How to find an error

How to find an error

Taking measurements, it is impossible to guarantee their accuracy, any device gives a certain error. To learn the accuracy of measurements or a class of accuracy of the device, it is necessary to define an absolute and relative error.

It is required to you

  • - several results of measurements or other sample;
  • - calculator.


1. Take measurements not less than 3-5 times to have an opportunity to count the valid value of parameter. Put the received results and divide them into the number of measurements, you received the valid value which is used in tasks instead of true (it cannot be defined). For example, if measurements yielded result 8, 9, 8, 7, 10, then the valid value will be equal (8+9+8+7+10)/5=8.4.

2. Find an absolute error of each measurement. For this purpose subtract the valid value from result of measurement, neglect signs. You receive 5 absolute errors, on one for each measurement. They will be equal in an example 8-8.4 = 0.4, 9-8.4 =0.6, 8-8.4=0.4, 7-8.4 =1.4, 10-8.4=1.6 (modules of results are taken).

3. To learn a relative error of each measurement, divide an absolute error into the valid (true) value. Then increase the received result by 100%, usually this size exactly is as a percentage measured. Find a relative error in an example thus: δ1=0.4/8.4=0.048 (or 4.8%), δ2=0.6/8.4=0.071 (or 7.1%), δ3=0.4/8.4=0.048 (or 4.8%), δ4=1.4/8.4=0.167 (or 16.7%), δ5=1.6/8.4=0.19 (or 19%).

4. In practice for the most exact display of an error use an average quadratic deviation. That to find it, square all absolute errors of measurement and put among themselves. Then divide this number into (N-1) where N is the number of measurements. Having calculated a root from the received result, you receive the average quadratic deviation characterizing an error of measurements.

5. To find a limit absolute error, find the minimum number which is obviously exceeding an absolute error or equal to it. In the reviewed example just choose the greatest value – 1.6. Also sometimes it is necessary to find a limit relative error, in that case find the number exceeding or equal to a relative error, it is equal in an example to 19%.

Author: «MirrorInfo» Dream Team