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A2: Data Analysis 3 – Error

The most updated lab writing instructional modules are available:

Learning Objectives

This module is designed to assist engineering instructors in strengthening lab instruction materials so that students should be able to:

  1. Define systematic and random error.
  2. Calculate the systematic error (aka bias) in a sample and explain its source.
  3. Calculate the random error (aka uncertainty) in a sample and recommend ways to reduce it.
  4. Differentiate systematic and random error.
  5. Present error in both absolute (as a quantity) and relative (as a percentage) terms.

What is Error?

Error is a difference between an expected value and a measured value and is categorized as either systematic (aka repeatable) or random (not following a pattern). Systematic errors can be attributed to problems in calibration or test configuration that can often be addressed or explained. Random errors are often associated with the precision of instruments used in measurement and can be addressed only by improving precision and test standardization.

Why Does the Technical Audience Value Error Analysis?

Quantifying the error in reported values provides an indication of the precision of the result. This is conveyed commonly by correctly reporting significant figures. For example, a value of 5.3 mm indicates a precision of ± 0.1 mm (± 2%). However, a rigorous error analysis might show that the uncertainty is actually ± 0.7 mm (± 13%), which significantly impacts the confidence I might have in the result. If an error analysis is not provided, your audience will likely take your results at face value, or worse, question your work for lack of rigor.

How is an Error Analysis Performed?

An error analysis can be conducted on either univariate or bivariate data. For univariate data, the analysis is simple:

  1. Calculate the differences of a series of measured values from a single expected value.
  2. Calculate the average of these differences. This is the systematic error, or bias, and it is either greater than or less than the expected value. Its sign is important.
  3. Calculate the standard deviation of these differences. This quantifies the random error, or uncertainty, and it occurs on either side of the average measured value. Two standard deviations capture 95% of the likely error. Three standard deviations capture 99.7% of the likely error.

For bivariate data, the analysis is similar, but rather than comparing to a single expected value, you are comparing data to expected values estimated by a trendline.

This is all better explained with an example. See an example of this here: Error Analysis Example.

What Expectations Does the Technical Audience Have for an Error Analysis?

  • Ensure accuracy of your procedure and results.
  • Report both the bias (or systematic error) and the uncertainty (or random error) in both absolute (with units) and relative (as a percentage) terms.
  • Describe a likely source or sources of the bias.
  • Describe the reasons for the random error.
  • Describe improvements to a testing procedure to reduce error.

 What are Some Common Mistakes Seen in Poorly Written Engineering Lab Reports?

  • Error is represented incorrectly with values presented with excessive and unrealistic levels of precision (e.g. 5.2343 mm).
  • Error analysis is not conducted; results stand alone without any discussion of bias or uncertainty.


  1. Kim, J., Kim, D., (2019) “How engineering students draw conclusions from lab reports and design project reports in junior-level engineering courses,” The Proceedings of 2019 ASEE Annual Conference and Exposition, Tampa, FL, June 2019. Available:
  2. “Argument Papers”, Purdue University, Purdue Online Writing Lab, Argument Papers,
  3. “Student Writing Guide”, University of Minnesota Department of Mechanical Engineering, Available: