Data Visualization
Central Limit Theorem Demonstrator
See the Central Limit Theorem in action: draw samples from a non-normal source distribution (uniform, exponential, Poisson, or Bernoulli), plot the histogram of sample means, and overlay the predicted Normal curve N(μ, σ²/n). Compare empirical vs theoretical mean and standard error, and watch convergence tighten as the sample size grows.
Quick start
Call this tool from your code in three languages.
curl -X POST 'https://api.elysiatools.com/en/api/tools/central-limit-theorem-demonstrator' \
-H 'Content-Type: application/json' \
-d '{"distribution":"exponential","sampleSize":30,"reps":5000,"bins":40,"seed":42,"precision":3}'API reference
Send a POST request with your inputs as JSON. File parameters require a separate upload first.
Endpoint
POST https://api.elysiatools.com/en/api/tools/central-limit-theorem-demonstratorParameters
| Name | Type | Required | Description |
|---|---|---|---|
| distribution | select | No | — |
| sampleSize | number | Yes | Draws per sample mean. Larger n → narrower, more normal sampling distribution. |
| reps | number | Yes | How many sample means to generate (histogram resolution). |
| bins | number | Yes | — |
| seed | number | No | Same seed → identical results (reproducible demos). |
MCP integration
Add this tool to your Model Context Protocol server so AI agents can list and call it.
Server configuration
Add this block to your MCP client configuration:
{
"mcpServers": {
"elysiatools-central-limit-theorem-demonstrator": {
"name": "central-limit-theorem-demonstrator",
"description": "See the Central Limit Theorem in action: draw samples from a non-normal source distribution (uniform, exponential, Poisson, or Bernoulli), plot the histogram of sample means, and overlay the predicted Normal curve N(μ, σ²/n). Compare empirical vs theoretical mean and standard error, and watch convergence tighten as the sample size grows.",
"baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=central-limit-theorem-demonstrator",
"command": "",
"args": [],
"env": {},
"isActive": true,
"type": "sse"
}
}
}List available tools
After connecting to the SSE endpoint, list the exposed tools:
{
"jsonrpc": "2.0",
"id": 1,
"method": "tools/list"
}Call this tool
Invoke the tool by its id, passing arguments built from its parameters:
{
"jsonrpc": "2.0",
"id": 2,
"method": "tools/call",
"params": {
"name": "central-limit-theorem-demonstrator",
"arguments": {
"distribution": "exponential",
"sampleSize": 30,
"reps": 5000,
"bins": 40,
"seed": 42,
"precision": 3
}
}
}