At measurement of any size there is always some deviation from true value as any device cannot yield exact result. To define possible rejections of the obtained data from exact value, use concepts of a relative and absolute error.
It is required to you
- - results of measurements;
- - calculator.
Instruction
1. First of all, take several measurements by the device of the same size to have an opportunity to count the valid value. The more it will be carried out measurements, the more precisely there will be a result. For example, weigh apple on electronic scales. Let's say you received results 0.106, 0.111, 0.098 kg.
2. Now count the valid value of size (valid as true it is impossible to find). For this purpose put the received results and divide them into the number of measurements, that is find an arithmetic average. The valid value will be equal in an example (0.106+0.111+0.098)/3=0.105.
3. For calculation of an absolute error of the first measurement subtract the valid value from result: 0.106-0.105=0.001. In the same way calculate absolute errors of other measurements. Pay attention irrespective of, the result with minus or with plus will turn out, the sign of an error always positive (that is you take the value module).
4. To receive a relative error of the first measurement, divide an absolute error into the valid value: 0.001/0.105=0.0095. Pay attention, usually relative error is measured as a percentage therefore increase the received number by 100%: 0.0095Õ100%=0.95%. In the same way consider relative errors of other measurements.
5. If the true value is already known, at once be accepted to calculation of errors, having excluded search of an arithmetic average of results of measurements. At once subtract the received result from true value, at the same time you will find an absolute error.
6. Then you divide an absolute error into true value and multiply by 100% - it will be a relative error. For example, the number of pupils 197, but rounded it to 200. In that case calculate a rounding error: 197-200=3, relative error: 3/197Õ100%=1.5%.