Mean, median, and mode are the three primary measures of central tendency in statistics. Each describes the center of a data set from a different angle and is computed differently.
Finding the median with an even count: Sort the data, then average the two middle values. For {2, 4, 6, 8} (n=4), the median = (4 + 6) / 2 = 5. There is no single middle value; you always average the pair.
These measures form the foundation of descriptive statistics. More advanced analysis such as finding how two variables relate to each other uses the Correlation Coefficient Calculator, which measures the strength of a linear relationship between two data sets.
Range is the simplest measure of spread. While mean, median, and mode describe the center of data, range describes how spread out the values are. The range answers: how wide is the full span of this data set?
| Measure | Formula | What It Tells You | Limitation |
|---|---|---|---|
| Range | max - min | Full span of data | Sensitive to outliers |
| Variance | avg squared deviations | Average spread from mean | Hard to interpret (squared units) |
| Std Deviation | sqrt(variance) | Typical distance from mean | Affected by outliers |
| IQR (not here) | Q3 - Q1 | Middle 50% spread | Robust to outliers |
For the default data set {1, 2, 3, 4, 4, 7, 7, 7, 9}, the range = 9 - 1 = 8. This tells you the data spans 8 units, but it does not tell you where most values cluster. Standard deviation (2.73 for this set) tells you the typical distance from the mean (4.89), which is more informative. When you need to estimate values between known data points in a set, see the Interpolation Calculator.
All four measures are used together to describe a data set. The table below summarizes their definitions, formulas, and best use cases.
| Measure | Definition | Example ({1,2,3,4,4,7,7,7,9}) | Best Used When |
|---|---|---|---|
| Mean | Sum of values divided by count | 44 / 9 = 4.89 | Symmetric data, no outliers |
| Median | Middle value of sorted data | 5th value = 4 | Skewed data or outliers present |
| Mode | Most frequently occurring value | 7 (appears 3 times) | Categorical or discrete data |
| Range | Maximum minus minimum | 9 - 1 = 8 | Quick spread check |
In a perfectly normal (bell curve) distribution, mean = median = mode. When these three values diverge, the data is skewed or contains outliers. A mean significantly higher than the median indicates right-skewed data with large outliers. Once you understand the summary statistics for a data set, tools like the Linear Interpolation Calculator help estimate values between known data points in that same set.
Data set: 4, 7, 2, 9, 4, 1, 7, 7, 3. Find the mean, median, mode, and range.