How to Calculate Mean, Mode, and Median
This calculator determines the three main measures of central tendency in descriptive statistics: arithmetic mean, median, and mode.
The Arithmetic Mean
The arithmetic mean is the most well-known measure: it is calculated by summing all values and dividing by their count.
Mean = (x1 + x2 + ... + xn) / n
The mean accounts for every value, but is sensitive to extreme values. A salary of 10 million in a group of 10 people drastically raises the mean, even though it does not represent the typical situation.
The Median
The median is the value that divides the ordered set into two equal halves: 50% of the data is below the median and 50% is above.
To calculate it: sort the values from smallest to largest. If n is odd, the median is the value at position (n+1)/2. If n is even, it is the mean of the two central values.
The median is robust against outliers: it is not influenced by extreme values.
The Mode
The mode is the value that appears most frequently. A set can be unimodal (one mode), bimodal (two modes), multimodal, or have no mode if all values appear with the same frequency.
When to Use Which Measure
- Mean: ideal for symmetrically distributed data without outliers (grades, temperatures)
- Median: preferable with skewed data or outliers (salaries, real estate prices)
- Mode: useful for categorical data or identifying the most common value (most sold size, most frequent response)