{"@context":{"dc":"http:\/\/purl.org\/dc\/elements\/1.1\/","skos":"http:\/\/www.w3.org\/2004\/02\/skos\/core#","skos:broader":{"@type":"@id"},"skos:inScheme":{"@type":"@id"},"skos:related":{"@type":"@id"},"skos:narrower":{"@type":"@id"},"skos:hasTopConcept":{"@type":"@id"},"skos:topConceptOf":{"@type":"@id"}},"@id":"https:\/\/digilab.ptb.de\/dkd\/refType\/vocab\/skos\/316","@type":"skos:Concept","skos:prefLabel":{"@language":"en-US","@value=":"standardDeviationPopulation"},"skos:inScheme":"https:\/\/digilab.ptb.de\/dkd\/refType\/vocab\/","dct:created":"2025-06-05 13:03:12","skos:definition":[{"@lang":"en-US","@value":"standard deviation of a population of measurement results\/values "},{"@lang":"de","@value":"Standardabweichung einer Grundgesamtheit von (Mess-)Werten "}],"skos:scopeNote":[{"@lang":"en-US","@value":"The standard deviation is the positive square root of the variance. "},{"@lang":"de","@value":"Die Standardabweichung ist die positive Quadratwurzel der Varianz. "},{"@lang":"en-US","@value":"For the standard deviation of a population, the divisor \"N\" has to be used.\n$s_N=\\sqrt{\\frac{1}{N}\\sum_{i=1}^{N}(x_i-\\bar{x})^2}$ "},{"@lang":"de","@value":"F\u00fcr die Standardabweichung einer Grundgesamtheit ist \"N\" als Divisor zu benutzen.\n$s_N=\\sqrt{\\frac{1}{N}\\sum_{i=1}^{N}(x_i-\\bar{x})^2}$ "},{"@lang":"en-US","@value":"A link via id\/refId can be used to identify the values used to determine the standard deviation. "},{"@lang":"de","@value":"\u00dcber eine Verkn\u00fcpfung per id\/refId kann identifiziert werden, aus welchen Werten die Standardabweichung bestimmt wurde. "}],"skos:historyNote":[{"@lang":"en-US","@value":"2025-06-05\nCreated "},{"@lang":"en-US","@value":"\n2025-06-05\nEdited scsope notes 2 and 3, added markdown formula\n "}],"skos:example":[{"@lang":"en-US","@value":"<dcc:data>\n\u00a0 \u00a0<dcc:list>\n\u00a0 \u00a0 \u00a0 <dcc:quantity id=\"singleValues\">\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<si:realXMLList>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <si:valueXMLList>0.5 0.6 0.7 0.8 0.9 1.0<\/si:valueXMLList>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <si:unitXMLList>\\kilogram<\/si:unitXMLList>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/si:realXMLList>\n\u00a0 \u00a0 \u00a0 <\/dcc:quantity>\n\u00a0 \u00a0 \u00a0 <dcc:quantity refType=\"math_standardDeviationPopulation\" refId=\"singleValues\">\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<si:real>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <si:value>0.17078251<\/si:value>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <si:unit>\\kilogram<\/si:unit>\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/si:real>\n\u00a0 \u00a0 \u00a0 <\/dcc:quantity>\n\u00a0 \u00a0<\/dcc:list>\n<\/dcc:data> "}],"skos:broader":["https:\/\/digilab.ptb.de\/dkd\/refType\/vocab\/skos\/292"],"skos:related":["https:\/\/digilab.ptb.de\/dkd\/refType\/vocab\/skos\/18","https:\/\/digilab.ptb.de\/dkd\/refType\/vocab\/skos\/99","https:\/\/digilab.ptb.de\/dkd\/refType\/vocab\/skos\/5","https:\/\/digilab.ptb.de\/dkd\/refType\/vocab\/skos\/295"]}