Error due to unknown reason is called?

Question

Examoogle · Accepted Answer

Random error

Explanation: Random errors are uncertainties in measurements caused by unpredictable fluctuations in experimental conditions. They are also known as accidental or chance errors because their exact causes are unknown and cannot be completely eliminated.

Working Principle: Random errors arise due to factors like minute changes in supply voltage, slight variations in mechanical friction, or small fluctuations in ambient temperature during the measurement process. Since these factors vary continuously and unpredictably, the results of repeated measurements oscillate around a mean value.

Key Formulas: $E_r = X_m - \bar{X}$ — where $E_r$ is the random error, $X_m$ is the measured value, and $\bar{X}$ is the mean of repeated measurements.; $\sigma = \sqrt{\frac{\sum(X_i - \bar{X})^2}{n-1}}$ — represents the standard deviation used to quantify the dispersion of random errors.

Key Points: Random errors follow a statistical distribution, typically Gaussian or Normal distribution.; They can be minimized by taking a large number of readings and calculating their arithmetic mean.; Unlike systematic errors, random errors cannot be corrected by calibration.; They are inherent to the measurement process and instrumentation sensitivity.

Advantages: Statistical analysis helps in estimating the precision of measurements.; Increasing sample size allows for convergence toward the true value.

Disadvantages: Cannot be eliminated completely.; Requires significant time for repeated measurements to ensure reliability.

Applications: Scientific research and experimental physics.; Quality control in manufacturing where precision is critical.

Additional Info: Gross errors occur due to human negligence, such as misreading an instrument scale or incorrect adjustment.. Systematic errors are due to identifiable causes like calibration defects, loading effects, or environmental factors that shift the mean away from the true value.

Answer: B is correct — Random errors represent unpredictable measurement uncertainties resulting from factors whose origins are unknown or uncontrollable.

Exam Tip: In exams, remember that if an error can be 'calibrated out', it is Systematic; if it varies based on individual reading, it is Random.

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