Reporting Mean or Median or Mode

Averages Can Be Deceiving

What You Need to Know About Averages

Most people assume that a simple statistic like a mean or a median tells the whole story. It doesn’t. Averages can clarify—but they can also mislead—depending on which one you use and how your data are distributed.

Understanding the mean, median, and mode helps you interpret test scores, salaries, evaluations, and research findings with greater accuracy.

CALCULATOR: I have included a basic calculator at the bottom of this page.

The Mean, Median, and Mode

Mean

The mean is the arithmetic average of a set of numbers. You calculate it by adding all the values and dividing by the number of values.
Example: For the data 1, 2, 3, 4, 5, the sum is 15 and the mean is 3.
The mean uses every value in the dataset, which makes it useful but also sensitive to extreme scores.

Median

The median is the middle value when numbers are arranged from lowest to highest. Half the values fall above it and half fall below it.
Example: In the set 1, 2, 3, 4, 5, the median is 3.
The median is especially helpful when data are skewed or contain outliers.

Mode

The mode is the most frequently occurring value in a dataset.
Example: In the set 1, 2, 2, 4, 5, the mode is 2.
The mode identifies the most common score, rating, or salary.

When Are the Mean, Median, and Mode the Same?

In large samples that follow a normal (bell‑shaped) distribution, the mean, median, and mode fall in the same place. But many real‑world datasets are not normal. They contain outliers or clusters of scores at the high or low end. In those cases, the mean can give a misleading impression of what is typical.

Unfortunately, even people who understand statistics often report the mean without considering whether their data are skewed.

Learn more in Applied Statistics

Examples

Salary Example

Salaries are often skewed because a few people earn far more than everyone else. Suppose nine employees earn between $30,000 and $60,000, and one earns $300,000. In this small fictitious sample, the mean salary is $67,000 (SD = 82.58), but the median is only $38,500. The range is $270,000.
This illustrates how a single high salary can distort the mean. In real companies, where some executives earn over a million dollars, the gap between mean and median can be even more dramatic.
These differences matter when discussing raises, comparing job offers, voting on budgets, or evaluating compensation in nonprofit organizations.

Teacher Evaluations

Student ratings are typically skewed toward the high end. When most ratings fall in the 4s on a 1–5 scale, the median often describes teacher performance better than the mean. Reporting only the mean can make scores appear higher than they really are.

Real Estate Prices

Housing markets often include a few very expensive homes that pull the mean upward. The median home price usually gives a more accurate picture of what buyers can expect in a typical neighborhood.

Research Reports

Sometimes researchers report an average age that doesn’t match the standard deviation. For example, a mean age of 19 with a standard deviation of 5 in a university sample suggests something is off. A standard deviation that large would imply many participants were around 14 or 24, which is unlikely for a typical college sample. This is another example of how averages can be misinterpreted or misreported.

Why This Matters in Education

Counselors, teachers, and parents often see test results. Scores may be distorted by a few very high or very low performers. It is best to consider the mean, median, and percentile ranks together. For more detail, see Applied Statistics: Concepts for Counselors.

If you need a refresher on terms like range or standard deviation, here is a link to a free glossary.

Abbreviations

M = Mean
Mdn = Median
Mo = Mode
Max = Largest value
Min = Smallest value
N = Number of scores
R = Range (Max – Min)
SD = Standard Deviation
Link: https://statistics.suttong.com/2022/01/variance-and-standard-deviation.html

Averages can be deceiving.

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Post Author

Geoffrey W. Sutton, Professor Emeritus of Psychology at Evangel University, holds a master’s degree in counseling and a PhD in psychology from the University of Missouri-Columbia. His postdoctoral work encompassed education and supervision in forensic and neuropsychology and psychopharmacology. As a licensed psychologist, he conducted clinical and neuropsychological evaluations and provided psychotherapy for patients in various settings, including schools, hospitals, and private offices. During his tenure as a professor, Dr. Sutton taught courses on psychotherapy, assessment, and research. He has authored over one hundred publications, including books, book chapters, and articles in peer-reviewed psychology journals. 

His website is https://suttong.com 

You can find Dr. Sutton's books on   AMAZON    and  GOOGLE. 

Many publications are free to download at ResearchGate   and Academia  

Find chapters and essays on Substack. [ @GeoffreyWSutton ]

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