Q-Q Plot Generator
Check normality (and more) in seconds. Paste your data, pick the distribution, and see the Q-Q plot with a reference line.
1. Paste your data
Use comma, space or new line separated values. Example: 12, 10.5, 9, 13, 14.2 ...
2. Choose distribution & options
Normal is the most common for normality tests.
3. Q-Q plot
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4. Sample vs Theoretical Quantiles
| # | Ordered sample | Theoretical quantile | Difference |
|---|
How this Q-Q plot generator works
This tool sorts your sample into order statistics \(x_{(1)}, \dots, x_{(n)}\) and pairs each one with a corresponding theoretical quantile from the chosen distribution. For the normal distribution, we first estimate the sample mean \(\hat{\mu}\) and standard deviation \(\hat{\sigma}\), then transform standard normal quantiles to match.
Formula for the hyperbolic plotting positions
We use the popular rule:
p_i = (i - 0.5) / n, i = 1, 2, ..., n
Then the theoretical quantile is \(q_i = F^{-1}(p_i)\), where \(F^{-1}\) is the inverse CDF of the selected distribution:
- Normal: \(q_i = \hat{\mu} + \hat{\sigma} \Phi^{-1}(p_i)\)
- Uniform(0,1): \(q_i = p_i\)
- Exponential(1): \(q_i = -\ln(1 - p_i)\)
Interpretation tips
- Points ~ straight line → good fit.
- Concave up/down → skewness.
- Ends deviating → heavy or light tails than expected.