How It Works
The mean (arithmetic average) is the most common measure of central tendency — calculated by summing all values and dividing by count.
Mean = Σx / n | Median = middle value of sorted data | Mode = most frequent value | Range = max − min
- The median is the middle value of a sorted dataset — more robust to outliers than the mean.
- The mode is the most frequently occurring value — useful for categorical or discrete data.
- The range measures spread: the distance from the smallest to the largest value.
Worked Example
Dataset: 4, 7, 2, 7, 9 (n = 5).
Sum
4 + 7 + 2 + 7 + 9 = 29
The dataset has a mean of 5.8 but a median of 7 — the two low values (2 and 4) pull the mean below the middle.
Mean, Median, Mode, and Range Explained
Four summary statistics at once
This tool computes the four basic summary statistics for a dataset at once: the mean, the median, the mode, and the range. The first three describe the "center" of your data from different angles, while the range describes how far it spreads from smallest to largest.
Seeing all four together is genuinely useful, because no single measure tells the whole story. A class’s average score, its middle score, its most common score, and the gap between best and worst each answer a different question about the same numbers.
How each measure is defined
The mean is the arithmetic average: add every value and divide by how many there are. The median is the middle value once the data is sorted — and for an even count, it is the average of the two middle values. The mode is whichever value appears most often.
The range rounds out the picture as a measure of spread, equal to the maximum minus the minimum. Center plus spread is the minimum you need to describe a dataset meaningfully.
When to use mean versus median
The mean uses every value, which makes it powerful but also sensitive: a few extreme numbers can pull it far from the typical value. The median ignores how extreme the outliers are and just reports the middle, so it resists distortion.
That is why incomes and house prices are usually reported as medians — a handful of very high values would inflate the mean and overstate what is "typical." For roughly symmetric data with no outliers, the mean and median land close together.
Reading skew from the numbers
Comparing the mean and median reveals the shape of the data. When the mean sits above the median, the distribution is skewed to the right, dragged up by high values; when it sits below, it is skewed left. When all three measures coincide, the data is symmetric.
The mode adds a third reference point. In a clean bell shape, mean, median, and mode all stack on top of one another, so any gap between them is a quick visual cue that the data leans one way.
A worked example
For the dataset 4, 7, 2, 7, 9, the sum is 29, so the mean is 29 ÷ 5 = 5.8. Sorting gives 2, 4, 7, 7, 9, so the median is the middle value, 7, and the mode is also 7 because it appears twice. The range is 9 − 2 = 7.
Notice the mean (5.8) sits below the median (7): the two low values, 2 and 4, pull the average down. That gap is a small example of left skew, and it shows why reporting only the mean could understate the typical score here.
No mode, ties, and what the range misses
If every value is unique there is no mode, and the calculator shows 0 to signal that. When two or more values tie for most frequent, only the first is reported, so multimodal data is summarized loosely. The range, meanwhile, reflects just the two extreme points and ignores everything in between.
The tool handles up to eight values, which suits homework and quick checks rather than large datasets. As always, set the count to match exactly how many values you entered so the statistics are based on the right numbers.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.