{"id":11426,"date":"2022-08-22T13:18:37","date_gmt":"2022-08-22T12:18:37","guid":{"rendered":"https:\/\/statanalytica.com\/blog\/?p=11426"},"modified":"2022-08-22T13:18:41","modified_gmt":"2022-08-22T12:18:41","slug":"important-statistics-equations","status":"publish","type":"post","link":"https:\/\/statanalytica.com\/blog\/important-statistics-equations\/","title":{"rendered":"Important Statistics Equations You Need To Be Aware Of"},"content":{"rendered":"\n<p class=\"has-luminous-vivid-orange-color has-luminous-vivid-orange-background-color has-text-color has-background\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-8-color\">Karl Pearson has beautifully said &#8211; &#8220;Statistics Is The Grammar Of Science&#8221;<\/mark><\/p>\n\n\n\n<p>Although statistics is said to be a part of mathematics. There are various <a href=\"https:\/\/statanalytica.com\/blog\/application-of-mathematics-in-statistics\/\" target=\"_blank\" rel=\"noreferrer noopener\">application of mathematics in statistics<\/a>.<\/p>\n\n\n\n<p>The mathematics of working with numeric data and analyzing it is called <a href=\"https:\/\/www.meta-calculator.com\/statistics-formula.php\" target=\"_blank\" rel=\"noreferrer noopener\">statistics<\/a>. More formally, it is the study of data collection, interpretation, organization, and presentation. According to statistical theory, a statistic is a function of a sample that doesn\u2019t depend on the sample\u2019s distribution. Statistics equations enable you to measure the tendencies of a population in various ways and work out the deviation of values.<\/p>\n\n\n\n<p>This branch of math enables you to draw insights from data and even predict patterns and possibilities by working with the facts of the numeric data. Here is a collection of important statistics math equations that students, statisticians, marketing analysts, financial analysts, and a wide array of professionals commonly use.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"statistics-probability-equations\"><\/span><strong>Statistics Probability Equations<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-6a150f4e24d1b\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #ff5104;color:#ff5104\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #ff5104;color:#ff5104\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-6a150f4e24d1b\" checked aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/statanalytica.com\/blog\/important-statistics-equations\/#statistics-probability-equations\" >Statistics Probability Equations<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/statanalytica.com\/blog\/important-statistics-equations\/#1-population-mean\" >#1 Population Mean<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/statanalytica.com\/blog\/important-statistics-equations\/#2-population-standard-deviation\" >#2 Population Standard Deviation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/statanalytica.com\/blog\/important-statistics-equations\/#3-population-variance\" >#3 Population Variance<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/statanalytica.com\/blog\/important-statistics-equations\/#4-sample-mean\" >#4 Sample Mean<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/statanalytica.com\/blog\/important-statistics-equations\/#5-sample-standard-deviation\" >#5 Sample Standard Deviation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/statanalytica.com\/blog\/important-statistics-equations\/#6-sample-variance\" >#6 Sample Variance<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/statanalytica.com\/blog\/important-statistics-equations\/#probability-statistics-equations\" >Probability Statistics Equations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/statanalytica.com\/blog\/important-statistics-equations\/#regression-equations-statistics\" >Regression Equations Statistics<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/statanalytica.com\/blog\/important-statistics-equations\/#conclusion\" >Conclusion<\/a><\/li><\/ul><\/nav><\/div>\n\n\n\n\n<p>Here are seven common statistics equations:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"1-population-mean\"><\/span><strong>#1 Population Mean<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>This term refers to the average of a characteristic in a population. The formula is:<\/p>\n\n\n\n<p>\u03bc = ( \u03a3 Xi ) \/ N<\/p>\n\n\n\n<p>Here, \u201c\u03bc\u201d is the population mean, \u201c\u03a3 Xi\u201d refers to the sum of the characteristics in the population, and \u201cN\u201d is the total size of the population.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"2-population-standard-deviation\"><\/span><strong>#2 Population Standard Deviation<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Standard deviation is a measure of the \u201cspread\u201d or the variability of scores in a data set, represented by:<\/p>\n\n\n\n<p>\u03c3 = sqrt [ \u03a3 ( Xi \u2013 \u03bc )<sup>2<\/sup> \/ N ]<\/p>\n\n\n\n<p>As you may have figured out, the term is represented by \u201c\u03c3.\u201d \u201cSqrt\u201d denotes the square root, and \u03a3 ( Xi \u2013 \u03bc )<sup>2 <\/sup>&nbsp;is the sum of the squared deviations of the values minus the population mean.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"3-population-variance\"><\/span><strong>#3 Population Variance<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The variance shows us the spread of the values in a population and is the square of the standard deviation. The formula is:<\/p>\n\n\n\n<p>\u03c3<sup>2<\/sup> =&nbsp; \u03a3 ( Xi \u2013 \u03bc )<sup>2<\/sup> \/ N&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"4-sample-mean\"><\/span><strong>#4 Sample Mean<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The average score of a sample on a specific variable is its sample mean, and its formula is:<\/p>\n\n\n\n<p>x_bar = ( \u03a3 xi ) \/ n<\/p>\n\n\n\n<p>It is the sum of the scores in the sample divided by the total number of data points in the sample.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"5-sample-standard-deviation\"><\/span><strong>#5 Sample Standard Deviation<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The term represents the spread of the scores in a sample for a specific variable. Here\u2019s its formula:<\/p>\n\n\n\n<p>s = sqrt [ \u03a3 ( xi \u2013 x_bar )2 \/ ( n \u2013 1 ) ]<\/p>\n\n\n\n<p>In this formula, the \u201c\u03a3 ( xi \u2013 x_bar )<sup>2<\/sup>\u201d represents the sum of squared deviations of scores from the sample mean.