Mean, Median & Mode Calculator & Guide
Find the mean, median, mode and range of any data set. Learn exactly how each measure of central tendency is calculated, when to use each one, and see fully worked examples.
Understanding Mean, Median & Mode
Mean, median and mode are the three most common “measures of central tendency” — different ways of describing the typical or central value in a set of numbers. Each one tells you something slightly different about your data.
How Each Measure Is Calculated
The formulas behind mean, median, mode and range
Mean (the average)
Add up every value in the data set, then divide by how many values there are. This is what most people mean by “average”.
Median (the middle value)
Arrange the values in ascending order. If there’s an odd number of values, the median is the one in the middle. If there’s an even number, average the two middle values.
Mode (the most frequent value)
Count how many times each value appears. The value that appears most often is the mode. A data set can have one mode, more than one mode, or no mode at all.
Range (the spread)
Although not a measure of central tendency, range is often calculated alongside the others. It shows how spread out the data is.
Quick Facts Checklist
Essential points to remember
Worked Example: Finding Mean, Median & Mode
Here’s exactly how to work through a real data set, step by step, using the numbers: 4, 8, 6, 5, 3, 8, 9.
Calculate the Mean
Add the values: 4 + 8 + 6 + 5 + 3 + 8 + 9 = 43. Divide by the count of values, which is 7. 43 ÷ 7 = 6.14 (to 2 decimal places).
Find the Median
Sort the values in order: 3, 4, 5, 6, 8, 8, 9. With 7 values (odd), the median is the 4th value: 6.
Identify the Mode
Count how often each value appears: 8 appears twice, every other value appears once. The mode is 8.
Calculate the Range
Subtract the lowest value from the highest: 9 − 3 = 6. The range of this data set is 6.
When to Use Each Measure
A side-by-side summary to help you pick the right measure for your data.
| Measure | Best Used For | Sensitive to Outliers? |
|---|---|---|
| Mean | Evenly distributed numerical data. | Yes — heavily affected by outliers. |
| Median | Skewed data, e.g. income, house prices, exam scores. | No — largely unaffected by outliers. |
| Mode | Categorical data, or finding the most common item. | No — based on frequency, not magnitude. |
| Range | Understanding the spread of the data. | Yes — determined entirely by the two extreme values. |
Mean, Median & Mode FAQ
Answers to the most frequently asked questions about calculating mean, median and mode.
The mean is the average of all values, found by adding them together and dividing by how many there are. The median is the middle value when the data is arranged in order. The mode is the value that appears most often in the data set.
When there is an even number of values, arrange the data in order and take the two middle numbers, then find their average by adding them together and dividing by two. That result is the median.
Yes. If two values appear with the same highest frequency, the data set is bimodal and has two modes. If more than two values share the highest frequency, it is multimodal. If every value appears the same number of times, the data set has no mode.
The median is less affected by extreme values, or outliers, than the mean. In data sets with a few very high or very low values, such as household incomes, the median often gives a more realistic picture of the typical value than the mean does.