{"id":4849,"date":"2017-12-07T07:21:28","date_gmt":"2017-12-07T07:21:28","guid":{"rendered":"https:\/\/data-flair.training\/blogs\/?p=4849"},"modified":"2021-08-25T17:26:13","modified_gmt":"2021-08-25T11:56:13","slug":"normal-distribution-in-r","status":"publish","type":"post","link":"https:\/\/data-flair.training\/blogs\/normal-distribution-in-r\/","title":{"rendered":"Normal Distribution in R &#8211; Implement Functions with the help of Examples!"},"content":{"rendered":"<p>In this tutorial, we will learn about Normal Distribution in R. We will cover different functions which helps in generating the normal distribution. Along with this, we will also include graphs for easy representation and understanding.<\/p>\n<p>Let&#8217;s start the tutorial.<\/p>\n<h2>What is Normal Distribution in R?<\/h2>\n<p>Generally, it is observed that the collection of random data from independent sources is distributed normally. We get a bell shape curve on plotting a graph with the value of the variable on the horizontal axis and the count of the values in the vertical axis. The centre of the curve represents the mean of the dataset.<\/p>\n<p>It has four inbuilt functions. They are described below:<\/p>\n<ul>\n<li>dnorm()<\/li>\n<li><span style=\"font-weight: 400\">qnorm()<\/span><\/li>\n<li><span style=\"font-weight: 400\">pnorm()<\/span><\/li>\n<li><span style=\"font-weight: 400\">rnorm()<\/span><\/li>\n<\/ul>\n<p>We use the following functions in the above-stated parameters:<\/p>\n<ul>\n<li>x is a vector of numbers.<\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">p is a vector of probabilities.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">n is the number of observations (sample size).<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Here, mean is the mean value of the sample data. Also, its default value is zero.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">sd is the standard deviation. Its default value is 1.<\/span><\/li>\n<\/ul>\n<p><em><strong>Must Learn &#8211; <a href=\"https:\/\/data-flair.training\/blogs\/r-vector-functions\/\">How to apply Functions over R Vectors<\/a><\/strong><\/em><\/p>\n<h3>Functions to Generate Normal Distribution in R<\/h3>\n<p>Below are the different functions to generate normal distribution in R programming:<\/p>\n<h4>1. dnorm()<\/h4>\n<p><b>Syntax<\/b><span style=\"font-weight: 400\">: dnorm(x, mean, sd)<\/span><br \/>\n<b><\/b><\/p>\n<p><b>For example<\/b><span style=\"font-weight: 400\">:<\/span><\/p>\n<p>Create a sequence of numbers between -10 and 10 incrementing by 0.1.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"null\">&gt; #Author DataFlair\r\n&gt; x &lt;- seq(-20, 20, by = .1)\r\n&gt; y &lt;- dnorm(x, mean = 5.0, sd = 1.0)\r\n&gt; plot(x,y, main = \"Normal Distribution\", col = \"blue\")<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<p><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/dnorm.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-63798\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/dnorm.jpg\" alt=\"dnorm() - Normal Distribution in R\" width=\"1299\" height=\"741\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/dnorm.jpg 1299w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/dnorm-150x86.jpg 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/dnorm-300x171.jpg 300w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/dnorm-768x438.jpg 768w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/dnorm-1024x584.jpg 1024w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/dnorm-520x297.jpg 520w\" sizes=\"auto, (max-width: 1299px) 100vw, 1299px\" \/><\/a><\/p>\n<h4>2. pnorm()<\/h4>\n<p><b>Syntax<\/b><span style=\"font-weight: 400\">:\u00a0<\/span>pnorm(x,mean,sd)<\/p>\n<p><b>For example<\/b><span style=\"font-weight: 400\">:<\/span><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"null\">&gt; #Author DataFlair\r\n&gt; x &lt;- seq(-20, 20, by = .1)\r\n&gt; y &lt;- pnorm(x, mean = 5.0, sd = 1.0)\r\n&gt; plot(x,y, main = \"pnorm()\", col = \"blue\")\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<p><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/pnorm.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-63799\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/pnorm.jpg\" alt=\"pnorm() - Normal Distribution in R\" width=\"1299\" height=\"741\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/pnorm.jpg 1299w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/pnorm-150x86.jpg 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/pnorm-300x171.jpg 300w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/pnorm-768x438.jpg 768w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/pnorm-1024x584.jpg 1024w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/pnorm-520x297.jpg 520w\" sizes=\"auto, (max-width: 1299px) 100vw, 1299px\" \/><\/a><\/p>\n<p><strong><em>You must definitely check the <a href=\"https:\/\/data-flair.training\/blogs\/r-numeric-and-character-functions\/\">Numeric and Character Functions in R<\/a><\/em><\/strong><\/p>\n<h4>3. qnorm()<\/h4>\n<p><b>Syntax<\/b><span style=\"font-weight: 400\">: q<\/span>norm(x,mean,sd)<\/p>\n<p><b>For example<\/b><span style=\"font-weight: 400\">:<\/span><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"null\">&gt; x &lt;- seq(0, 1, by = 0.02)\r\n&gt; y &lt;- qnorm(x, mean = 2, sd = 1) #DataFlair\r\n&gt; plot(x,y, main = \"qnorm()\", col = \"blue\")\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<p><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/qnorm.