{"id":3266,"date":"2023-05-02T06:13:45","date_gmt":"2023-05-02T06:13:45","guid":{"rendered":"https:\/\/thermibel.be\/faq\/how-is-standard-deviation-calculated\/"},"modified":"2023-06-27T11:50:30","modified_gmt":"2023-06-27T11:50:30","slug":"how-is-standard-deviation-calculated","status":"publish","type":"faq","link":"https:\/\/thermibel.be\/en\/faq\/how-is-standard-deviation-calculated\/","title":{"rendered":"How is standard deviation calculated?"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">In the case of a series of n measurements of the same quantity, the <strong>dispersion of the results obtained<\/strong> around the mean is characterised by the average quadratic deviation <em>\u03c3<\/em> which is given by the following formula:<br>$$ \\sigma = \\sqrt {\\frac{{\\mathop \\sum \\nolimits_{i = 1}^n {{\\left( {{x_i} &#8211; \\bar x} \\right)}^2}}}{{n &#8211; 1}}} $$<\/p>\n\n\n\n<p class=\"inl-math wp-block-paragraph\">In the case of a large numbers of measurement, the result of measurement number <em>i<\/em> (<em>i <\/em>= 1,2,3,&#8230;,n) is designated by $$ \\bar x $$ and the average $$ \\bar x = \\frac{{\\mathop \\sum \\nolimits_{i = 1}^n {x_i}}}{n} $$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Increasing the number of measurements <strong>decreases<\/strong> the significance of chance errors and an average of the results can be accepted as the result of a series of measurements.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The \u201cGUM\u201d (Guide to Uncertainty in Measurements) however recommends weighting this standard deviation by a coefficient, known as the \u201cStudent\u2019s\u201d, symbol s, <strong>if the number of measurements is less than or equal to 5.<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For 3 measurements, s=9.2<\/li>\n\n\n\n<li>For 4 measurements, s=6.6<\/li>\n\n\n\n<li>For 5 measurements, s=5.5<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the standard deviation formula becomes:<br>$$ \\sigma = \\frac{s}{{3\\sqrt n }}\\sqrt {\\frac{{\\mathop \\sum \\nolimits_{i = 1}^n {{\\left( {{x_i} &#8211; \\bar x} \\right)}^2}}}{{n &#8211; 1}}} $$<\/p>\n\n\n\n<p class=\"inl-math wp-block-paragraph\">Be careful not to confuse the standard deviation with the spread which is the difference between the minimum and maximum values of the quantities measured: $$ e = {x_{max}} &#8211; {x_{min}} $$.<\/p>\n","protected":false},"featured_media":0,"template":"","format":"standard","class_list":["post-3266","faq","type-faq","status-publish","format-standard","hentry"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.9 - aioseo.com -->\n\t<meta name=\"description\" content=\"In the case of a series of n measurements of the same quantity, the dispersion of the results obtained around the mean is characterised by the average quadratic deviation \u03c3 which is given by the following formula:$$ \\sigma = \\sqrt {\\frac{{\\mathop \\sum \\nolimits_{i = 1}^n {{\\left( {{x_i} - \\bar x} \\right)}^2}}}{{n - 1}}} $$ In\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<link rel=\"canonical\" href=\"https:\/\/thermibel.be\/en\/faq\/how-is-standard-deviation-calculated\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 4.9.9\" \/>\n\t\t<meta property=\"og:locale\" content=\"en_US\" \/>\n\t\t<meta property=\"og:site_name\" content=\"Thermibel - Un Haut Degr\u00e9 de Qualit\u00e9\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"How is standard deviation calculated? 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