Questions: Error Analysis and Statistics in Analytical Chemistry

Question 1

A chemist measures a standard solution of known concentration 5 times and gets: 10.02, 9.98, 10.01, 10.03, 9.99 mmol/L. The known value is 10.05 mmol/L. Which statement best characterizes these results?

• A. High precision and high accuracy
• B. High precision but low accuracy
• C. Low precision but high accuracy
• D. Low precision and low accuracy

Answer: (B)

The replicate measurements are tightly clustered (standard deviation ≈ 0.02 mmol/L), indicating high precision. However, the average (~10.01) is consistently below the known value of 10.05, suggesting a systematic error — perhaps a calibration offset. High precision with systematic bias is the classic signature of a systematic (determinate) error.

Question 2

The standard deviation of a set of measurements and the standard error of the mean both measure the same uncertainty, just expressed differently.

• T. True
• F. False

Answer: False

Standard deviation (s) quantifies the spread of individual replicate measurements around their mean. Standard error of the mean (SEM = s/√n) quantifies how precisely the sample mean estimates the true population mean. As you take more replicates, SEM decreases (your estimate of the mean improves), but s does not necessarily change (the inherent variability of individual measurements remains).

Question 3

Distinguish between random (indeterminate) error and systematic (determinate) error in an analytical measurement, and explain which type can be reduced by averaging more replicates.

Model answer: Random error causes scatter around the true value in an unpredictable direction each measurement; it can be reduced by averaging more replicates. Systematic error shifts all measurements in the same direction (bias) and cannot be corrected by replication — it requires identifying and eliminating the source (e.g., recalibrating the instrument).

Averaging works on random error because positive and negative deviations cancel over many measurements. Systematic error, being directional and consistent, cannot cancel — every replicate carries the same bias. This is why calibration, blanks, and reference standards are essential: they catch systematic errors that replication alone would miss.