Question

Which error can be minimized by increasing the number of observations?

• A. Systematic error
• B. Random error
• C. Method error
• D. Personal error

Hint:

- Random errors affect precision and can be minimized by averaging multiple runs. - Systematic errors affect accuracy and cannot be fixed by averaging; they require instrument recalibration or method modification.

Answer 1

The Correct Option is B

Concept: Experimental measurements are subject to errors, which can be broadly categorized into determinate (systematic) errors and indeterminate (random) errors.

Step 1: Analyze Systematic (Determinate) Errors Systematic errors possess a definite cause, have a reproducible magnitude, and shift all measurements in a single direction (either consistently higher or consistently lower than the true value). Examples include poorly calibrated balances, contaminated reagents (method errors), or persistent visual parallax errors by the analyst (personal errors). Because these errors are unidirectional and constant, taking multiple measurements will not reduce their impact; the average value will simply be precise but inaccurate.

Step 2: Analyze Random (Indeterminate) Errors Random errors arise from small, uncontrollable, and unpredictable fluctuations in experimental parameters (such as minor temperature variations, voltage noise in an instrument, or mechanical vibrations). These errors follow a standard Gaussian normal distribution, meaning they are equally likely to cause positive or negative deviations around the mean value. By significantly increasing the total number of observations (\(n\)), individual positive and negative random variations tend to cancel each other out during averaging. According to statistical principles, the standard error of the mean (\(\text{SEM}\)) decreases inversely with the square root of the sample size: \[ \text{SEM} = \frac{s}{\sqrt{n}} \] As \(n \rightarrow \infty\), the calculated sample mean approaches the true population mean, effectively minimizing the impact of random errors.