Mean, median, mode: which to report in your paper

TL;DR: This post answers a specific question that trips up many student researchers: when to report the mean, median, or mode in a research paper, and why choosing the wrong one can misrepresent your findings. It is written for high school students who have collected data and are now writing up their results. After reading, you will be able to select the correct measure of central tendency for your dataset and justify that choice in your methods or results section. If your research is complete and ready for peer review, the Princeton Journal of Pre-Collegiate Research publishes original student work across all academic disciplines.

Introduction

The mean, median, and mode are all measures of central tendency, but they do not all tell the same story. Reporting the mean when your data is heavily skewed, for example, can produce a summary statistic that does not represent a single actual data point in your dataset. This is not a minor stylistic choice. Peer reviewers at academic journals specifically assess whether the statistical reporting in a results section matches the characteristics of the data. Choosing the wrong measure of central tendency is one of the most common reasons student papers receive revision requests or desk rejections at the methods and results review stage. This post explains exactly when to use mean, median, or mode in your paper, and how to justify that decision clearly.

Mean, median, mode: which to report in your paper?

Report the mean when your data is continuous, normally distributed, and free of significant outliers. Report the median when your data is skewed, contains outliers, or is measured on an ordinal scale. Report the mode when your data is categorical or when you need to identify the most frequently occurring value. In most quantitative student research papers, the median is underused and the mean is overused.

Each measure describes the centre of a dataset differently, and the right choice depends on three things: the type of data you collected, the shape of its distribution, and the presence of outliers.

The mean is the arithmetic average. You add all values and divide by the number of observations. It is the appropriate measure when your data is continuous (such as height, temperature, or test scores) and when the distribution is roughly symmetrical. The mean uses every data point in its calculation, which makes it sensitive to extreme values. A single outlier can pull the mean far from where most of your data sits.

The median is the middle value when all observations are ranked in order. It is resistant to outliers because it depends only on rank position, not on the actual values at the extremes. The median is the correct choice when your distribution is skewed. For example, if you are reporting household income in a community sample, a small number of very high earners will inflate the mean significantly. The median gives a more accurate picture of the typical household. Ordinal data, such as Likert scale survey responses, should also be reported with the median rather than the mean, because the intervals between scale points are not guaranteed to be equal.

The mode is the value that appears most frequently. It is the only appropriate measure of central tendency for nominal or categorical data. If your study recorded participants' preferred learning style (visual, auditory, or kinaesthetic), you cannot calculate a mean or median. The mode tells you which category was most common. The mode can also be useful for continuous data when you want to identify clustering, but it is rarely the primary summary statistic in a quantitative results section.

In practice, many student papers benefit from reporting more than one measure. If your data is skewed, reporting both the median and the mean, and noting the difference between them, demonstrates to reviewers that you understand your distribution. The American Psychological Association's Publication Manual (7th edition) recommends reporting measures of central tendency alongside measures of variability, such as standard deviation or interquartile range, so that readers can assess the spread of your data as well as its centre.

Before selecting your measure, examine your data visually. A histogram or box plot will reveal skewness and outliers far more clearly than summary statistics alone. If your distribution is approximately bell-shaped, the mean is appropriate. If it has a long tail in either direction, use the median. If your variable is categorical, use the mode.

What happens if you report the wrong measure?

Reporting the wrong measure of central tendency does not simply produce an inaccurate number. It produces a misleading interpretation of your findings, and reviewers are trained to identify this.

The most common error in student papers is reporting the mean for skewed data. Consider a hypothetical study measuring the number of hours per week high school students spend on extracurricular activities. If most students report between two and five hours, but a small group of competitive athletes report twenty or more hours, the mean might be eight hours. That figure does not describe a typical student in the sample. The median, which might be four hours, is the accurate summary. A reviewer reading a results section that reports a mean of eight hours without acknowledging the skewness of the distribution will flag this immediately.

A second consequence is that the wrong measure can lead to incorrect conclusions in the discussion section. If a student paper concludes that the average student spends eight hours per week on extracurriculars and then draws policy or behavioural inferences from that figure, the entire argument rests on a misrepresentation of the data. This is not a formatting problem. It is a validity problem, and it affects the credibility of the research itself.

The fix is straightforward: check the shape of your distribution before selecting a summary statistic, and state your reasoning in the methods section. A sentence such as, "Because the distribution of scores was positively skewed (skewness = 1.8), the median was used as the primary measure of central tendency," demonstrates statistical literacy and satisfies peer review standards.

For further guidance on structuring your results and methods sections, the post on how to edit your own research paper before submission covers the specific checks that matter most before you submit.

What are the most common mistakes students make when reporting central tendency?

The four most common errors are: reporting the mean for skewed data without acknowledging the skew, applying the mean to ordinal variables such as Likert scales, omitting measures of variability alongside the chosen measure of central tendency, and failing to justify the choice of statistic in the methods section. Each of these errors is identifiable in peer review and each has a specific fix.

Using the mean for Likert scale data is widespread in student survey research. A five-point scale from "strongly disagree" to "strongly agree" is ordinal: the distance between points one and two is not necessarily the same as the distance between points four and five. Calculating a mean of 3.4 implies a precision that the scale does not support. The median, or a frequency distribution showing how many respondents selected each option, is more appropriate. Researchers in psychology and education frequently report both the median and the frequency distribution for ordinal data.

Omitting variability is the second major error. A mean or median reported alone tells the reader where the centre of your data is, but not how spread out the data is around that centre. Two datasets can have identical means and completely different distributions. Standard deviation accompanies the mean; interquartile range accompanies the median. Both should appear in your results section.