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-63800\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/qnorm.jpg\" alt=\"qnorm()\" width=\"1299\" height=\"741\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/qnorm.jpg 1299w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/qnorm-150x86.jpg 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/qnorm-300x171.jpg 300w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/qnorm-768x438.jpg 768w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/qnorm-1024x584.jpg 1024w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/qnorm-520x297.jpg 520w\" sizes=\"auto, (max-width: 1299px) 100vw, 1299px\" \/><\/a><\/p>\n<h4>4. rnorm()<b><\/b><\/h4>\n<p><b>Syntax<\/b><span style=\"font-weight: 400\">: rnorm(n, mean, sd)<\/span><br \/>\n<b><\/b><\/p>\n<p><b>For example<\/b><span style=\"font-weight: 400\">:<\/span><\/p>\n<p>Create a sample of 50 numbers which are normally distributed.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"null\">#Author Dataflair\r\ny &lt;- rnorm(50)\r\nhist(y, main = \"Normal Distribution\", col = \"darkorange\")\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<p><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/rnorm.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-63801\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/rnorm.jpg\" alt=\"rnorm() - Normal Distribution in R\" width=\"1299\" height=\"741\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/rnorm.jpg 1299w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/rnorm-150x86.jpg 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/rnorm-300x171.jpg 300w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/rnorm-768x438.jpg 768w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/rnorm-1024x584.jpg 1024w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2017\/12\/rnorm-520x297.jpg 520w\" sizes=\"auto, (max-width: 1299px) 100vw, 1299px\" \/><\/a><\/p>\n<h2>Statistical Process Control &#8211; A Case Study of Normal Distribution<\/h2>\n<p>Statistical Process Control (SPC) was developed at the Bell Labs in the 1920s by Dr Walter Shewhart. The underlying concepts of SPC were implemented in Japanese industries after the end of World War 2. Due to its quality as a tool to improve the product through reduction of process variation, it is being used all around the world.<\/p>\n<p>Reduction of variation is one of the key goals of industries to improve their product quality. There are two main causes that contribute towards the variation &#8211;<strong> common causes<\/strong> and <strong>special causes<\/strong>. With the help of distribution, processes are evaluated based on how centred they are, that is, how close the distribution is towards the mean.<\/p>\n<p>With the help of frequency distributions, control limits with known probabilities are established. <em>Control Limits are useful in minimizing the false alarms, that is, minimizing the probability of finding problems where none exist.<\/em> A normal distribution is greatly utilized in Statistical Process Control.<\/p>\n<p>Normal Distribution plays a quintessential role in SPC. With the help of normal distributions, the probability of obtaining values beyond the limits is determined. In a Normal Distribution, the probability that a variable will be within +1 or -1 standard deviation of the mean is 0.68. This means that 68% of the values will be within 1 standard deviation of the mean. Furthermore, the probability that the variable will be within 2 of the average will be 0.95 and will have a probability of 0.997 within 3 of the average.<\/p>\n<p>Knowing that 99.7% of the values will fall within 3 standard deviations of the average, it is considered with confidence that value beyond 3 will be highly unlikely. That is if there is no significant change in the process.<\/p>\n<h2>Summary<\/h2>\n<p>We have studied about normal distribution in R in detail. Moreover, we have learned different functions which are used in generating normal distribution. In the above-mentioned information, we have used graphs, syntax and examples which helps you a lot in an understanding the R normal distribution and their functions.<\/p>\n<p><em><strong>Now, it&#8217;s time for learning <a href=\"https:\/\/data-flair.training\/blogs\/binomial-and-poisson-distribution\/\">Binomial and Poisson Distribution in R Programming<\/a><\/strong><\/em><\/p>\n<p>Still, if you have any query regarding normal distribution in R, ask in the comment section.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this tutorial, we will learn about Normal Distribution in R. We will cover different functions which helps in generating the normal distribution. Along with this, we will also include graphs for easy representation&#46;&#46;&#46;<\/p>\n","protected":false},"author":6,"featured_media":63802,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[51],"tags":[9121,20636,20635,20637],"class_list":["post-4849","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-r","tag-normal-distribution-in-r","tag-r-dnorm-function","tag-r-normal-distribution-functions","tag-r-pnorm-function"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Normal Distribution in R - Implement Functions with the help of Examples! - DataFlair<\/title>\n<meta name=\"description\" content=\"Learn about the normal distribution in R along with its functions; dnorm(), pnorm(), qnorm() and rnorm() with the help of syntax and examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/data-flair.training\/blogs\/normal-distribution-in-r\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Normal Distribution in R - Implement Functions with the help of Examples! 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