Mean, Median, Mode, Range Calculator
Paste any list of numbers and get the mean, median, mode, range, geometric mean, sum and more — plus a labeled bar chart of your values.
What is Mean, Median, Mode, and Range?
Mean, median, mode and range are the four workhorse summaries of a data set. Mean and median describe the center — a typical value. Mode describes the most common value. Range describes the spread from smallest to largest. Together they give a quick fingerprint of a data set before you reach for more advanced tools like standard deviation.
The harmonic mean is the reciprocal of the average of reciprocals, H = n / Σ(1/xᵢ) — the right average for rates and ratios (like average speed over equal distances), and it's only defined when every value is strictly positive.
The midrange is simply (max + min) / 2 — the exact midpoint between the smallest and largest value. It's quick to compute but, like range, very sensitive to outliers.
Mean, median, mode and range explained, measure by measure
Each of the five measures below gets a plain-English definition, its formula (with every symbol spelled out), a small diagram of what it's actually measuring, and a worked example — all in one card, so you never have to jump between sections to piece it together.
Mean (arithmetic average)
The mean is the balance point of the data: add everything up and divide by how many values you have. It uses every number, which makes it precise but also sensitive — a single huge outlier can drag it a long way from what most values look like.
Median (middle value)
Sort the data from small to large; the median is the value sitting in the middle. With an even count you average the two middle values. Because it ignores how extreme the outer values are, the median is the summary of choice for skewed data like income or house prices.
Mode (most frequent value)
The mode is whichever value shows up most often. A data set can have one mode, several (bimodal / multimodal) if there is a tie, or none at all when every value is unique. It's the only summary here that also works on non-numeric data like colors or product brands.
Range (spread from min to max)
Range is the simplest measure of how spread out the data is: subtract the smallest value from the largest. It's a single number that captures the total width of the data — but because it only looks at the two endpoints, a single outlier can inflate it dramatically.
Geometric mean
Instead of adding values and dividing, the geometric mean multiplies them and takes the Nth root. It's the natural average for growth rates, ratios, and percentages — anything where the underlying process is multiplicative. Only defined for strictly positive numbers.
Common mistakes
- Forgetting to sort before finding the median. The middle position of the original list is not the median.
- Reporting only one mode. When two or more values tie for the top frequency, all of them are modes.
- Confusing "range" with "the range of values". Statistical range is a single number (max − min), not the list of values in between.
- Averaging categorical data. Use mode, not mean, for things like brand names or colors.
- Assuming mean = typical. With skewed data, the median is usually the more honest "typical" value.
Features of this calculator
- Nine summary stats at once — mean, median, mode, range, geometric mean, largest, smallest, sum and count
- Multimodal aware — lists every value tied for the top frequency, or says outright when there is no mode
- Labeled bar chart of your values in entry order with hover tooltips showing the exact number
- Show/hide step-by-step working — sort, sum, mean, median, mode and range in order
- Handles negative numbers, decimals and duplicates; strips currency symbols and thousand separators automatically
- Copy the full result summary in one click, or send the same dataset to Standard Deviation, Weighted Mean or the full Statistics tool
Frequently asked questions
+What's the difference between mean and median?
Mean is the arithmetic average; median is the middle value after sorting. Mean is pulled by outliers, median is not.
+Can a data set have more than one mode?
Yes — a data set is bimodal with two modes, and multimodal with more. If every value is unique, there is no mode at all.
+When should I use median instead of mean?
Whenever the data is skewed or has outliers — income, home prices, response times.
+Does mode work on non-numeric data?
Yes. Mode is the most frequent category, so it works on colors, brands, or any labeled values. Mean, median and range do not.
+What if my data set is empty?
None of these statistics are defined for an empty set. The calculator will ask you to enter at least one value.