Mean Median Mode Calculator
Calculate mean, median, and mode for your datasets with detailed explanations
📊 Mean (Average) Calculator
Calculate the Average
Mean Calculator: Calculate the arithmetic mean (average) of your dataset by adding all values and dividing by the count.
Mathematical Formulas
Where: x̄ = mean, Σx = sum of all values, n = number of values
Where: f = frequency, x = class midpoint, Σf = total frequency
Best Used When: Data is normally distributed without extreme outliers, and you want to include all values in your analysis.
Choose Data Type
Enter Your Data
📚 Understanding the Mean
What is the Mean?
The mean, also called the arithmetic average, is the most common measure of central tendency. It represents the "typical" value in a dataset by balancing all values equally. Every number in your dataset contributes to the final result.
When to Use the Mean
Best for: Normally distributed data, continuous variables, and when you want all values to influence the result equally. Examples include test scores, heights, temperatures, and sales figures.
Avoid when: Data has extreme outliers, is heavily skewed, or contains categorical data. In these cases, the median might be more representative.
Real-World Applications
The mean is used everywhere: calculating GPA, determining average income, measuring performance metrics, analyzing survey results, and quality control in manufacturing. It's the foundation for many advanced statistical calculations.
Pro Tip: Always check for outliers before using the mean. A single extreme value can significantly skew the average, making it less representative of your typical data point.
📈 Median Calculator
🎯 Find the Middle Value
Median Calculator: Find the middle value in your dataset when arranged in order from smallest to largest.
📐 Mathematical Formulas
Where: n = number of values, x = sorted data values
Where: L = lower boundary of median class, n = total frequency, F = cumulative frequency before median class, f = frequency of median class, h = class width
Best Used When: Data has outliers, is skewed, or when you want a value that represents the "typical" middle point.
Choose Data Type
Enter Your Data
📚 Understanding the Median
What is the Median?
The median is the middle value in a dataset when arranged in ascending order. It divides your data into two equal halves - 50% of values are below the median, and 50% are above it. Unlike the mean, the median is not affected by extreme values.
When to Use the Median
Best for: Skewed data, datasets with outliers, income distributions, real estate prices, and ordinal data. The median gives you a better sense of the "typical" value when extreme values are present.
Examples: Median household income (not affected by billionaires), median home prices (not skewed by luxury properties), median test scores in a class with some very low or high scores.
Median vs Mean
If the median is much different from the mean, your data is likely skewed. When median < mean, the data is right-skewed (pulled by high values). When median > mean, the data is left-skewed (pulled by low values).
Real-World Applications
Government agencies use median income for policy decisions, real estate markets report median home prices, medical research uses median survival times, and businesses analyze median customer spending to understand typical behavior.
Pro Tip: The median is your go-to measure when dealing with income, prices, or any data where a few extreme values might mislead you about what's "typical" in your dataset.
📋 Mode Calculator
🎯 Find the Most Common Value
Mode Calculator: Identify the value(s) that appear most frequently in your dataset.
📐 Mathematical Formulas
The value(s) that appear most often in the dataset
Where: L = lower boundary of modal class, f₁ = frequency of modal class, f₀ = frequency of class before modal class, f₂ = frequency of class after modal class, h = class width
Types: No mode (all values appear once), Unimodal (one mode), Bimodal (two modes), Multimodal (multiple modes)
Best Used When: Working with categorical data, finding the most popular choice, or identifying the most common occurrence.
Choose Data Type
Enter Your Data
📚 Understanding the Mode
What is the Mode?
The mode is the value that appears most frequently in a dataset. Unlike mean and median, the mode can be used with any type of data - numerical, categorical, or ordinal. A dataset can have no mode, one mode, or multiple modes.
Types of Modal Distributions
No Mode: All values appear with the same frequency (often just once each).
Unimodal: One value appears most frequently.
Bimodal: Two values tie for the highest frequency.
Multimodal: Three or more values tie for the highest frequency.
When to Use the Mode
Best for: Categorical data (colors, brands, preferences), finding the most popular choice, quality control (most common defect), and understanding customer behavior patterns.
Examples: Most popular product size, most common error type, most frequent customer complaint, most chosen survey response.
Real-World Applications
Retailers use mode to determine which products to stock more of, manufacturers identify the most common defects, pollsters find the most popular candidate, and researchers identify the most common responses in surveys.
Pro Tip: The mode is the only measure of central tendency that can be used with categorical data. It's also useful for identifying patterns and the most "typical" occurrence in your dataset.