Mean, median, mode, and range
Also known as: measures of central tendency
Mean, median, mode, and range are the four basic ways to summarize a data set: the mean is the average, the median is the middle value, the mode is the most frequent value, and the range is the difference between the largest and smallest values.
Mean, median, mode, and range are the foundational tools of descriptive statistics — four numbers that summarize a whole data set. The mean is the arithmetic average: add every value and divide by the count. The median is the middle value once the data is sorted. The mode is the value that appears most often. The range measures spread: the maximum minus the minimum.
Take the data set 2, 4, 4, 6, 9. The mean is (2 + 4 + 4 + 6 + 9) ÷ 5 = 5. The median is the third of the five sorted values, 4. The mode is 4, since it appears twice. The range is 9 − 2 = 7. When a data set has an even number of values, the median is the average of the two middle values; a set can also have no mode or several modes.
Choosing between mean and median is where the concept gets interesting. The mean uses every value, so a single outlier can drag it dramatically — one billionaire moving into a small town skyrockets the mean income while barely touching the median. That's why medians are preferred for skewed data like home prices and incomes, and why test questions love asking how adding or removing a value changes each measure.
These statistics appear across many standardized and licensing exams. The GRE tests them heavily in quantitative reasoning, including in weighted-average and mixture problems, and the Series 65 and Series 66 exams cover mean, median, mode, and range as descriptive statistics used to analyze investment returns.
Key takeaways
- Mean = sum of values ÷ number of values; median = middle value of the sorted data.
- Mode is the most frequent value; range = maximum − minimum.
- With an even number of values, the median is the average of the two middle values.
- Outliers pull the mean but barely affect the median, which is why skewed data is summarized with medians.
- The GRE, Series 65, and Series 66 exams all test these descriptive statistics.