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Mean, Median, Mode, Range Calculator
Calculate the key descriptive metrics of a dataset, including the arithmetic mean, median, mode, and range, with step-by-step calculations.
Enter Dataset
Results
| Mean (Average) | — |
|---|---|
| Median | — |
| Range | — |
| Mode | — |
| Geometric Mean | — |
| Largest | — |
| Smallest | — |
| Sum | — |
| Count | — |
| Sorted Data Set | — |
Understanding Mean, Median, Mode, and Range
These four values are fundamental descriptive statistics used to summarize and analyze numerical datasets. They provide context about the central values and variability of your data.
Mean
The **Mean** (specifically, the arithmetic mean) is what most people refer to as the average. You calculate it by adding up all the numbers in a dataset and then dividing that sum by the count of numbers.
$$\text{Mean} = \frac{\text{Sum of all terms}}{\text{Count of all terms}}$$
Median
The **Median** is the physical middle value when the numbers in the dataset are arranged in ascending or descending order.
- If the count of numbers is **odd**, the median is the single middle value.
- If the count of numbers is **even**, the median is the average of the two middle values.
Mode
The **Mode** is the value that appears most frequently in your dataset.
- A dataset can have a single mode (**unimodal**).
- It can have multiple modes (**bimodal** or **multimodal**) if two or more values share the highest frequency.
- If all numbers appear an equal number of times, the dataset has **no mode**.
Range
The **Range** is the simplest measure of statistical dispersion. It is the difference between the highest value and the lowest value in the dataset.
$$\text{Range} = \text{Maximum value} - \text{Minimum value}$$