Failing to justify the choice in the methods section leaves reviewers to infer your reasoning. State explicitly which measure you used and why. This is a one-sentence addition that demonstrates methodological awareness and significantly strengthens your paper.

Confusing descriptive and inferential statistics is a related error. The mean, median, and mode are descriptive statistics. They describe your sample. They do not, on their own, support causal claims or generalisations to a broader population. Student papers sometimes present a difference in means between two groups as evidence of an effect without conducting an appropriate inferential test. Descriptive statistics set the stage; inferential statistics carry the argument.

How to decide which measure to report, step by step

1. Identify your variable type. Is the variable nominal (categories with no order, such as eye colour), ordinal (ranked categories, such as survey ratings), or continuous (measured on a numerical scale, such as temperature or time)? Nominal data requires the mode. Ordinal data requires the median. Continuous data may use the mean or median depending on distribution.

2. Examine the distribution visually. Plot a histogram or box plot of your data before calculating any summary statistics. Look for skewness (a long tail to the left or right) and for outliers (values far from the bulk of the data). Most statistical software, including R, Python, and SPSS, produces these plots in seconds.

3. Check for outliers. If outliers are present and cannot be removed on principled grounds, report the median. If you do report the mean, note the outliers explicitly and consider reporting both measures so readers can assess the impact.

4. Select the appropriate measure. Symmetrical continuous data: use the mean. Skewed continuous data or ordinal data: use the median. Categorical data: use the mode.

5. Pair the measure with a variability statistic. Mean: report standard deviation. Median: report interquartile range. Mode: report frequency counts or percentages.

6. State your choice in the methods section. Write one sentence explaining which measure you used and why. Reference the distribution characteristics you observed.

7. Review the submission guidelines for your target journal to confirm any specific reporting requirements. The submission guidelines at princeton-jpcr.org/submit specify formatting and reporting expectations for papers submitted to PJPCR.

If you are working in the social sciences, psychology, or a related field, the APA format guide for high school research papers covers the specific conventions for reporting statistics in APA style, which is the standard for most behavioural and social science submissions.

PJPCR publishes original quantitative and qualitative research across all academic disciplines. If your data analysis is complete and your paper is ready for peer review, review the submission guidelines at princeton-jpcr.org/submit.

Frequently asked questions about mean, median, and mode in research papers

What is a measure of central tendency in research?

A measure of central tendency is a single value that summarises the centre of a dataset. The three main measures are the mean (arithmetic average), the median (middle value in a ranked dataset), and the mode (most frequently occurring value). Each measure is appropriate for different data types and distributions, and choosing correctly is a fundamental part of quantitative research reporting.

Researchers use these measures to describe samples before conducting inferential tests. They appear in the results section of a paper and are typically accompanied by a measure of variability, such as standard deviation or interquartile range, to give readers a complete picture of the data.

How long does it take to get a research paper peer reviewed?

Peer review timelines vary by journal. At PJPCR, the standard review and publication timeline is 2 to 3 months from submission to a final decision. A fast-track option is available for students who need a quicker turnaround. Understanding the peer review process at PJPCR can help you plan your submission timeline effectively.

The review process involves an initial screening for scope and quality, assignment to qualified peer reviewers, a structured review period, and a decision that may include a request for revisions. Submitting a statistically sound paper, including correctly reported measures of central tendency, reduces the likelihood of a revision request on methodological grounds.

Do I need a statistics course to publish a research paper in high school?

No. Many publishable high school research papers use straightforward descriptive statistics, including mean, median, and mode, without advanced statistical methods. What matters is that the statistics you use are appropriate for your data and correctly interpreted. Reviewers assess whether your analysis matches your research question, not whether you used the most complex available method.

Qualitative research papers, which analyse text, interviews, or observations rather than numerical data, do not require statistical analysis at all. PJPCR accepts both quantitative and qualitative research. Browse published issues to see the range of methodological approaches that have been accepted.

What makes a high school research paper statistically publishable?

A statistically publishable paper demonstrates that the analysis method matches the data type, that summary statistics are paired with appropriate measures of variability, and that the conclusions drawn are supported by the analysis conducted. Reviewers look for internal consistency: the methods section should describe the same analysis that appears in the results section, and the discussion should not overstate what the statistics actually show.

Common reasons for revision requests include reporting the mean for skewed or ordinal data, omitting standard deviation or interquartile range, and drawing causal conclusions from descriptive statistics alone. Addressing these issues before submission significantly strengthens a paper's chances of acceptance.

What kinds of research does PJPCR publish?

PJPCR publishes original, peer-reviewed research by pre-collegiate students across the sciences, social sciences, humanities, and interdisciplinary fields. Both quantitative and qualitative papers are accepted. Research does not need to involve laboratory work or advanced statistical modelling to be considered. The journal is selective and does not guarantee acceptance, but submission and peer review are free, and a publication fee applies for accepted papers.

Students whose work involves survey data, observational studies, literature-based analysis, or experimental design are all encouraged to review the submission guidelines to confirm their work falls within scope. The social sciences section welcomes research that applies statistical methods including correctly chosen measures of central tendency to original datasets.

Conclusion

Selecting the correct measure of central tendency is not a minor formatting decision. It determines whether your results section accurately represents your data. The core principle is straightforward: use the mean for symmetrical continuous data, the median for skewed or ordinal data, and the mode for categorical data. Always pair your chosen measure with an appropriate measure of variability, and always state your reasoning in the methods section. These three practices address the most common statistical reporting errors that appear in student papers at the peer review stage.

If your research is complete, your analysis is sound, and your paper is ready for peer review, submit it to PJPCR at princeton-jpcr.org/submit.