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"6-sample-variance\"><\/span><strong>#6 Sample Variance<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>It is the square of the sample standard deviation and is denoted by s<sup>2<\/sup>, like so:<\/p>\n\n\n\n<p>s<sup>2<\/sup> = \u03a3 ( xi \u2013 x_bar )<sup>2<\/sup> \/ ( n \u2013 1 )<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probability-statistics-equations\"><\/span><strong>Probability Statistics Equations<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The probability of something represents the possibility of an outcome of an event. It is a test of the likelihood of something happening. The most common way of explaining this is the coin toss \u2013 the possibility of the coin showing heads or tails is half and half.&nbsp;&nbsp;<\/p>\n\n\n\n<p>The formula for the probability of an event E is:<\/p>\n\n\n\n<p>P(E) = Number of positive outcomes\/Number of total outcomes = n(E)\/n(S)<\/p>\n\n\n\n<p>There are many <strong>&nbsp;statistics<\/strong> <strong>equations that<\/strong> are used by students and professionals alike. If A and B are two events, then:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Bayes Formula<\/td><td>P(A|B) = P(B|A) P(A)\/P(B)<\/td><\/tr><tr><td>Conditional Probability<\/td><td>P(A|B) = P(A\u2229B)\/P(B)<\/td><\/tr><tr><td>Disjoint Events<\/td><td>P(A\u2229B) = 0<\/td><\/tr><tr><td>Independent Events<\/td><td>P(A\u2229B) = P(A)P(B)<\/td><\/tr><tr><td>Mutually Exclusive Events<\/td><td>P(A\u222aB) = P(A) + P(B)<\/td><\/tr><tr><td>Probability Range<\/td><td>The likelihood of an event ranges from 0 to 1. This is expressed mathematically as 0 \u2264 P(A) \u2264 1.<\/td><\/tr><tr><td>Rule of Addition<\/td><td>P(A\u222aB) = P(A) + P(B) \u2013 P(A\u2229B)<\/td><\/tr><tr><td>Rule of Complementary Events<\/td><td>P(A\u2019) + P(A) = 1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regression-equations-statistics\"><\/span><strong>Regression Equations Statistics<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Regression equations allow us to determine whether there is any relationship between two data sets. The equations facilitate regression analysis, one of the most popular methods to determine the connection between dependent and independent variables.&nbsp;<\/p>\n\n\n\n<p>The equations help assess the strength of the connection between two variables and depending on the outcome; the equations may be used to model the relationship between the variables later.<\/p>\n\n\n\n<p>A simple regression analysis is measuring the height growth of a child. Let\u2019s say you measure the child\u2019s height annually and determine that they grow three inches every year. This trend of growth may be modeled using a regression equation.<\/p>\n\n\n\n<p>Real-world regression analysis examples include calculating the odds of natural disasters and price changes in commodities of all kinds.<\/p>\n\n\n\n<p>The formula for regression is:<\/p>\n\n\n\n<p>Y = a + bX + \u2208<\/p>\n\n\n\n<p>The \u201cY\u201d is the dependent variable, and as you can guess, \u201cX\u201d is the independent variable. The \u201ca\u201d represents the intercept, \u201cb\u201d is the slope, and \u201c\u2208\u201d is the error.<\/p>\n\n\n\n<p>Working out the values of the intercept and slope is as simple as applying the following formula:<\/p>\n\n\n\n<p>a = (\u03a3y)(\u03a3x<sup>2<\/sup>) &#8211; (\u03a3x)(\u03a3xy)\/ n(\u03a3x<sup>2<\/sup>) &#8211; (\u03a3x)<sup>2<\/sup><\/p>\n\n\n\n<p>b = n (\u03a3xy) &#8211; (\u03a3x)(\u03a3y) \/n(\u03a3x<sup>2<\/sup>) &#8211; (\u03a3x)<sup>2<\/sup><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"conclusion\"><\/span><strong>Conclusion<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Statistics is considered to be a game changer, and statistical techniques are created to examine the key factors of vast data. Various organisations and governments utilise statistical methods to compute a collective characteristic about workers or people. This property then influences the decisions that the organisations and governments make.<\/p>\n\n\n\n<p>Today, we have discussed all the important statistics equations that are useful to improve your statistics knowledge. Try to remember these equations as, without these, you can not solve any of the statistics-related problems.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Karl Pearson has beautifully said &#8211; &#8220;Statistics Is The Grammar Of Science&#8221; Although statistics is said to be a part of mathematics. There are various application of mathematics in statistics. The mathematics of working with numeric data and analyzing it is called statistics. More formally, it is the study of data collection, interpretation, organization, and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":11428,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[1153],"tags":[1507,1508,1505,1506],"class_list":["post-11426","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sponsored","tag-important-statistics-equations","tag-statistics-equation-types","tag-statistics-equations","tag-what-are-statistics-equation"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/statanalytica.com\/blog\/wp-json\/wp\/v2\/posts\/11426","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statanalytica.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statanalytica.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statanalytica.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statanalytica.com\/blog\/wp-json\/wp\/v2\/comments?post=11426"}],"version-history":[{"count":0,"href":"https:\/\/statanalytica.com\/blog\/wp-json\/wp\/v2\/posts\/11426\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/statanalytica.com\/blog\/wp-json\/wp\/v2\/media\/11428"}],"wp:attachment":[{"href":"https:\/\/statanalytica.com\/blog\/wp-json\/wp\/v2\/media?parent=11426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statanalytica.com\/blog\/wp-json\/wp\/v2\/categories?post=11426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statanalytica.com\/blog\/wp-json\/wp\/v2\/tags?post=11426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}