{"id":1685,"date":"2024-05-17T19:34:12","date_gmt":"2024-05-17T23:34:12","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=chapter&#038;p=1685"},"modified":"2024-05-17T19:49:43","modified_gmt":"2024-05-17T23:49:43","slug":"the-mean-and-standard-deviation-of-poisson-distributions","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/the-mean-and-standard-deviation-of-poisson-distributions\/","title":{"raw":"The Mean and Standard Deviation of Poisson Distributions","rendered":"The Mean and Standard Deviation of Poisson Distributions"},"content":{"raw":"<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nCalculate the mean and standard deviation of Poisson distributions.\r\n\r\n<\/div>\r\n<\/div>\r\n<h2>Calculating the Mean<\/h2>\r\n<ul>\r\n \t<li>The mean of a Poisson distribution is the mean that is stated in the problem:<\/li>\r\n \t<li>mean [latex]=\u00a0 \\lambda [\/latex]<\/li>\r\n<\/ul>\r\n<h2>Calculating the Standard Deviation<\/h2>\r\n<ul>\r\n \t<li>We can also easily calculate the standard deviation of a Poisson distribution:<\/li>\r\n \t<li>standard deviation [latex]= \\sigma = \\sqrt{\\lambda} [\/latex]<\/li>\r\n<\/ul>\r\n<h2>Example 33.1<\/h2>\r\n<span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: There are, on average, 28,000 bankruptcies filed in Canada per year according to the <a href=\"https:\/\/ised-isde.canada.ca\/site\/office-superintendent-bankruptcy\/en\/statistics-and-research\/insolvency-statistics-canada-march-2023#t2\">Office of the Superintendent of Bankruptcy<\/a> in Canada<span style=\"font-size: 20.5333px\">.<\/span>\r\n\r\n<span style=\"color: #003366\"><strong>Question<\/strong><\/span>: What are the mean and standard deviation for this problem?\r\n\r\n<span style=\"color: #003366\"><strong>Solution<\/strong><\/span>: <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/05\/Example33-1.xlsx\">Click here<\/a> to download the Excel solution. Also, see the solutions below:\r\n<ul>\r\n \t<li>mean [latex] = \\lambda = 28,000 [\/latex]<\/li>\r\n \t<li>standard deviation [latex]= \\sigma = \\sqrt{\\lambda} = \\sqrt{28,000} = 167.33201 [\/latex]<\/li>\r\n<\/ul>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Calculate the mean and standard deviation of Poisson distributions.<\/p>\n<\/div>\n<\/div>\n<h2>Calculating the Mean<\/h2>\n<ul>\n<li>The mean of a Poisson distribution is the mean that is stated in the problem:<\/li>\n<li>mean [latex]=\u00a0 \\lambda[\/latex]<\/li>\n<\/ul>\n<h2>Calculating the Standard Deviation<\/h2>\n<ul>\n<li>We can also easily calculate the standard deviation of a Poisson distribution:<\/li>\n<li>standard deviation [latex]= \\sigma = \\sqrt{\\lambda}[\/latex]<\/li>\n<\/ul>\n<h2>Example 33.1<\/h2>\n<p><span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: There are, on average, 28,000 bankruptcies filed in Canada per year according to the <a href=\"https:\/\/ised-isde.canada.ca\/site\/office-superintendent-bankruptcy\/en\/statistics-and-research\/insolvency-statistics-canada-march-2023#t2\">Office of the Superintendent of Bankruptcy<\/a> in Canada<span style=\"font-size: 20.5333px\">.<\/span><\/p>\n<p><span style=\"color: #003366\"><strong>Question<\/strong><\/span>: What are the mean and standard deviation for this problem?<\/p>\n<p><span style=\"color: #003366\"><strong>Solution<\/strong><\/span>: <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/05\/Example33-1.xlsx\">Click here<\/a> to download the Excel solution. Also, see the solutions below:<\/p>\n<ul>\n<li>mean [latex]= \\lambda = 28,000[\/latex]<\/li>\n<li>standard deviation [latex]= \\sigma = \\sqrt{\\lambda} = \\sqrt{28,000} = 167.33201[\/latex]<\/li>\n<\/ul>\n","protected":false},"author":865,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1685","chapter","type-chapter","status-publish","hentry"],"part":237,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1685","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/users\/865"}],"version-history":[{"count":7,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1685\/revisions"}],"predecessor-version":[{"id":1694,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1685\/revisions\/1694"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/237"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1685\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/media?parent=1685"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=1685"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/contributor?post=1685"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/license?post=1685"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}