ERROR AND UNCERTAINTY ANALYSIS : EXPLANATION, SOLVED EXAMPLES AND PRACTICE PROBLEMS OF ERROR AND UNCERTAINTY

Error is a very important concept of Physics and Mathematics. It is generally said that nothing is Perfect, this statement is also true in the context of scientific calculations or measurements. Some content of Error always exists in any scientific results. So it is not possible to find the exact value of measurements. The study of error can help us to reduce the content of error in calculations. This topic is also an inseparable part of many exams like CSIR-NET/JRF, GATE, JEST, IIT-JAM, NEET, JEE, etc.

What to be discussed -

  1. What is Error
  2. Formulae to calculate Error
  3. Solved Problem of Error
  4. What is RMS Error
  5. Solved Problem of RMS Error
  6. What is Uncertainty
  7. How to measure uncertainty
  8. Solved Problem
  9. Practice Problems of Error and Uncertainty Analysis

What is Error - The deviation of the measured value from true value is known as error. When we measured any quantity, it has two things, the first is the true value of that quantity which we cannot measure exactly and the other is the uncertainty in that measurement.

Error = Measured Value-True Value

Propagation of Error - Error is propagating through the Arithmetic operations. You should also remember that total Error is always the sum of errors in all quantities, whether it is addition or substruction. While we make mistake or error in measuring the two quantities and when we apply an arithmetic operation even subtraction then the total error will be the sum of each error. The following are the ways to find the total absolute error while we applying arithmetic operations on two or more quantities.