The Mean Median Mode Range Calculator finds all four classic summary statistics from a single pasted data set: the mean, the median, the mode, and the range. Paste values separated by commas, spaces or line breaks, and the calculator sorts the list, computes each measure, and shows the arithmetic for every step.
These four numbers together give a fast, complete first look at any list of values: where the center sits (three different ways) and how wide the data spreads from smallest to largest.
Calculate the mean
The mean, or arithmetic average, is the sum of all values divided by the count.
mean = Σx / nWorked example: find the mean of 4, 8, 15, 16, 23, 42.
1. Add the values. 4 + 8 + 15 + 16 + 23 + 42 = 108.
2. Divide by the count. 108 ÷ 6 = 18.
Calculate the median
The median is the middle value once the data is sorted, found differently depending on whether the count is odd or even. Odd count: the value at position (n + 1) / 2. Even count: the average of the two central values.
Worked example: the same set, 4, 8, 15, 16, 23, 42 (n = 6, even, already sorted).
The two central values are 15 and 16, so the median is (15 + 16) / 2 = 15.5.
Calculate the mode
The mode is the value (or values) that appear most frequently. A set can have no mode (every value unique), one mode (unimodal), or several modes (multimodal). For the example set, 4, 8, 15, 16, 23, 42, each value appears exactly once, so this set has no mode.
Worked example with a repeated value: 3, 5, 5, 7, 9.
The value 5 appears twice, more than any other value, so the mode is 5.
Calculate the range
The range is the simplest measure of spread: the maximum value minus the minimum value.
range = max − minWorked example: the original set, 4, 8, 15, 16, 23, 42.
Range = 42 − 4 = 38.
The range uses only the two most extreme values and ignores everything in between, which makes it fast to calculate but sensitive to a single unusually high or low observation.
Put all four measures together
| Measure | Value for 4, 8, 15, 16, 23, 42 | What it shows |
|---|---|---|
| Mean | 18 | Arithmetic average, pulled by every value |
| Median | 15.5 | Middle value, resistant to outliers |
| Mode | none | Most frequent value |
| Range | 38 | Spread from smallest to largest |
The mean (18) and median (15.5) sit fairly close together here, a rough sign that this particular data set is not heavily skewed by a large outlier. When mean and median diverge substantially in a real data set, that gap is itself useful information about the shape of the distribution.
Know the limits of the range as a spread measure
Because range depends only on the two most extreme values, two data sets can have identical ranges while looking completely different everywhere else. A set with one high outlier and everything else clustered tightly can show the same range as a set where values are spread evenly across the whole span.
For a fuller picture of spread, variance and standard deviation account for every value, not just the two extremes.
Work through a second data set
Find all four measures for 2, 4, 4, 6, 9. 1. Mean. 2 + 4 + 4 + 6 + 9 = 25, and 25 ÷ 5 = 5. 2. Median. With 5 sorted values, the middle position holds 4.
3. Mode. The value 4 appears twice, more than any other, so the mode is 4.
4. Range. 9 − 2 = 7.
This set shows the mean (5) sitting slightly above both the median and mode (4), a small hint of mild right skew from the higher value 9 pulling the average upward.
Frequently asked questions
What are mean, median, mode and range?
Mean is the arithmetic average (sum divided by count). Median is the middle value of sorted data. Mode is the most frequent value. Range is the maximum minus the minimum.
How do you calculate the range of a data set?
Subtract the minimum value from the maximum value: range = max − min. For 4, 8, 15, 16, 23, 42, the range is 42 − 4 = 38.
Can a data set have more than one mode?
Yes. A set with two equally frequent most-common values is bimodal, and a set with three or more is multimodal. A set where every value is unique has no mode at all.
Why might mean and median be different for the same data?
They differ when the data is skewed, meaning a few unusually high or low values pull the mean away from the middle while the median, based only on position, stays closer to the bulk of the data.
Is range a good measure of spread?
It is a quick, simple measure, but it only uses the two extreme values and ignores everything in between, so it can be misleading if either extreme is an unusual outlier rather than representative of the data's typical spread.
How is range different from interquartile range?
Range uses the full minimum and maximum. Interquartile range (IQR) uses only the middle 50 percent of the data (Q3 minus Q1), which makes IQR more resistant to distortion from a single extreme value.
What if my data set has no mode?
That simply means no value repeats; the mean, median and range calculations are unaffected, and the mode is reported as none.
Summary
The four classic summary statistics, mean, median, mode and range, give a fast overview of a data set: for 4, 8, 15, 16, 23, 42, the mean is 18, the median is 15.5, there is no mode since every value is unique, and the range is 38.
Comparing mean and median offers a quick check for skew, while the range, though simple, only reflects the two extreme values rather than the full spread of the data.