What action reduces random error in XRF measurements?

• A. Repetition of measurement
• B. Calibration
• C. Increasing detector voltage only
• D. Reducing sample mass

Answer: (A)

Random error in XRF comes from unpredictable fluctuations in counting and detector response. Repeating measurements and averaging them reduces this scatter because random fluctuations tend to cancel out, so the result converges toward the true value. With Poisson counting statistics, the uncertainty grows with the square root of the counts, so increasing the total counts (via multiple measurements or longer counting) lowers the relative error roughly as 1 over the square root of the number of measurements. Calibration addresses systematic bias, not random jitter, so it doesn’t reduce random error. Increasing detector voltage or reducing sample mass can alter signal and noise in ways that don’t reliably lower random error.