variance.json

{
    "id": "variance",
    "summary": "Variance",
    "description": "Computes the sample variance of an array of numbers by calculating the square of the standard deviation (see ``sd()``). It is defined to be the expectation of the squared deviation of a random variable from its expected value. Basically, it measures how far the numbers in the array are spread out from their average value.\n\nAn array without non-`null` elements resolves always with `null`.",
    "categories": [
        "math > statistics",
        "reducer"
    ],
    "parameters": [
        {
            "name": "data",
            "description": "An array of numbers.",
            "schema": {
                "type": "array",
                "items": {
                    "type": [
                        "number",
                        "null"
                    ]
                }
            }
        },
        {
            "name": "ignore_nodata",
            "description": "Indicates whether no-data values are ignored or not. Ignores them by default. Setting this flag to `false` considers no-data values so that `null` is returned if any value is such a value.",
            "schema": {
                "type": "boolean"
            },
            "default": true,
            "optional": true
        }
    ],
    "returns": {
        "description": "The computed sample variance.",
        "schema": {
            "type": [
                "number",
                "null"
            ]
        }
    },
    "examples": [
        {
            "arguments": {
                "data": [
                    -1,
                    1,
                    3
                ]
            },
            "returns": 4
        },
        {
            "arguments": {
                "data": [
                    2,
                    3,
                    3,
                    null,
                    4,
                    4,
                    5
                ]
            },
            "returns": 1.1
        },
        {
            "arguments": {
                "data": [
                    -1,
                    1,
                    null,
                    3
                ],
                "ignore_nodata": false
            },
            "returns": null
        },
        {
            "description": "The input array is empty: return `null`.",
            "arguments": {
                "data": []
            },
            "returns": null
        }
    ],
    "links": [
        {
            "rel": "about",
            "href": "http://mathworld.wolfram.com/Variance.html",
            "title": "Variance explained by Wolfram MathWorld"
        }
    ],
    "process_graph": {
        "mean": {
            "process_id": "mean",
            "arguments": {
                "data": {
                    "from_parameter": "data"
                }
            }
        },
        "apply": {
            "process_id": "apply",
            "arguments": {
                "data": {
                    "from_parameter": "data"
                },
                "process": {
                    "process-graph": {
                        "subtract": {
                            "process_id": "subtract",
                            "arguments": {
                                "x": {
                                    "from_parameter": "x"
                                },
                                "y": {
                                    "from_parameter": "context"
                                }
                            }
                        },
                        "power": {
                            "process_id": "power",
                            "arguments": {
                                "base": {
                                    "from_node": "subtract"
                                },
                                "p": 2
                            },
                            "result": true
                        }
                    }
                },
                "context": {
                    "from_node": "mean"
                }
            }
        },
        "mean2": {
            "process_id": "mean",
            "arguments": {
                "data": {
                    "from_node": "apply"
                },
                "ignore_nodata": {
                    "from_parameter": "ignore_nodata"
                }
            },
            "result": true
        }
    }
}