The four measures, side by side
These statistics answer different questions about the same list of numbers. The mean adds everything up and divides by how many values there are, so every number pulls on it. The median ignores magnitude and looks only at position: sort the values and take the one in the middle (or the average of the two middle values when the count is even). The mode is simply the value that appears most often, and the range measures the total spread from smallest to largest.
Because they are built differently, they can disagree, and that disagreement is informative. When the mean sits well above the median, a few large values are stretching the average upward; when it sits below, small values are dragging it down.
Which average should you trust?
No single measure is "correct" — the right one depends on the shape of the data and the decision you are making.
- Use the mean for roughly symmetric data with no extreme outliers, such as exam scores in a typical class.
- Prefer the median for skewed data like incomes or house prices, where a handful of very large values would distort the mean.
- Reach for the mode when the data is categorical or when the most common value matters most, such as the most-sold shoe size.
- Read the range alongside any average — two datasets can share a mean yet differ wildly in spread.
Reading the chart and avoiding mistakes
The bar chart plots your values in the order you entered them, which makes outliers and clusters easy to spot at a glance. A single very tall or very short bar is exactly the kind of point that separates the mean from the median.
A few common slips: forgetting that a dataset can have no mode (when every value is unique) or several modes (when values tie for the top frequency); confusing the median position with the median value; and treating the range as a measure of typical spread when it only reflects the two extreme points.
Formula
mean = Σx/n; median = middle of sorted data; mode = most frequent value; range = max − minFrequently asked questions
- What if there is no mode?
- If every value appears the same number of times, the dataset has no mode. If several values tie for the highest frequency, they are all modes.