# Standard deviation

- Human page: https://happytails.ai/en/calculators/standard-deviation/
- Markdown: https://happytails.ai/en/calculators/standard-deviation.md
- Structured JSON: https://happytails.ai/agents/en/calculators/standard-deviation/index.json
- Visibility: public

## Tool capabilities

| Property | Value |
| --- | --- |
| Tool ID | `standard-deviation` |
| Category | calculators |
| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |
| Browser execution | Automatic updates after valid input or file selection. |
| Browser processing | Browser; see tool notes for network behavior. |
| HTTP API | /api/v1/tools/standard-deviation/run |
| Browser-agent interface | run_current_tool |

### Inputs and settings

Text input: Numbers.

Example or placeholder shown in the interface (not a validated fixture):

```text
2, 4, 6
```

Separate numbers with commas, spaces or new lines. Choose sample or population in the settings. Results update as you type. Up to 1,000,000 characters.

No additional settings are declared for this tool.

### HTTP contract

API calls process supplied data on the server. The website origin is `https://happytails.ai`. Server API hosting is not connected on the public website yet. Use your local server origin to test these requests.

```http
POST https://happytails.ai/api/v1/tools/standard-deviation/run
Content-Type: application/json
```

[Detailed operation reference](https://happytails.ai/en/api/tools/standard-deviation.md) · [Shared API guide](https://happytails.ai/en/api.md)

#### Limits

| Limit | Value |
| --- | --- |
| request_bytes | 8388608 |
| input_characters | 1000000 |
| files_bytes | 5242880 |
| max_files | 0 |
| timeout_seconds | 12 |

#### Complete input schema

```json
{
  "type": "object",
  "additionalProperties": false,
  "properties": {
    "input": {
      "type": "string",
      "maxLength": 1000000,
      "default": "",
      "description": "Plain text input. File tools use files instead unless otherwise documented."
    },
    "options": {
      "type": "object",
      "additionalProperties": false,
      "properties": {}
    }
  }
}
```

#### Complete output schema

```json
{
  "type": "object",
  "required": [
    "tool",
    "result"
  ],
  "properties": {
    "tool": {
      "type": "string"
    },
    "result": {
      "type": "object",
      "required": [
        "text",
        "files"
      ],
      "properties": {
        "text": {
          "type": [
            "string",
            "null"
          ]
        },
        "data": {
          "description": "Parsed JSON when the textual result is JSON."
        },
        "name": {
          "type": "string"
        },
        "mime": {
          "type": "string"
        },
        "files": {
          "type": "array",
          "items": {
            "type": "object",
            "required": [
              "name",
              "mime",
              "bytes",
              "base64"
            ],
            "properties": {
              "name": {
                "type": "string"
              },
              "mime": {
                "type": "string"
              },
              "bytes": {
                "type": "integer"
              },
              "base64": {
                "type": "string",
                "contentEncoding": "base64"
              }
            }
          }
        }
      }
    }
  }
}
```

#### Error and retry handling

Failures return a non-200 status and `error.code` plus `error.message`. Correct invalid input before retrying; retry server-busy responses with bounded backoff. Returned files contain Base64 data, not persistent download URLs. Decode and inspect the output before treating conversion as successful. See the shared API guide for the complete status and timeout rules.

### Browser-agent workflow

1. Open the human page in a browser that supports WebMCP.
2. Discover the interface exposed by that page; use its actual schema.
3. Select files on the page first when the tool requires files.
4. Call `run_current_tool` with valid input and settings.
5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.

Calls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.

### Planning specification

Population versus sample formulas, data count and rounding; input examples.

This describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.

### Complete machine-readable capability record

```json
{
  "id": "standard-deviation",
  "category": "calculators",
  "built": true,
  "requirements": "Population versus sample formulas, data count and rounding; input examples.",
  "implementation": {
    "fields": [],
    "experience": {
      "automatic": true,
      "single": false,
      "label": "Numbers",
      "placeholder": "2, 4, 6",
      "help": "Separate numbers with commas, spaces or new lines. Choose sample or population in the settings. Results update as you type. Up to 1,000,000 characters.",
      "action": null
    },
    "mode": "automatic",
    "interactive": false
  },
  "execution": "POST /api/v1/tools/standard-deviation/run",
  "api": {
    "id": "standard-deviation",
    "name": "Standard deviation",
    "category": "calculators",
    "description": "Calculate the mean and standard deviation of a set of numbers.",
    "notes": "",
    "human_path": "/en/calculators/standard-deviation/",
    "method": "POST",
    "endpoint": "/api/v1/tools/standard-deviation/run",
    "schema_url": "/api/v1/tools/standard-deviation",
    "input_schema": {
      "type": "object",
      "additionalProperties": false,
      "properties": {
        "input": {
          "type": "string",
          "maxLength": 1000000,
          "default": "",
          "description": "Plain text input. File tools use files instead unless otherwise documented."
        },
        "options": {
          "type": "object",
          "additionalProperties": false,
          "properties": {}
        }
      }
    },
    "output_schema": {
      "type": "object",
      "required": [
        "tool",
        "result"
      ],
      "properties": {
        "tool": {
          "type": "string"
        },
        "result": {
          "type": "object",
          "required": [
            "text",
            "files"
          ],
          "properties": {
            "text": {
              "type": [
                "string",
                "null"
              ]
            },
            "data": {
              "description": "Parsed JSON when the textual result is JSON."
            },
            "name": {
              "type": "string"
            },
            "mime": {
              "type": "string"
            },
            "files": {
              "type": "array",
              "items": {
                "type": "object",
                "required": [
                  "name",
                  "mime",
                  "bytes",
                  "base64"
                ],
                "properties": {
                  "name": {
                    "type": "string"
                  },
                  "mime": {
                    "type": "string"
                  },
                  "bytes": {
                    "type": "integer"
                  },
                  "base64": {
                    "type": "string",
                    "contentEncoding": "base64"
                  }
                }
              }
            }
          }
        }
      }
    },
    "processing": "Server; same transformation code as browser tools",
    "limits": {
      "request_bytes": 8388608,
      "input_characters": 1000000,
      "files_bytes": 5242880,
      "max_files": 0,
      "timeout_seconds": 12
    }
  },
  "agent_processing": "Server; same transformation code as browser tools",
  "browser_agent": {
    "supported": true,
    "name": "run_current_tool",
    "discovery": "WebMCP on the human page in a supporting browser",
    "verification": "See audit/API-AUDIT.md; availability is not verification"
  }
}
```

## Page guide

Calculate the mean and standard deviation of a set of numbers.

## How to use Standard deviation

1. Enter your text in the input field.
2. The result updates as you type. Adjust the available settings if needed.
3. Review the result, then use Copy result or a download link when available.

## What to expect

Calculate the mean and standard deviation of a set of numbers. The output shows population and sample standard deviations separately. A sample standard deviation needs at least two values.

## Useful next steps

- [Average](https://happytails.ai/en/calculators/average/): Find the mean, median, sum, minimum, and maximum of a list of numbers. ([Markdown](https://happytails.ai/en/calculators/average.md))

- [Lcm](https://happytails.ai/en/calculators/lcm/): Find the least common multiple of whole numbers. ([Markdown](https://happytails.ai/en/calculators/lcm.md))

- [Rounding](https://happytails.ai/en/calculators/rounding/): Round a number to a chosen number of decimal places. ([Markdown](https://happytails.ai/en/calculators/rounding.md))

- [Scientific notation](https://happytails.ai/en/calculators/scientific-notation/): Write a number in scientific notation. ([Markdown](https://happytails.ai/en/calculators/scientific-notation.md))