{"id":2131,"date":"2023-03-26T19:40:15","date_gmt":"2023-03-26T19:40:15","guid":{"rendered":"https:\/\/advantagecalculators.com\/?page_id=2131"},"modified":"2023-03-26T20:12:16","modified_gmt":"2023-03-26T20:12:16","slug":"empirical-rule-calculator","status":"publish","type":"page","link":"https:\/\/advantagecalculators.com\/empirical-rule-calculator\/","title":{"rendered":"Empirical Rule Calculator"},"content":{"rendered":"\n\n\n<div class=\"\">\n   <div class=\"row\">\n    <div class=\"col-md-6\">\n      <div>\n        <label for=\"mean\" class=\"form-label\">Mean<\/label>\n        <input type=\"number\" class=\"form-control\" id=\"mean\" placeholder=\"Enter mean\" required \/>\n      <\/div>\n      <div>\n        <label for=\"stddev\" class=\"form-label\">Standard Deviation<\/label>\n        <input type=\"number\" class=\"form-control\" id=\"stddev\" placeholder=\"Enter standard deviation\" required \/>\n      <\/div>\n      <button id=\"calculate\" class=\"\">Calculate<\/button>\n    <\/div>\n    <div class=\"col-md-6\">\n      <div class=\"card\">\n        <div class=\"card-header\">\n          Results\n        <\/div>\n        <ul class=\"list-group list-group-flush\">\n          <li class=\"list-group-item\">68% Rule: <strong><span id=\"rule68\"><\/span><\/strong><\/li>\n          <li class=\"list-group-item\">95% Rule: <strong><span id=\"rule95\"><\/span><\/strong><\/li>\n          <li class=\"list-group-item\">99.7% Rule: <strong><span id=\"rule997\"><\/span><\/strong><\/li>\n        <\/ul>\n      <\/div>\n    <\/div>\n  <\/div>\n<\/div>\n\n\n\n\n<script>\nconst meanInput = document.querySelector('#mean');\nconst stddevInput = document.querySelector('#stddev');\nconst rule68 = document.querySelector('#rule68');\nconst rule95 = document.querySelector('#rule95');\nconst rule997 = document.querySelector('#rule997');\nconst calculateButton = document.querySelector('#calculate');\n\ncalculateButton.addEventListener('click', () => {\n\n  const mean = parseFloat(meanInput.value);\n  const stddev = parseFloat(stddevInput.value);\n\n  const diff68 = stddev;\n  const diff95 = 2 * stddev;\n  const diff997 = 3 * stddev;\n\n  rule68.textContent = `Between ${mean - diff68} and ${mean + diff68}`;\n  rule95.textContent = `Between ${mean - diff95} and ${mean + diff95}`;\n  rule997.textContent = `Between ${mean - diff997} and ${mean + diff997}`;\n});\n<\/script>\n\n\n\n<style>\nul.list-group.list-group-flush {\n    margin: 0 0 0 0;\n}\ninput#mean, input#stddev {\n    margin-bottom: 20px;\n}\n\nul{padding-left:2rem;}\nul{margin-top:0;margin-bottom:1rem;}\nstrong{font-weight:bolder;}\nlabel{display:inline-block;}\n\n.row{--bs-gutter-x:1.5rem;--bs-gutter-y:0;display:flex;flex-wrap:wrap;margin-top:calc(var(--bs-gutter-y) * -1);margin-right:calc(var(--bs-gutter-x) * -.5);margin-left:calc(var(--bs-gutter-x) * -.5);}\n.row>*{flex-shrink:0;width:100%;max-width:100%;padding-right:calc(var(--bs-gutter-x) * .5);padding-left:calc(var(--bs-gutter-x) * .5);margin-top:var(--bs-gutter-y);}\n@media (min-width:768px){\n.col-md-6{flex:0 0 auto;width:50%;}\n}\n.form-label{margin-bottom:.5rem;}\n.form-control{display:block;width:100%;padding:.375rem .75rem;font-size:1rem;font-weight:400;line-height:1.5;color:#212529;background-color:#fff;background-clip:padding-box;border:1px solid #ced4da;-webkit-appearance:none;-moz-appearance:none;appearance:none;border-radius:.25rem;transition:border-color .15s ease-in-out,box-shadow .15s ease-in-out;}\n@media (prefers-reduced-motion:reduce){\n.form-control{transition:none;}\n}\n.form-control:focus{color:#212529;background-color:#fff;border-color:#86b7fe;outline:0;box-shadow:0 0 0 .25rem rgba(13,110,253,.25);}\n.form-control::placeholder{color:#6c757d;opacity:1;}\n.form-control:disabled{background-color:#e9ecef;opacity:1;}\n\n.card{position:relative;display:flex;flex-direction:column;min-width:0;word-wrap:break-word;background-color:#fff;background-clip:border-box;border:1px solid rgba(0,0,0,.125);border-radius:.25rem;  margin-top: 28px;}\n.card>.list-group{border-top:inherit;border-bottom:inherit;}\n.card>.list-group:last-child{border-bottom-width:0;border-bottom-right-radius:calc(.25rem - 1px);border-bottom-left-radius:calc(.25rem - 1px);}\n.card>.card-header+.list-group{border-top:0;}\n.card-header{padding:.5rem 1rem;margin-bottom:0;background-color:rgba(0,0,0,.03);border-bottom:1px solid rgba(0,0,0,.125);}\n.card-header:first-child{border-radius:calc(.25rem - 1px) calc(.25rem - 1px) 0 0;}\n.list-group{display:flex;flex-direction:column;padding-left:0;margin-bottom:0;border-radius:.25rem;}\n.list-group-item{position:relative;display:block;padding:.5rem 1rem;color:#212529;text-decoration:none;background-color:#fff;border:1px solid rgba(0,0,0,.125);}\n.