{"id":57,"date":"2022-12-20T15:02:36","date_gmt":"2022-12-20T15:02:36","guid":{"rendered":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/?page_id=57"},"modified":"2025-04-28T15:14:35","modified_gmt":"2025-04-28T15:14:35","slug":"dz-statistisch-kenngroessen","status":"publish","type":"page","link":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/dz-statistisch-kenngroessen\/","title":{"rendered":"Statistisch Kenngr\u00f6\u00dfen"},"content":{"rendered":"\n<p>Hier erf\u00e4hrst du, wie man folgende statistische Kenngr\u00f6\u00dfen berechnet:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Durchschnitt \/ arithmetisches Mittel<\/li>\n\n\n\n<li>Median<\/li>\n\n\n\n<li>Modus bzw. Modalwert<\/li>\n\n\n\n<li>Maximum<\/li>\n\n\n\n<li>Minimum<\/li>\n\n\n\n<li>Spannweite<\/li>\n<\/ul>\n\n\n\n<p><strong>Beispielaufgabe: In der nachfolgende Liste finden sich die Anzahl der Abonnenten (in Millionen) der aufgez\u00e4hlten YouTube-Kan\u00e4len (Stand 2024). Berechnen Sie das arithmetische Mittel, den Median, den Modalwert das Maximum, das Minimum und die Spannweite.<\/strong> <strong>Passende Informationen finden Sie im Lernvideo. Die L\u00f6sung gibt es weiter unten \ud83d\ude42<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>T-Series<\/td><td>258 Mio.<\/td><\/tr><tr><td>MrBeast<\/td><td>236 Mio.<\/td><\/tr><tr><td>Set India<\/td><td>168 Mio.<\/td><\/tr><tr><td>WWE<\/td><td>99,3 Mio.<\/td><\/tr><tr><td>Vlad and Niki<\/td><td>109 Mio.<\/td><\/tr><tr><td>Cocomelon &#8211; Nursery Rhymes<\/td><td>171 Mio.<\/td><\/tr><tr><td>Kids Diana Show<\/td><td>118 Mio<\/td><\/tr><tr><td>PewDiePie<\/td><td>111 Mio.<\/td><\/tr><tr><td>Zee Music Company<\/td><td>104 Mio.<\/td><\/tr><tr><td>Like Nastya<\/td><td>112 Mio.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n<style>.kt-accordion-id57_2cdf9c-ea .kt-accordion-inner-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:0px;}.kt-accordion-id57_2cdf9c-ea .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;padding-top:var(--global-kb-spacing-sm, 1.5rem);padding-right:var(--global-kb-spacing-sm, 1.5rem);padding-bottom:var(--global-kb-spacing-sm, 1.5rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kt-accordion-id57_2cdf9c-ea > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;background:#f2f2f2;color:#555555;padding-top:10px;padding-right:14px;padding-bottom:10px;padding-left:14px;}.kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap .kt-blocks-accordion-icon-trigger:before{background:#555555;}.kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger{background:#555555;}.kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:before{background:#f2f2f2;}.kt-accordion-id57_2cdf9c-ea > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header:hover, \n\t\t\t\tbody:not(.hide-focus-outline) .kt-accordion-id57_2cdf9c-ea .kt-blocks-accordion-header:focus-visible{color:#444444;background:#eeeeee;border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion--visible .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:before{background:#444444;}.kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger, body:not(.hide-focus-outline) .kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger{background:#444444;}.kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:before{background:#eeeeee;}.kt-accordion-id57_2cdf9c-ea .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id57_2cdf9c-ea > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{color:#ffffff;background:#444444;border-top-color:#444444;border-top-style:solid;border-right-color:#444444;border-right-style:solid;border-bottom-color:#444444;border-bottom-style:solid;border-left-color:#444444;border-left-style:solid;}.kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger{background:#ffffff;}.kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id57_2cdf9c-ea:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#444444;}@media all and (max-width: 1024px){.kt-accordion-id57_2cdf9c-ea .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}}@media all and (max-width: 1024px){.kt-accordion-id57_2cdf9c-ea > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}}@media all and (max-width: 1024px){.kt-accordion-id57_2cdf9c-ea > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header:hover, \n\t\t\t\tbody:not(.hide-focus-outline) .kt-accordion-id57_2cdf9c-ea .kt-blocks-accordion-header:focus-visible{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}}@media all and (max-width: 1024px){.kt-accordion-id57_2cdf9c-ea .