Mean, Median, Mode & Range Calculator
Find the average (mean), middle value (median), most frequent value (mode), and range for any data set.
Mean Median Mode — interactive calculator, computed instantly in your browser.
Descriptive Statistics: Measures of Central Tendency & Data Dispersion
Mean vs. Median in Symmetrical vs. Skewed Distributions
Key Difference: In skewed datasets with extreme outliers (like real estate prices or household income), the Median provides a more representative measure of typical center than the Mean.
In descriptive statistics, measures of central tendency summarize an entire dataset with a single representative score. The three primary metrics are the arithmetic mean, the median, and the mode, complemented by the statistical range to measure dispersion.
1. Core Statistical Definitions & Formulas
- Mean ($\bar{x}$): The sum of all observations divided by the total number of observations:
\bar{x} = \frac{\sum_{i=1}^n x_i}{n}
- Median: The numerical value separating the higher half from the lower half of sorted data. For odd $n$, it is at position $\frac{n+1}{2}$. For even $n$, it is the mean of positions $\frac{n}{2}$ and $\frac{n}{2}+1$.
- Mode: The value that occurs with highest frequency. Datasets can be unimodal, bimodal, multimodal, or have no mode.
- Range: The difference between the highest and lowest values ($R = x_{\max} - x_{\min}$).
🔗 Statistical Data Analysis Tools
Measures of central tendency summarize large datasets into representative single metrics. For deeper statistical dispersion and variance modeling, access our complete ➗ Math & Statistics Hub.
Measure sample variance, standard deviation, or scientific magnitude with the specialized tools below.
Frequently Asked Questions (Mean Median Mode)
A few billionaires or luxury mansions would skew the Mean artificially high, misrepresenting ordinary earners. The Median represents the true 50th percentile where half the population earns more and half earns less.
Yes. If two values tie for the highest frequency, the dataset is bimodal. If three or more tie, it is multimodal. If every number appears exactly once, there is no mode.