Precision increases with the square root of

• A. The number of measurements squared
• B. The measurement time
• C. The number of measurements
• D. The square root of the number of measurements

Answer: (D)

Averaging independent measurements reduces random noise, and the precision of the mean improves as the square root of how many measurements you take. If each measurement has random variation, the standard error of the mean is the single-measurement spread divided by sqrt(N). So the more measurements, the more precise your result, with the improvement scaling with the square root of the number of measurements. For example, increasing from 1 to 4 measurements improves precision by a factor of 2, and increasing to 9 measurements improves it by a factor of 3. The measurement time per reading doesn’t by itself determine precision; the key is increasing the number of independent measurements to average. The other options would imply linear or quadratic gains or tie precision directly to time rather than count.