Math
Mean, Median & Mode Calculator
Calculate mean, median, mode, range, standard deviation, and more from any set of numbers. Accepts comma, space, or newline-separated input.
Enter a list of numbers above to see all statistics.
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Core Formulas
Mean
x̄ = Σxᵢ ÷ n
Median
Middle of sorted values
Mode
Most frequent value(s)
Range
Max − Min
Pop. Std Dev
σ = √(Σ(xᵢ − x̄)² ÷ n)
Sample Std Dev
s = √(Σ(xᵢ − x̄)² ÷ (n−1))
Which Measure of Central Tendency to Use
Mean — best for symmetric distributions with no extreme outliers (e.g. test scores, measurement errors).
Median — best for skewed data or when outliers are present (e.g. household income, house prices, response times).
Mode — most useful for categorical data or when identifying the most common value matters (e.g. most popular shoe size, most common error code).
Frequently asked questions
What is the difference between mean, median, and mode?
The mean (average) is the sum of all values divided by the count. The median is the middle value when the dataset is sorted — half of values fall below it, half above. The mode is the value that appears most frequently. Each measure describes the 'centre' of the data differently.
When should you use the median instead of the mean?
Use the median when the data is skewed or contains outliers. For example, income data typically uses the median because a few very high earners inflate the mean and make it unrepresentative of the typical person. The mean is best when data is roughly symmetric and normally distributed.
What if a dataset has no mode?
If all values appear exactly once, there is no mode (or the dataset is considered multimodal with every value). If two values tie for most frequent, the dataset is bimodal. This calculator reports all modes when more than one value ties for highest frequency.
What is the difference between population and sample standard deviation?
Population standard deviation (σ) divides by n and is used when you have data for the entire population. Sample standard deviation (s) divides by n−1 (Bessel's correction) and is used when your data is a sample from a larger population. Use sample std dev in most real-world analysis.
How is the range calculated?
Range = Maximum value − Minimum value. It is the simplest measure of data spread, showing the full extent of variation. It is sensitive to outliers — a single extreme value significantly changes the range.