Uncertainty & Error Analysis

Uncertainty

The range of values within which the true value of a measurement is believed to lie; expresses confidence in the measurement.

Error

Deviation of a measured value from the true or expected value.

Accuracy

Closeness of a measurement to the standard or known true value.

Precision

Closeness of two or more measurements to each other.

Random Error

Unpredictable fluctuations during data collection that cause different readings under the same conditions; arises from uncontrolled variables and affects precision.

Systematic Error

A consistent bias in measurements due to instrument flaws, calibration errors, or flaws in the experimental design; affects accuracy.

Parallax Error

Reading error caused by viewing the measurement scale from an angle rather than straight on.

Percent Error

A measure of accuracy expressed as a percent: (|x − xT| / xT) × 100%.

Percent Difference

A measure of how far apart two measurements are in percentage:

|x1 − x2| / [(x1 + x2)/2] × 100%.

Mean

The average of a set of numbers, calculated as the sum divided by the count.

Variance

The average of the squared deviations from the mean: Σ(x − x̄)² / N.

Standard Deviation

The square root of the variance; a measure of how spread out the values are around the mean.

Absolute Uncertainty

The uncertainty expressed with the same unit as the quantity, e.g., 25.00 ± 0.05 Ω.

Relative Uncertainty

The absolute uncertainty divided by the measured value, typically expressed as a percentage.

Least Count

The smallest value that can be read from a measuring device; the instrument's resolution.