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit;}\n.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit;}\n.list-group-item:disabled{color:#6c757d;pointer-events:none;background-color:#fff;}\n.list-group-item+.list-group-item{border-top-width:0;}\n.list-group-flush{border-radius:0;}\n.list-group-flush>.list-group-item{border-width:0 0 1px;}\n.list-group-flush>.list-group-item:last-child{border-bottom-width:0;}\n.mb-3{margin-bottom:1rem!important;}\n  \n<\/style>\n\n\n\n\n<div style=\"height:44px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<div class=\"lightweight-accordion bordered\"><details><summary class=\"lightweight-accordion-title\"><h2>Empirical Rule Calculator User Guide<\/h2><\/summary><div class=\"lightweight-accordion-body\">\n\n<p>This is our tool that helps you apply the Empirical Rule in statistics with ease! This tool is designed to quickly calculate the range of data you can expect to find within 1, 2, and 3 standard deviations from the mean.<\/p>\n\n\n\n<p>How to use the Empirical Rule Calculator:<\/p>\n\n\n\n<ol>\n<li>Enter the mean value of your data in the &#8220;Mean&#8221; field.<\/li>\n\n\n\n<li>Enter the standard deviation value of your data in the &#8220;Standard Deviation&#8221; field.<\/li>\n\n\n\n<li>Click on the &#8220;Calculate&#8221; button.<\/li>\n<\/ol>\n\n\n\n<p>And just like that, you&#8217;ll get your results!<\/p>\n\n\n\n<p>The results are presented in three ranges:<\/p>\n\n\n\n<ul>\n<li>The 68% range: data within 1 standard deviation of the mean<\/li>\n\n\n\n<li>The 95% range: data within 2 standard deviations of the mean<\/li>\n\n\n\n<li>The 99.7% range: data within 3 standard deviations of the mean<\/li>\n<\/ul>\n\n\n\n<p>If your data falls outside of these ranges, it could indicate that your data is unusual and may require further analysis.<\/p>\n\n\n\n<p>This tool is especially useful for students and professionals who need to quickly calculate the range of data they can expect to find within a certain standard deviation from the mean. It is also helpful for anyone who wants to better understand their data.<\/p>\n\n<\/div><\/details><\/div>\n\n\n<div style=\"height:44px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-rank-math-toc-block\" id=\"rank-math-toc\"><h2>Table of Contents<\/h2><nav><ul><li ><a href=\"#empirical-rule-calculator-an-easy-way-to-understand-normal-distribution\">Empirical Rule Calculator: An Easy Way to Understand Normal Distribution<\/a><\/li><li ><a href=\"#what-is-the-empirical-rule\">What is the Empirical Rule?<\/a><\/li><li ><a href=\"#how-does-the-empirical-rule-apply-to-normal-distribution\">How Does the Empirical Rule Apply to Normal Distribution?<\/a><\/li><li ><a href=\"#using-the-empirical-rule-calculator\">Using the Empirical Rule Calculator<\/a><\/li><\/ul><\/nav><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"empirical-rule-calculator-an-easy-way-to-understand-normal-distribution\">Empirical Rule Calculator: An Easy Way to Understand Normal Distribution<\/h2>\n\n\n\n<p>Are you trying to understand normal distribution and probability? Do you need help with statistical analysis? The Empirical Rule is a fundamental concept in statistics that can help you understand and analyze data. In this blog post, we&#8217;ll explain what the Empirical Rule is, how it applies to <a href=\"https:\/\/www.scribbr.com\/statistics\/normal-distribution\/\" target=\"_blank\" rel=\"noreferrer noopener\">normal distribution<\/a>, and how to use our Empirical Rule Calculator to calculate probabilities and analyze data.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"what-is-the-empirical-rule\">What is the Empirical Rule?<\/h2>\n\n\n\n<p>The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical principle that describes the distribution of data in a normal distribution. The rule states that:<\/p>\n\n\n\n<ul>\n<li>Approximately 68% of data falls within one standard deviation of the mean.