{"id":2547,"date":"2013-05-19T20:31:17","date_gmt":"2013-05-20T04:31:17","guid":{"rendered":"http:\/\/www.mysqltutorial.org\/?page_id=2547"},"modified":"2023-10-08T19:42:01","modified_gmt":"2023-10-09T02:42:01","slug":"mysql-standard-deviation","status":"publish","type":"page","link":"https:\/\/www.mysqltutorial.org\/mysql-aggregate-functions\/mysql-standard-deviation\/","title":{"rendered":"MySQL Standard Deviation Functions"},"content":{"rendered":"\n<p><b>Summary<\/b>: in this tutorial, you will learn how to use <b>MySQL standard deviation<\/b> functions to calculate populate standard deviation and sample standard deviation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Introduction to standard deviation<\/h2>\n\n\n\n<p>Standard deviation is a measure of how spread out the values in a data set are. The standard deviation shows how much variation exists from the <a href=\"https:\/\/www.mysqltutorial.org\/mysql-aggregate-functions\/mysql-avg\/\">average<\/a> (mean).<\/p>\n\n\n\n<p>A low standard deviation shows that the values in the data set are close to the mean. The high standard deviation indicates that the values of the dataset are spread out over a large range of values.<\/p>\n\n\n\n<p>A standard deviation is a square root of the <a href=\"https:\/\/www.mysqltutorial.org\/mysql-aggregate-functions\/mysql-variance\/\">variance<\/a>, which can be calculated by using the following steps:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Step 1<\/strong>. Calculate the average of all values in the data set to get the average or mean e.g., suppose the data set consists of 1, 2, and 3, the mean is (1+2+3)\/3 = 2.<\/li>\n\n\n\n<li><strong>Step 2<\/strong>. Compute the difference of the value from the mean for each value, and square the result of each e.g., (1-2)<sup>2<\/sup>= (-1)<sup>2<\/sup> = 1, (2-2)<sup>2<\/sup> = (0)<sup>2<\/sup> = 0, (3-2)<sup>2<\/sup> = (1)<sup>2<\/sup> = 1.<\/li>\n\n\n\n<li><strong>Step 3<\/strong>. Calculate the average values in step 2, which produces the variance. Then take a square root of the variance to get the standard deviation of all values in the data set e.g., square root of ((1 + 0 + 1)\/3) = 0.816497<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Population standard deviation vs. sample standard deviation<\/h3>\n\n\n\n<p>If all values in the data set are taken into the calculation, this standard deviation is called <strong>population standard deviation<\/strong>. However, if a subset of values or a sample is taken into the calculation, this standard deviation is called <strong>sample standard deviation<\/strong>.<\/p>\n\n\n\n<p>A sigma letter (\u03c3) represents the standard deviation. The following equations illustrate how to calculate population standard deviation and sample standard deviation:<\/p>\n\n\n\n<p>Population standard deviation:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"189\" height=\"65\" src=\"https:\/\/www.mysqltutorial.org\/wp-content\/uploads\/2013\/05\/mysql-population-standard-deviation-formula.gif\" alt=\"MySQL population standard deviation formula\" class=\"wp-image-2548\" title=\"MySQL population standard deviation formula\"\/><\/figure>\n\n\n\n<p>Sample standard deviation:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"216\" height=\"65\" src=\"https:\/\/www.mysqltutorial.org\/wp-content\/uploads\/2013\/05\/mysql-sample-standard-deviation-formula.gif\" alt=\"MySQL sample standard deviation formula\" class=\"wp-image-2549\" title=\"MySQL sample standard deviation formula\"\/><\/figure>\n\n\n\n<p>The calculation of population standard deviation and sample standard deviation is slightly different. When calculating the variance of sample standard deviation, divide by N-1 instead of N, where N is the number of values in the data set.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">MySQL standard deviation functions<\/h2>\n\n\n\n<p>MySQL makes it easy for you to calculate the population standard deviation and sample standard deviation.