Key points at a glance
- The mean uses every value; the median follows the ordered positions.
- Distribution and research question determine which measure helps.
- Also report variation, units and usable observations.
Which centre answers your question?
The arithmetic mean divides the sum of observations by their count. The median is the middle value after sorting; with an even number of observations, it lies between the two middle positions. Both describe a centre, but they can answer different questions when data are skewed.
The NIST statistics handbook explains why several measures of location are useful. Consider the scale, distribution shape and meaning of high or low values. The word “average” alone is ambiguous when readers cannot tell which measure you calculated.
An original numerical example
Five invented task times are 10, 12, 13, 15 and 50 minutes. Their mean is 20 minutes and their median is 13 minutes. Both values are correct. The mean fully reflects the long fifth observation, while the median identifies the middle position.
The 50-minute observation is not automatically an error. The task may have been interrupted or genuinely difficult. Check recording and context before choosing a summary. Include the unit and explain why the measures differ.
Report centre and variation together
A single central measure hides differences between observations. Add a suitable measure of spread and, where helpful, a range or visualisation. Choose the combination to fit the data and disciplinary conventions. A median with quartiles may convey more about highly skewed values than a mean with no indication of shape.
State the number of observations actually used. When a variable has missing responses, the initial sample total must not silently describe every calculation. In group comparisons, verify that both groups represent the same kind of measurement.
Round when presenting results rather than rounding intermediate calculations early. The number of decimal places should reflect measurement precision rather than merely look precise.
Phrase the result proportionately
You might write: “The median task time across five observed cases was 13 minutes; one case was much longer at 50 minutes.” That conveys more about distribution than “the average was 13 minutes”, which also hides the chosen measure.
A descriptive statistic alone does not establish a difference in a wider population or explain its cause. If your question concerns those claims, plan suitable further analysis and consider sampling and uncertainty.
Final submission context
Formal details can feel like a separate writing task, but they matter just as much for a printed submission. Anything missing, misplaced or inconsistently formatted in the document will also appear in the bound copy.
Use this guide together with your cover page, table of contents, page numbers, source notes and appendices. Prepare the final PDF for printing and binding only after the complete file has been checked.
Practical check before PDF export
- Do headings, chapter structure and page numbers match?
- Are sources, figures and tables included completely?
- Are required elements such as declarations, appendices or the cover page included where required?
- Did you open and check the final PDF after exporting it?
Checklist
- Check scale and distribution.
- Name the chosen measure.
- Investigate unusual values.
- Report variation, units and sample size.
- Match rounding and claims to data quality.
Common mistakes
- Calling both mean and median simply “the average”.
- Deleting a high value without investigation.
- Claiming a general effect from five descriptive observations.
Print and bind your finished thesis
Once you have checked the content and final PDF, configure the printed copies to match your submission requirements.
Configure printing and bindingRelated content
Explore related guidance on thesis structure, sources, formatting and final submission.
Frequently asked questions
Is the median always better with outliers?
It is less affected by extremes but answers a different question. If a total or arithmetic expectation matters, the mean may remain relevant. Report both when that helps readers.
Do I always need normally distributed data?
Not to calculate a mean or median. Assumptions matter when you plan additional inferential procedures and interpret their results.
How do I find the median for an even number of values?
Sort the observations and average the two middle values. Exclude missing-value codes and other nonobservations appropriately first.