Mean, Median, Mode, Range Calculator
Calculate central tendency measures with real-time visualization
Mean, median, mode, and range are the four basic measures taught in every statistics course. Each answers a different question about your data. This calculator computes all four simultaneously from any list of numbers, with step-by-step explanations that make it useful for checking homework or understanding how the measures are derived.
Definitions and Formulas
Each measure captures a different aspect of a data set. Together they give you a compact description of the distribution.
Mean = Sum of all values / Count of values Median = Middle value when sorted (or average of two middles) Mode = Value(s) that appear most frequently Range = Maximum value - Minimum value
For {2, 3, 3, 5, 7}: Mean = 4, Median = 3, Mode = 3, Range = 5.
When Each Measure Is Most Useful
No single measure tells the whole story. Skewed data sets can have very different means and medians. Bimodal data (two peaks) has two modes. Using all four together gives a much richer picture of your data than any one alone.
| Measure | Best Used When |
|---|---|
| Mean | Data is symmetric, no extreme outliers |
| Median | Data is skewed or has outliers (e.g., salaries, home prices) |
| Mode | Finding most common value; categorical data |
| Range | Quick assessment of total spread |
Frequently Asked Questions
Can a data set have more than one mode?⌄
Yes. A data set is bimodal if two values tie for the highest frequency, and multimodal if more than two do. If all values appear the same number of times (each exactly once), the data set has no mode.
How do I find the median of an even number of values?⌄
When there is an even number of values, the median is the average of the two middle values when sorted. For {2, 4, 6, 8}, the two middle values are 4 and 6, so median = (4+6)/2 = 5.
Can the mean be affected by outliers?⌄
Yes, significantly. Adding one extreme value to a data set can shift the mean dramatically while barely affecting the median. This is why average income and average home price statistics often use the median: a few billionaires or mansions would distort the mean and make it unrepresentative of the typical person.
What is the difference between range and interquartile range?⌄
Range = max - min, which considers all values including extreme outliers. Interquartile range (IQR) = Q3 - Q1, which only considers the middle 50% of data. IQR is more robust to outliers and better represents typical variation in the data.