Mean, Median and Mode Explained
Mean, median and mode are the three measures of central tendency — each tells you something different about a set of numbers. Understanding when to use each one is essential for correct data analysis.
Mean (Average) = Sum of all values / Count of values
Example: (10 + 20 + 30 + 40 + 50) / 5 = 30
Median = Middle value when sorted in order
Example: 10, 20, [30], 40, 50 → Median = 30
Even count: (20 + 30) / 2 = 25
Mode = Most frequently occurring value
Example: 10, 20, 20, 30, 40 → Mode = 20
Range = Maximum value - Minimum value
Example: 50 - 10 = 40
Weighted Average = Sum of (Value × Weight) / Sum of Weights
When to Use Mean vs Median
Use the mean when your data has no extreme outliers — it works well for normally distributed data like test scores or temperatures. Use the median when your data has outliers or is skewed — for example median household income is more meaningful than mean income because a few billionaires would dramatically skew the mean upward making it unrepresentative of typical people.
When Is Mode Most Useful?
Mode is most useful for categorical data or when you need to know the most common value. For example a shoe store would use mode to know which shoe size to stock most of. Mode is the only measure of central tendency that can be used with non-numerical data.
Frequently Asked Questions
How do I calculate the average of a set of numbers? +
Add all the numbers together and divide by how many numbers there are. Example: to find the average of 10, 20, 30, 40, 50 — add them: 10+20+30+40+50 = 150, then divide by 5 numbers: 150/5 = 30. This is the arithmetic mean or average. Use our calculator above by simply entering your numbers separated by commas.
What is the difference between mean and average? +
In everyday use mean and average refer to the same thing — the arithmetic mean. However in statistics there are multiple types of averages: arithmetic mean (most common), geometric mean (used for growth rates), harmonic mean (used for rates and ratios) and weighted mean (where some values count more than others). When people say "average" they almost always mean arithmetic mean.
How do I find the median of an even set of numbers? +
Sort the numbers in order. For an even count of numbers there is no single middle value. Take the two middle numbers and find their average. Example: 10, 20, 30, 40 — the two middle numbers are 20 and 30. Median = (20+30)/2 = 25. Our calculator handles both even and odd counts automatically.
What if there is no mode in a data set? +
If every number appears exactly once then there is no mode — the data set has no single most frequent value. If two numbers appear with equal frequency the data set is bimodal with two modes. If three or more numbers share the highest frequency it is multimodal. Our calculator identifies all modes when multiple values share the highest frequency.
When should I use weighted average instead of regular average? +
Use weighted average when different values have different levels of importance or contribution. Common examples: calculating GPA where credit hours are the weights, course final grade where exams count more than homework, investment portfolio returns where each asset has a different percentage allocation, or employee performance scores where different criteria have different importance levels.