Mean, Median, Mode Calculator
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About Mean, Median, Mode Calculator
Measures of Central Tendency
Central tendency describes where data clusters. The three primary measures are mean (arithmetic average), median (middle value), and mode (most frequent value). Each reveals different aspects of your data and is useful in different situations. Together with measures of spread (range, standard deviation), they provide a complete picture of any dataset's distribution.
Definitions and Formulas
Mean: Sum of all values divided by count. Sensitive to outliers. Median: Middle value when data is sorted. For even counts, average the two middle values. Resistant to outliers. Mode: Most frequently occurring value. Can have multiple modes (bimodal, multimodal) or no mode. Range: Maximum minus minimum. Simple measure of spread.
When to Use Each Measure
Use mean for symmetric data without outliers (test scores, heights). Use median for skewed data or data with outliers (income, house prices). Use mode for categorical data or finding the most common value (shoe sizes, favorite colors). Reports often include all three to provide complete context.
Frequently Asked Questions
Why is median better than mean for income data?
Income data is right-skewed (a few very high earners pull the mean up). Median represents the typical person better because it is not affected by extreme values at either end.
Can a dataset have no mode?
Yes. If every value appears only once, there is no mode. If all values appear equally often, some definitions say there is no mode while others say all values are modes.
What does it mean when mean equals median?
When mean equals median, the distribution is symmetric (data spreads evenly around the center). In a perfectly normal (bell-curve) distribution, mean = median = mode.
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