About the Mean / Median / Mode / Range
This calculator finds all four basic summary measures at once: mean, median, mode, and range. Each describes the data differently, and comparing them is the quickest way to detect skew, outliers, or a dataset that a single average would misrepresent.
The formula
Mean = Σx / n; Median = middle value; Range = max − minThe mean is the arithmetic average, the median the middle value once sorted, the mode the most frequent value, and the range the gap between largest and smallest.
How to use this calculator
- 1Enter your Value 1. The field starts at
5, which you can overwrite. - 2Enter your Value 2. The field starts at
3, which you can overwrite. - 3Enter your Value 3. The field starts at
8, which you can overwrite. - 4Enter your Value 4. The field starts at
3, which you can overwrite. - 5Enter your Value 5. The field starts at
7, which you can overwrite. - 6Enter your Value 6. The field starts at
3, which you can overwrite. - 7Enter your Value 7. The field starts at
9, which you can overwrite. - 8Enter your Value 8. The field starts at
2, which you can overwrite. - 9Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Value 1 | 5 |
| Value 2 | 3 |
| Value 3 | 8 |
| Value 4 | 3 |
| Value 5 | 7 |
| Value 6 | 3 |
| Value 7 | 9 |
| Value 8 | 2 |
Result
Mean: 5.0000
Median: 4
Mode: 3
Range: 7
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
The relationship between mean and median reveals the shape of the distribution. In symmetric data they nearly coincide. When the mean sits well above the median, a few large values are pulling it up — right skew, which is what income data always shows. When it sits below, the tail runs the other way.
Each measure has a domain where it is the right choice. Use the mean for symmetric numerical data, the median for skewed data or when outliers are present, and the mode for categorical data where averaging is meaningless — you cannot compute the mean favourite colour, but you can identify the most common one.
Things worth knowing
- A dataset can have no mode, one mode, or several if values tie for most frequent.
- With an even number of values, the median is the average of the two middle ones.
- The range uses only two values, so a single outlier defines it. The interquartile range is more robust.
- A large gap between mean and median is a reliable signal of skew.
- Sort your data before finding the median. Skipping that step is the most common error.
Frequently asked questions
What is the difference between mean, median, and mode?+
The mean is the total divided by the count, the median is the middle value when sorted, and the mode is the most frequent value. They agree in symmetric data and diverge when it is skewed.
Which average should I use?+
The mean for symmetric numerical data, the median when outliers or skew are present, and the mode for categorical data. Income is reported as a median precisely because a few very high earners distort the mean.
Can a dataset have more than one mode?+
Yes. If two or more values tie for highest frequency the data is bimodal or multimodal, which often indicates two distinct subgroups mixed together. If every value appears once, there is no mode.
What does the range tell me?+
The total spread between the smallest and largest values. It is easy to compute but fragile, since one extreme value determines it entirely. The interquartile range is a more stable measure of spread.