Statistics Calculator Online Free Tool
Statistics Calculator
Statistical Analysis
Enter your dataset to calculate comprehensive statistics automatically
Enter Your Data
Separate values with commas, spaces, or line breaks
Statistical Measures
BASIC MEASURES
CENTRAL TENDENCY
DISPERSION
QUARTILES
DISTRIBUTION SHAPE
This statistics calculator computes the key descriptive statistics for a data set: mean, median, mode, range, variance, standard deviation, and more. Enter your numbers separated by commas and get a full summary instantly. Understanding these measures helps you describe, compare, and interpret data in any context from school assignments to business analysis.
Key Descriptive Statistics
Descriptive statistics summarize the main features of a data set. Measures of central tendency (mean, median, mode) describe where the data clusters. Measures of spread (range, variance, standard deviation) describe how dispersed the data is around the center.
| Statistic | What It Measures | When Most Useful |
|---|---|---|
| Mean | Average value | Symmetric distributions without outliers |
| Median | Middle value | Skewed distributions or when outliers exist |
| Mode | Most frequent value | Categorical data or finding peaks |
| Range | Spread (max - min) | Quick overview of spread |
| Std Deviation | Average distance from mean | Quantifying variability |
| Variance | Std deviation squared | Used in further calculations |
Sample vs Population Statistics
When your data represents a sample (a subset of a larger group), use the sample formulas (dividing by n-1 for variance). When your data is the complete population, use population formulas (dividing by n). The n-1 denominator in sample variance is Bessel's correction, which provides an unbiased estimate of the population variance.
Population Variance: σ² = Σ(xi - μ)² / N Sample Variance: s² = Σ(xi - x̄)² / (n-1) Standard Deviation: σ or s = √(variance)
Frequently Asked Questions
When should I use mean vs median?⌄
Use the median when data is skewed or has outliers. Income data is a classic example: a few very high earners pull the mean up significantly, while the median better represents the typical person. Use the mean when data is roughly symmetric with no extreme outliers, as it uses all values and is more sensitive to the full distribution.
What does standard deviation tell you?⌄
Standard deviation tells you how spread out data points are from the mean. A small standard deviation means data clusters tightly around the mean. A large one means data is spread widely. In a normal distribution, about 68% of values fall within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3.
What is a percentile?⌄
A percentile tells you what percentage of values fall below a given value. The 25th percentile (Q1) means 25% of values are below it. The 50th percentile is the median. The 75th percentile (Q3) means 75% of values are below it. Test scores are often reported as percentiles to show performance relative to others.
What is the interquartile range (IQR)?⌄
IQR = Q3 - Q1. It measures the spread of the middle 50% of data, making it resistant to outliers. Values more than 1.5 × IQR below Q1 or above Q3 are considered potential outliers. IQR is used in box plots and is a better measure of spread than range for skewed distributions.