<\/p>\n\n\n\n<p>To calculate population standard deviation, you use one of the following functions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>STD(expression)<\/code> &#8211; returns the population standard deviation of the expression. The STD function returns NULL if there is no matching row.<\/li>\n\n\n\n<li><code>STDDEV(expression)<\/code> &#8211; is equivalent to the <code>STD<\/code> function. It is provided to be compatible with Oracle Database only.<\/li>\n\n\n\n<li><code>STDEV_POP(expression)<\/code> &#8211; is equivalent to the <code>STD<\/code> function.<\/li>\n<\/ul>\n\n\n\n<p>To calculate the sample standard deviation, you use the <code>STDDEV_SAMP (expression)<\/code> function.<\/p>\n\n\n\n<p>MySQL also provides some functions for population variance and sample variance calculation:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>VAR_POP(expression)<\/code> &#8211; calculates the population standard variance of the expression.<\/li>\n\n\n\n<li><code>VARIANCE(expression)<\/code> &#8211; is equivalent to the <code>VAR_POP<\/code> function.<\/li>\n\n\n\n<li><code>VAR_SAMP(expression)<\/code> &#8211; calculates the sample standard variance of the expression.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Examples of MySQL standard deviation functions<\/h2>\n\n\n\n<p>Let&#8217;s take a look at the <code>orders<\/code> table in the <a title=\"MySQL Sample Database\" href=\"https:\/\/www.mysqltutorial.org\/getting-started-with-mysql\/mysql-sample-database\/\">sample database<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"144\" height=\"184\" src=\"https:\/\/www.mysqltutorial.org\/wp-content\/uploads\/2019\/08\/orders.png\" alt=\"\" class=\"wp-image-8094\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Examples of population standard deviation functions<\/h3>\n\n\n\n<p>First, the following query returns the customer numbers and the number of orders from the <code>orders<\/code> table:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-1\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\"><span class=\"hljs-keyword\">SELECT<\/span> customerNumber, \n       <span class=\"hljs-keyword\">COUNT<\/span>(*) orderCount\n<span class=\"hljs-keyword\">FROM<\/span> orders\n<span class=\"hljs-keyword\">WHERE<\/span> <span class=\"hljs-keyword\">status<\/span> = <span class=\"hljs-string\">'Shipped'<\/span>\n<span class=\"hljs-keyword\">GROUP<\/span> <span class=\"hljs-keyword\">BY<\/span> customerNumber;<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-1\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Second, the following statement calculates the population standard deviation of the number of orders of the customers:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-2\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\"><span class=\"hljs-keyword\">SELECT<\/span> <span class=\"hljs-keyword\">FORMAT<\/span>(<span class=\"hljs-keyword\">STD<\/span>(orderCount),<span class=\"hljs-number\">2<\/span>)\n<span class=\"hljs-keyword\">FROM<\/span> (<span class=\"hljs-keyword\">SELECT<\/span> customerNumber, <span class=\"hljs-keyword\">count<\/span>(*) orderCount\n<span class=\"hljs-keyword\">FROM<\/span> orders\n<span class=\"hljs-keyword\">GROUP<\/span> <span class=\"hljs-keyword\">BY<\/span> customerNumber) t;<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-2\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p><a class=\"sql\" href=\"https:\/\/www.mysqltutorial.org\/tryit\/query\/mysql-standard-deviation\/#2\" target=\"_blank\" rel=\"noopener noreferrer\">Try It Out<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"197\" height=\"44\" src=\"https:\/\/www.mysqltutorial.org\/wp-content\/uploads\/2013\/05\/MySQL-STD-function.png\" alt=\"MySQL STD function\" class=\"wp-image-2556\" title=\"MySQL STD function\"\/><\/figure>\n\n\n\n<p>Notice that the <a href=\"https:\/\/www.mysqltutorial.org\/mysql-string-functions\/mysql-format-function\/\">FORMAT function<\/a> is used for formatting the result of the <code>STD<\/code> function.