Average Calculator
Find mean, median, and average of a dataset.
About this topic
Mean The mathematical average of a dataset.
The mean, commonly called the average, is found by adding every value in a dataset and dividing the sum by the number of values. For example, the mean of 2, 4, 6, 8, and 10 is 30 ÷ 5 = 6. The mean uses every observation, which makes it useful for summarising data, but unusually high or low values can pull it away from what is typical.
Key formulas & rules
- •Formula: Sum / Count
- •Uses all data points
- •Sensitive to extreme outliers
- •Often called the 'average'
- •Used for symmetric distributions
Examples
| Input | Output | Note |
|---|---|---|
| [2, 4, 6, 8, 10] | 6 | Evenly spaced |
| [1, 2, 3, 4, 100] | 22 | Pulled by outlier |
| [5, 5, 5, 5] | 5 | All same |
| [10, 20, 30] | 20 | Simple average |
Real-world uses
Median The exact middle value of a sorted dataset.
The median is the middle value after all observations are arranged from smallest to largest. With an odd number of values, it is the single middle number; with an even number, it is the average of the two middle numbers. For example, the median of 1, 2, 3, 4, and 100 is 3. Because extreme values have little effect on the median, it is often useful for describing income, house prices, or other datasets with outliers.
Key formulas & rules
- •Sort data low to high first
- •Odd count: exact middle
- •Even count: average two middles
- •Robust against outliers
- •50th percentile
Examples
| Input | Output | Note |
|---|---|---|
| [1, 2, 3, 4, 100] | 3 | Unaffected by 100 |
| [1, 2, 3, 4] | 2.5 | Average of 2 and 3 |
| [10, 20, 30] | 20 | Middle value |
| [5, 5, 5, 5] | 5 | All same |
Real-world uses
Mode The most frequently occurring value.
The mode is the value that appears most often in a dataset. A dataset may have one mode, more than one mode, or no mode if every value occurs equally often. For example, in 2, 4, 4, 4, and 7, the mode is 4; in 1, 2, and 3, there is no mode. Unlike the mean and median, the mode can also describe categories, such as the most common shoe size or most popular product choice.
Key formulas & rules
- •Most frequent value
- •Can be no mode
- •Can be multiple modes
- •Used for categorical data
- •Not affected by outliers
Examples
| Input | Output | Note |
|---|---|---|
| [2, 4, 4, 4, 7] | 4 | Unimodal |
| [1, 2, 3] | None | All unique |
| [1, 1, 2, 2, 3] | 1, 2 | Bimodal |
| [5, 5, 5, 5] | 5 | All same |
Real-world uses
Range The difference between the highest and lowest values.
The range describes the overall spread of a dataset by measuring the distance between its largest and smallest values. Subtract the minimum value from the maximum value. For example, in 3, 7, and 15, the range is 15 − 3 = 12. It is easy to calculate and gives a quick sense of variation, but it depends only on the two extreme values, so a single outlier can make the range appear unusually large.
Key formulas & rules
- •Formula: Max - Min
- •Quick to calculate
- •Sensitive to outliers
- •Measures total spread
- •Only uses two data points
Examples
| Input | Output | Note |
|---|---|---|
| [3, 7, 15] | 12 | 15 - 3 |
| [1, 2, 3, 4, 100] | 99 | 100 - 1 |
| [5, 5, 5] | 0 | No spread |
| [-10, 0, 10] | 20 | 10 - (-10) |
Real-world uses
Modes & formulas
Mean (Average)
This is the standard average. It is highly sensitive to extreme outliers — one massive number will pull the mean significantly higher.
Median
The median is robust against outliers. For 1, 2, 3, 4, 100, the median is 3, whereas the mean would be 22.
Mode
A dataset can have no mode (if all numbers are unique), one mode (unimodal), or multiple modes (bimodal, trimodal).
Range
The range gives a quick idea of how widely the data varies, but it is highly sensitive to extreme outliers.