Interactive statistics
Distribution laboratory
Paste measurements or counts, inspect a chart and compare models suited to the data type. Or identify the distribution that generated a sample: a compatible model is not a certainty.
Analyze a sample
Enter 5 to 2,000 numbers. Choose the decimal separator before analyzing.
Your data stay in your browser and are not sent to the server.
Results
Histogram and curves
The bars show density, not counts: their total area is 1. Show or hide each curve.
Read bins as a table
| From | To | Count | Density |
|---|
Model comparison
Distance D compares the empirical distribution with each model fitted to the same data. Smaller means only closer among the models shown; it is not a significance test.
| Model | Estimated parameters | D (descriptive) |
|---|
Confidence interval for the mean
Use the sample you just analyzed. The chosen confidence level controls the interval width.
Independent observations and a representative sample are needed. With small samples, an approximately Normal population matters; the laboratory’s model comparison does not establish that assumption. Strongly skewed data can make this interval unreliable.
Analyze integer counts
Enter 5 to 2,000 counts between 0 and 100, separated by commas, semicolons or spaces. Each value should refer to the same interval or number of trials.
Your data stay in your browser and are not sent to the server.
Frequencies and theoretical probabilities
Blue: observed relative frequency. Red: Poisson. Green: Binomial, if the number of trials is known.
| k | Count | Observed | Poisson | Binomial |
|---|
The table stops at the largest observed count; a theoretical distribution may assign probability to larger values too.
Model comparison
D is the maximum distance between observed and fitted discrete cumulative distributions. It is descriptive, not a p-value. Do not compare these numbers with the continuous-model results.
| Model | Estimated parameters | D (descriptive) |
|---|
Which distribution is hidden?
The computer generates a random sample without revealing which of six models produced it. Five produce continuous measurements; Poisson produces integer counts. Inspect the data, choose a hypothesis, then reveal the answer.
Inspect the sample
Show the numeric values
Answer and comparison
| Model | Estimated parameters | D (descriptive) |
|---|
Calculate from summary statistics
If you know only the sample size, mean and standard deviation, calculate an interval without entering every observation. Use a period or comma for decimals, without thousands separators; n from 5 to 2,000.
Independent observations and a representative sample are needed. With small samples, an approximately Normal population matters; the laboratory’s model comparison does not establish that assumption. Strongly skewed data can make this interval unreliable.
Seven worked examples
We begin with an example about mean weight, then explore teaching scenarios showing the effects of σ, sample size, confidence level and an interval that includes zero.