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id57_2cdf9c-ea > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#444444;border-top-style:solid;border-right-color:#444444;border-right-style:solid;border-bottom-color:#444444;border-bottom-style:solid;border-left-color:#444444;border-left-style:solid;}}@media all and (max-width: 767px){.kt-accordion-id57_2cdf9c-ea .kt-accordion-inner-wrap{display:block;}.kt-accordion-id57_2cdf9c-ea .kt-accordion-inner-wrap .kt-accordion-pane:not(:first-child){margin-top:0px;}.kt-accordion-id57_2cdf9c-ea .kt-accordion-panel-inner{border-top:0px solid transparent;border-right:0px solid transparent;border-bottom:0px solid transparent;border-left:0px solid transparent;}.kt-accordion-id57_2cdf9c-ea > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top:0px solid #f2f2f2;border-right:0px solid #f2f2f2;border-bottom:0px solid #f2f2f2;border-left:0px solid #f2f2f2;}.kt-accordion-id57_2cdf9c-ea > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header:hover, \n\t\t\t\tbody:not(.hide-focus-outline) .kt-accordion-id57_2cdf9c-ea .kt-blocks-accordion-header:focus-visible{border-top-color:#eeeeee;border-top-style:solid;border-right-color:#eeeeee;border-right-style:solid;border-bottom-color:#eeeeee;border-bottom-style:solid;border-left-color:#eeeeee;border-left-style:solid;}.kt-accordion-id57_2cdf9c-ea .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id57_2cdf9c-ea > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{border-top-color:#444444;border-top-style:solid;border-right-color:#444444;border-right-style:solid;border-bottom-color:#444444;border-bottom-style:solid;border-left-color:#444444;border-left-style:solid;}}<\/style>\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id57_2cdf9c-ea kt-accordion-has-4-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"true\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane57_e33832-12\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Lernvideo statistische Kenngr\u00f6\u00dfen (arithmetisches Mittel, Median, Maximum, Minimum, Spannweite)<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" hcb-fetch-image-from=\"https:\/\/www.youtube.com\/watch?v=UxKgca3l1G4\" title=\"Statistische Kennwerte - Durchschnitt | Median | Modalwert | Max | Min | Spannweite\" width=\"800\" height=\"450\" src=\"https:\/\/www.youtube.com\/embed\/UxKgca3l1G4?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane57_a17eb7-c4\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">L\u00f6sung Beispielaufgabe<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p>Bevor wir die Kenngr\u00f6\u00dfen berechnen k\u00f6nnen, m\u00fcssen die gegebenen Daten in eine <strong>Rangliste zun\u00e4chst sortiert<\/strong> werden:<\/p>\n\n\n\n<p><strong>Rangliste<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>WWE<\/td><td>99,3<\/td><\/tr><tr><td>Zee Music Company<\/td><td>104<\/td><\/tr><tr><td>Vlad and Niki<\/td><td>109<\/td><\/tr><tr><td>PewDiePie<\/td><td>111<\/td><\/tr><tr><td>Like Nastya<\/td><td>112<\/td><\/tr><tr><td>Kids Diana Show<\/td><td>118<\/td><\/tr><tr><td>Set India<\/td><td>168<\/td><\/tr><tr><td>Cocomelon &#8211; Nursery Rhymes<\/td><td>171<\/td><\/tr><tr><td>MrBeast<\/td><td>236<\/td><\/tr><tr><td>T-Series<\/td><td>258<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Der <strong>Durchschnitt <\/strong>wird auch als arithmetisches Mittel bezeichnet und wie folgt berechnet:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>Durchschnitt = \\frac{Summe\\ aller\\ Werte}{Anzahl\\ aller\\ Werte} = \\frac{99,3+104+109+111+112+118+168+171+236+258}{10} = 148,63<\/pre><\/div>\n\n\n\n<p>Der <strong>Median<\/strong> ist der Zentralwert der Rangliste. Also der Wert, der genau in der Mitte steht. Bei einer geraden Anzahl von Werten, muss er also wie folgt berechnet werde:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>x_{med} = \\frac{112+118}{2} = 115<\/pre><\/div>\n\n\n\n<p>Um die <strong>Spannweite (engl. &#8222;Range&#8220; = R) <\/strong>zu berechnen, m\u00fcssen wir vom gr\u00f6\u00dften Wert den kleinsten Wert abziehen:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>R=x_{max}-x_{min} = 258 - 99,3 = 158,7<\/pre><\/div>\n\n\n\n<p>Der <strong>Modus oder Modalwert<\/strong> ist der Wert, der am h\u00e4ufigsten vorkommt. In dieser Aufgabe kommt jeder Wert nur 1x vor. Somit ist jeder Wert auch zugleich der Modalwert.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane57_877e6d-47\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Digitale \u00dcbungsaufgaben<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-16\" class=\"h5p-iframe\" data-content-id=\"16\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Statistische Kenngr\u00f6\u00dfen berechnen\"><\/iframe><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hier erf\u00e4hrst du, wie man folgende statistische Kenngr\u00f6\u00dfen berechnet: Beispielaufgabe: In der nachfolgende Liste finden sich die Anzahl der Abonnenten<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"colormag_page_container_layout":"default_layout","colormag_page_sidebar_layout":"default_layout","footnotes":""},"class_list":["post-57","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/pages\/57","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/comments?post=57"}],"version-history":[{"count":21,"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/pages\/57\/revisions"}],"predecessor-version":[{"id":1243,"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/pages\/57\/revisions\/1243"}],"wp:attachment":[{"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/media?parent=57"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}