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Examples of sample standard deviation functions<\/h3>\n\n\n\n<p>Suppose you only want to evaluate shipped orders in the orders table.<\/p>\n\n\n\n<p>First, the following query returns the customer numbers and the number of shipped orders:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-3\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\"><span class=\"hljs-keyword\">SELECT<\/span> customerNumber, <span class=\"hljs-keyword\">count<\/span>(*) orderCount\n<span class=\"hljs-keyword\">FROM<\/span> orders\n<span class=\"hljs-keyword\">WHERE<\/span> <span class=\"hljs-keyword\">status<\/span> = <span class=\"hljs-string\">'Shipped'<\/span>\n<span class=\"hljs-keyword\">GROUP<\/span> <span class=\"hljs-keyword\">BY<\/span> customerNumber;<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-3\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p>Second, the following query uses the <code>STDDEV_SAMP<\/code> function to calculate the sample standard deviation:<\/p>\n\n\n<pre class=\"wp-block-code\" aria-describedby=\"shcb-language-4\" data-shcb-language-name=\"SQL (Structured Query Language)\" data-shcb-language-slug=\"sql\"><span><code class=\"hljs language-sql\"><span class=\"hljs-keyword\">SELECT<\/span> <span class=\"hljs-keyword\">FORMAT<\/span>(<span class=\"hljs-keyword\">STDDEV_SAMP<\/span>(orderCount),<span class=\"hljs-number\">2<\/span>)\n<span class=\"hljs-keyword\">FROM<\/span> (<span class=\"hljs-keyword\">SELECT<\/span> customerNumber, <span class=\"hljs-keyword\">count<\/span>(*) orderCount\n<span class=\"hljs-keyword\">FROM<\/span> orders\n<span class=\"hljs-keyword\">WHERE<\/span> <span class=\"hljs-keyword\">status<\/span> = <span class=\"hljs-string\">'Shipped'<\/span>\n<span class=\"hljs-keyword\">GROUP<\/span> <span class=\"hljs-keyword\">BY<\/span> customerNumber) t;<\/code><\/span><small class=\"shcb-language\" id=\"shcb-language-4\"><span class=\"shcb-language__label\">Code language:<\/span> <span class=\"shcb-language__name\">SQL (Structured Query Language)<\/span> <span class=\"shcb-language__paren\">(<\/span><span class=\"shcb-language__slug\">sql<\/span><span class=\"shcb-language__paren\">)<\/span><\/small><\/pre>\n\n\n<p><a class=\"sql\" href=\"https:\/\/www.mysqltutorial.org\/tryit\/query\/mysql-standard-deviation\/#4\" target=\"_blank\" rel=\"noopener noreferrer\">Try It Out<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"246\" height=\"47\" src=\"https:\/\/www.mysqltutorial.org\/wp-content\/uploads\/2013\/05\/MySQL-STDDEV_SAMP-function.png\" alt=\"MySQL STDDEV_SAMP function\" class=\"wp-image-2557\" title=\"MySQL STDDEV_SAMP function\"\/><\/figure>\n\n\n\n<p>In this tutorial, we have introduced you to the standard deviation concept. Then, we showed you how to use the MySQL standard deviation functions to calculate the population standard deviation and sample standard deviation of an expression.<\/p>\n<div class=\"helpful-block-content\" data-title=\"\">\n\t<header>\n\t\t<div class=\"wth-question\">Was this tutorial helpful? <\/div>\n\t\t<div class=\"wth-thumbs\">\n\t\t\t<button\n\t\t\t\tdata-post=\"2547\"\n\t\t\t\tdata-post-url=\"https:\/\/www.mysqltutorial.org\/mysql-aggregate-functions\/mysql-standard-deviation\/\"\n\t\t\t\tdata-post-title=\"MySQL Standard Deviation Functions\"\n\t\t\t\tdata-response=\"1\"\n\t\t\t\tclass=\"wth-btn-rounded wth-yes-btn\"\n\t\t\t>\n\t\t\t\t<svg\n\t\t\t\t\txmlns=\"http:\/\/www.w3.org\/2000\/svg\"\n\t\t\t\t\tviewBox=\"0 0 24 24\"\n\t\t\t\t\tfill=\"none\"\n\t\t\t\t\tstroke=\"currentColor\"\n\t\t\t\t\tstroke-width=\"2\"\n\t\t\t\t\tstroke-linecap=\"round\"\n\t\t\t\t\tstroke-linejoin=\"round\"\n\t\t\t\t\tclass=\"feather feather-thumbs-up block w-full 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