Simulate Random Data
Other Distribution Types
Student's t: Degrees of Freedom
How to read these plots
- Histogram: Ever wondered what your data really looks like? A histogram groups your numbers into ranges and draws bars showing how many values land in each one — instantly revealing whether your data is balanced, skewed, has outliers, or even multiple peaks.
- Q-Q Plot: Compares your data to a normal distribution. Points close to a straight line suggest your data is approximately normal. Curves away from the line indicate patterns in the data, such as S-shaped curves for heavy or light tails, upward or downward curves at the ends for skewness, or systematic deviations that suggest outliers or other non-normal behavior.
- Normal Distribution: A symmetric, bell-shaped distribution where most values cluster near the mean and fewer values appear at the extremes.
Why this happens:
Many real-world outcomes are influenced by numerous small, independent factors—such as genetics, environment, or minor measurement variations—that push values slightly higher or lower. These effects tend to balance out, so most outcomes end up near the average while extreme values are rare. This is why normal distributions often appear in practice, a phenomenon explained by the Central Limit Theorem.
Examples:
Human height, exam scores, and measurement errors often follow this pattern.
Randomness connection:
Normal distributions frequently arise from random variation, but randomness alone does not always produce a bell curve. When many small random influences add together and balance out, a normal distribution emerges; otherwise, data may follow other distributions, like income (skewed) or rare-event counts (Poisson).
Note:
Not all measurements are normally distributed. Some real-world data—such as income, waiting times, or extreme-event counts—can be skewed or follow different statistical distributions.
Set parameters and click Run Simulation to see results.
Set parameters and click Compute CI.