<\/li>\n\n\n\n<li>Approximately 95% of data falls within two standard deviations of the mean.<\/li>\n\n\n\n<li>Approximately 99.7% of data falls within three standard deviations of the mean.<\/li>\n<\/ul>\n\n\n\n<p>This rule applies to any normal distribution, regardless of the mean or standard deviation. Understanding the Empirical Rule is essential for analyzing and interpreting data in a wide range of fields, including finance, science, and engineering.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"how-does-the-empirical-rule-apply-to-normal-distribution\">How Does the Empirical Rule Apply to Normal Distribution?<\/h2>\n\n\n\n<p>Normal distribution, also known as Gaussian distribution, is a type of probability distribution that describes the distribution of a set of data. In a normal distribution, the data is distributed symmetrically around the mean, with the majority of data falling near the mean and less data falling further away from the mean.<\/p>\n\n\n\n<p>The Empirical Rule applies to normal distribution by describing the distribution of data within standard deviations of the mean. The rule states that approximately 68% of data falls within one standard deviation of the mean, 95% falls within two <a href=\"https:\/\/en.wikipedia.org\/wiki\/Standard_deviation\" target=\"_blank\" rel=\"noreferrer noopener\">standard deviation<\/a>s, and 99.7% falls within three standard deviations.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"using-the-empirical-rule-calculator\">Using the Empirical Rule Calculator<\/h2>\n\n\n\n<p>Calculating probabilities and understanding normal distribution can be challenging, especially for those new to statistical analysis. That&#8217;s why we&#8217;ve developed an easy-to-use Empirical Rule Calculator that can help you analyze data and calculate probabilities with ease.<\/p>\n\n\n\n<p>To use the calculator, simply input the mean and standard deviation of your data set. The calculator will then show you the percentage of data that fall within one, two, and three standard deviations of the mean, as well as the range of values within each standard deviation.<\/p>\n\n\n\n<p>For example, let&#8217;s say you have a data set with a mean of 50 and a standard deviation of 10. Using the Empirical Rule Calculator, you can see that approximately 68% of data falls within one standard deviation of the mean (between 40 and 60), 95% falls within two standard deviations (between 30 and 70), and 99.7% falls within three standard deviations (between 20 and 80).<\/p>\n\n\n\n<p>The Empirical Rule is a fundamental principle in statistical analysis that describes the distribution of data in a normal distribution. Understanding the rule is essential for interpreting and analyzing data in a wide range of fields. Our Empirical Rule Calculator makes it easy to calculate probabilities and understand normal distribution with just a few clicks. Try it out today and see how it can help you with your data analysis!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mean Standard Deviation Calculate Results 68% Rule: 95% Rule: 99.7% Rule: Empirical Rule Calculator: An Easy Way to Understand Normal &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"Empirical Rule Calculator\" class=\"read-more button\" href=\"https:\/\/advantagecalculators.com\/empirical-rule-calculator\/#more-2131\" aria-label=\"More on Empirical Rule Calculator\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"_links":{"self":[{"href":"https:\/\/advantagecalculators.com\/wp-json\/wp\/v2\/pages\/2131"}],"collection":[{"href":"https:\/\/advantagecalculators.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/advantagecalculators.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/advantagecalculators.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/advantagecalculators.com\/wp-json\/wp\/v2\/comments?post=2131"}],"version-history":[{"count":16,"href":"https:\/\/advantagecalculators.com\/wp-json\/wp\/v2\/pages\/2131\/revisions"}],"predecessor-version":[{"id":2429,"href":"https:\/\/advantagecalculators.com\/wp-json\/wp\/v2\/pages\/2131\/revisions\/2429"}],"wp:attachment":[{"href":"https:\/\/advantagecalculators.com\/wp-json\/wp\/v2\/media?parent=2131"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}