{ "schemaVersion": 1, "slug": "standard-deviation-calculator", "category": "math", "kind": "implementation", "independentValidation": false, "implementationHash": "6da238a68892e9c8017bfa7a09ec07a9466b99e35c95c9d6ff9ca0966a82a763", "provenance": "Generated from the calculation contract used by the published page. Publication is not external validation.", "sourceFiles": [ "data/calculators/standard-deviation-calculator.json", "src/engine.js" ], "runtimeSource": "/sources/engine.txt", "runtimeHash": "5c888d8898afbdee36267bb9977829e1e2ac568f6677c8ee87469c139864645c", "scope": "The compute function records implemented equations, constants, lookup tables and custom rules. Inputs record defaults and allowed values; outputs record precision and units. Defaults are examples, not recommendations. General background references are not evidence for this specific algorithm.", "publishedFormula": { "formula": "μ = Σx/n; σ² = Σ(x−μ)²/n; s² = Σ(x−μ)²/(n−1); σ = √σ²; s = √s²; SE = s/√n", "vars": [], "note": "The primary statistic can be switched. Unrepresentable numeric results are rejected; an overflowing sum of squares alone is omitted when the variance remains representable." }, "externalEvidence": null, "contract": { "compute": "try{if(false)throw new Error('inputError');const calculate=function(){const h=(function context() {\n const DAY=86400000;\n const own=(o,k)=>Object.prototype.hasOwnProperty.call(o,k);\n const fail=()=>{throw new Error('inputError');};\n const num=(v,min=-Infinity,max=Infinity,integer=false)=>{\n if(!Number.isFinite(v)||vmax||(integer&&!Number.isInteger(v)))fail();return v;\n };\n const choice=(v,values)=>{if(!values.includes(v))fail();return v;};\n const date=s=>{if(typeof s!=='string'||!/^\\d{4}-\\d{2}-\\d{2}$/.test(s)||s.startsWith('0000'))fail();const d=new Date(s+'T00:00:00Z');if(!Number.isFinite(+d)||d.toISOString().slice(0,10)!==s)fail();return d;};\n const iso=d=>{if(!Number.isFinite(+d)||d.getUTCFullYear()<1||d.getUTCFullYear()>9999)fail();return d.toISOString().slice(0,10);};\n const shift=(d,n)=>{const r=new Date(+d+n*DAY);iso(r);return r;};\n const month=(d,n)=>{const r=new Date(+d);r.setUTCDate(1);r.setUTCMonth(r.getUTCMonth()+n);const end=new Date(+r);end.setUTCMonth(end.getUTCMonth()+1,0);r.setUTCDate(Math.min(d.getUTCDate(),end.getUTCDate()));iso(r);return r;};\n const weekdays=['Sunday','Monday','Tuesday','Wednesday','Thursday','Friday','Saturday'];\n const work=(d,count)=>{let n=Math.floor(count/7)*5;for(let k=0;k{let n=(b.getUTCFullYear()-a.getUTCFullYear())*12+b.getUTCMonth()-a.getUTCMonth();if(n>=0&&+month(a,n)>+b)n--;if(n<0&&+month(a,n)<+b)n++;return n;};\n return {DAY,own,fail,num,choice,date,iso,shift,month,weekdays,work,wholeMonths};\n})();const result=(function(v,h){\n const {fail}=h,text=String(v.values).trim();if(!text||text.length>100000||/^,|,$|,\\s*,/.test(text))fail();const parts=text.split(/[\\s,]+/);if(parts.length>10000||!parts.every(x=>/^[+-]?(?:\\d+\\.?\\d*|\\.\\d+)(?:e[+-]?\\d+)?$/i.test(x)&&Number.isFinite(Number(x))))fail();\n const xs=parts.map(Number),count=xs.length,origin=xs[0];let sum=0,err=0;for(const x of xs){const d=x-origin;if(!Number.isFinite(d))fail();const y=d-err,t=sum+y;err=(t-sum)-y;sum=t;}\n const center=sum/count,mean=origin+center;if(!Number.isFinite(mean))fail();const scale=Math.max(...xs.map(x=>Math.abs((x-origin)-center)));let ss=0;err=0;if(scale)for(const x of xs){const d=((x-origin)-center)/scale,y=d*d-err,t=ss+y;err=(t-ss)-y;ss=t;}\n const populationSD=scale*Math.sqrt(ss/count),sampleSD=count>1?scale*Math.sqrt(ss/(count-1)):null,populationVariance=populationSD**2,sampleVariance=count>1?sampleSD**2:null,sumSquares=scale**2*ss;\n if(!Number.isFinite(populationVariance)||(scale>0&&populationVariance===0)||(sampleVariance!==null&&!Number.isFinite(sampleVariance)))fail();\n return {populationSD,sampleSD,populationVariance,sampleVariance,mean,standardError:count>1?sampleSD/Math.sqrt(count):null,count,sumSquares:Number.isFinite(sumSquares)?sumSquares:null};\n })({\"values\":(values),\"resultKind\":(resultKind)},h);return result;};const out=calculate();return Object.fromEntries([\"populationSD\",\"sampleSD\",\"populationVariance\",\"sampleVariance\",\"mean\",\"standardError\",\"count\",\"sumSquares\"].map(k=>[k,out[k]??null]).concat(Object.entries(out).filter(([k])=>k.startsWith('__'))));}catch(error){return Object.assign(Object.fromEntries([\"populationSD\",\"sampleSD\",\"populationVariance\",\"sampleVariance\",\"mean\",\"standardError\",\"count\",\"sumSquares\"].map(k=>[k,null])),{__error:error.message==='openingsExceedWallArea'?'openingsExceedWallArea':'inputError'});}", "inputs": [ { "name": "values", "type": "text", "default": "10, 12, 23, 23, 16, 23, 21, 16", "step": 1, "preserveEmpty": true }, { "type": "select", "default": "populationSD", "options": [ { "value": "populationSD" }, { "value": "sampleSD" }, { "value": "populationVariance" }, { "value": "sampleVariance" } ], "advanced": true, "name": "resultKind" } ], "outputs": [ { "name": "populationSD", "precision": 4, "unit": "", "notation": "auto" }, { "name": "sampleSD", "precision": 4, "unit": "", "optional": true, "notation": "auto" }, { "name": "populationVariance", "precision": 4, "unit": "", "notation": "auto" }, { "name": "sampleVariance", "precision": 4, "unit": "", "optional": true, "notation": "auto" }, { "name": "mean", "precision": 4, "unit": "", "notation": "auto" }, { "name": "standardError", "precision": 4, "unit": "", "optional": true, "notation": "auto" }, { "name": "count", "precision": 0, "unit": "", "notation": "auto" }, { "name": "sumSquares", "precision": 4, "unit": "", "optional": true, "notation": "auto" } ], "interpret": null } }