leads to systematic error.
Standard error is random error, represented by a standard deviation. Sampling error is systematic error, represented by a bias in the mean.
Random sampling is picking a subject at random. Systematic sampling is using a pattern to pick subjects, I.e. picking every third person.
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