{"id":1817,"date":"2023-07-24T21:01:52","date_gmt":"2023-07-24T21:01:52","guid":{"rendered":"https:\/\/statorials.org\/pl\/srednia-z-tabeli-czestotliwosci\/"},"modified":"2023-07-24T21:01:52","modified_gmt":"2023-07-24T21:01:52","slug":"srednia-z-tabeli-czestotliwosci","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/srednia-z-tabeli-czestotliwosci\/","title":{"rendered":"Jak obliczy\u0107 \u015bredni\u0105 z tabeli cz\u0119sto\u015bci (z przyk\u0142adami)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Mo\u017cesz obliczy\u0107 \u015bredni\u0105 z tabeli cz\u0119sto\u015bci, korzystaj\u0105c z nast\u0119puj\u0105cego wzoru:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u015arednia = \u03a3fx \/ \u03a3f<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : fantazyjny symbol oznaczaj\u0105cy \u201esum\u0119\u201d<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>f<\/strong> : Cz\u0119stotliwo\u015b\u0107 okre\u015blonej warto\u015bci<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x<\/strong> : Warto\u015b\u0107 w tabeli cz\u0119stotliwo\u015bci<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Poni\u017csze przyk\u0142ady pokazuj\u0105, jak zastosowa\u0107 t\u0119 formu\u0142\u0119 w praktyce.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 1: \u015brednia liczba zwyci\u0119stw<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017csza tabela cz\u0119stotliwo\u015bci przedstawia \u0142\u0105czn\u0105 liczb\u0119 zwyci\u0119stw 30 dru\u017cyn pi\u0142karskich w danej lidze:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-17620 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/frequencemoyenne1.png\" alt=\"\" width=\"157\" height=\"227\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Do obliczenia \u015bredniej liczby zwyci\u0119stw mo\u017cemy u\u017cy\u0107 poni\u017cszego wzoru:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u015arednia = (0*2 + 1*3 + 2*7 + 3*8 + 4*7 + 5*3) \/ (2 + 3 + 7 + 8 + 7 + 3)<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u015arednia = (0 + 3 + 14 + 24 + 28 + 15) \/ (30)<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u015arednia = (84) \/ (30)<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u015arednia = <strong>2,8<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u015arednia liczba zwyci\u0119stw wynosi <strong>2,8<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 2: \u015arednia liczba zwierz\u0105t domowych<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017csza tabela cz\u0119sto\u015bci przedstawia ca\u0142kowit\u0105 liczb\u0119 zwierz\u0105t nale\u017c\u0105cych do 20 r\u00f3\u017cnych rodzin w danej okolicy:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-17621 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/frequencemoyenne2.png\" alt=\"\" width=\"165\" height=\"201\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Aby obliczy\u0107 \u015bredni\u0105 liczb\u0119 posiadanych zwierz\u0105t, mo\u017cemy skorzysta\u0107 z nast\u0119puj\u0105cego wzoru:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u015arednia = (0*2 + 1*10 + 2*4 + 3*3 + 4*1) \/ (2 + 10 + 4 + 3 + 1)<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u015arednia = (0 + 10 + 8 + 9 + 4) \/ (20)<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u015arednia = (31) \/ (20)<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u015arednia = <strong>1,55<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u015arednia liczba posiadanych zwierz\u0105t wynosi <strong>1,55<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 3: \u015arednia wielko\u015b\u0107 gospodarstwa domowego<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017csza tabela cz\u0119sto\u015bci przedstawia wielko\u015b\u0107 gospodarstw domowych 40 r\u00f3\u017cnych gospodarstw domowych na danym obszarze:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-17623 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/frequencemoyenne3.png\" alt=\"\" width=\"211\" height=\"269\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Aby obliczy\u0107 \u015bredni\u0105 wielko\u015b\u0107 gospodarstwa domowego, mo\u017cemy skorzysta\u0107 z nast\u0119puj\u0105cego wzoru:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u015arednia = (1*2 + 2*4 + 3*14 + 4*13 + 5*4 + 6*2 + 7*1) \/ (2 + 4 + 14 + 13 + 4 + 2+1)<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u015arednia = (2 + 8 + 42 + 52 + 20 + 12 + 7) \/ (40)<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u015arednia = (143) \/ (40)<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u015arednia = <strong>3,575<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u015arednia wielko\u015b\u0107 gospodarstwa domowego wynosi <strong>3575 os\u00f3b<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pl\/mediana-tabeli-czestosci\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 median\u0119 z tabeli cz\u0119sto\u015bci<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/tryb-z-tabeli-czestotliwosci\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 mod z tabeli cz\u0119stotliwo\u015bci<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/wykres-\u0142odygi-i-liscia-oznacza-tryb-mediany\/\" target=\"_blank\" rel=\"noopener\">Jak znale\u017a\u0107 \u015bredni\u0105, median\u0119 i mod\u0119 na wykresach \u0142odyg i li\u015bci<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/mediana-sredniego-histogramu\/\" target=\"_blank\" rel=\"noopener\">Jak oszacowa\u0107 \u015bredni\u0105 i median\u0119 histogram\u00f3w<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/kiedy-uzywac-sredniej-vs-mediany\/\" target=\"_blank\" rel=\"noopener\">Kiedy stosowa\u0107 \u015bredni\u0105 a kiedy median\u0119<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mo\u017cesz obliczy\u0107 \u015bredni\u0105 z tabeli cz\u0119sto\u015bci, korzystaj\u0105c z nast\u0119puj\u0105cego wzoru: \u015arednia = \u03a3fx \/ \u03a3f Z\u0142oto: \u03a3 : fantazyjny symbol oznaczaj\u0105cy \u201esum\u0119\u201d f : Cz\u0119stotliwo\u015b\u0107 okre\u015blonej warto\u015bci x : Warto\u015b\u0107 w tabeli cz\u0119stotliwo\u015bci Poni\u017csze przyk\u0142ady pokazuj\u0105, jak zastosowa\u0107 t\u0119 formu\u0142\u0119 w praktyce. Przyk\u0142ad 1: \u015brednia liczba zwyci\u0119stw Poni\u017csza tabela cz\u0119stotliwo\u015bci przedstawia \u0142\u0105czn\u0105 liczb\u0119 zwyci\u0119stw 30 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1817","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jak obliczy\u0107 \u015bredni\u0105 z tabeli cz\u0119sto\u015bci (z przyk\u0142adami)<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 \u015bredni\u0105 warto\u015b\u0107 z tabeli cz\u0119sto\u015bci, podaj\u0105c kilka przyk\u0142ad\u00f3w.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pl\/srednia-z-tabeli-czestotliwosci\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak obliczy\u0107 \u015bredni\u0105 z tabeli cz\u0119sto\u015bci (z przyk\u0142adami)\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 \u015bredni\u0105 warto\u015b\u0107 z tabeli cz\u0119sto\u015bci, podaj\u0105c kilka przyk\u0142ad\u00f3w.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/srednia-z-tabeli-czestotliwosci\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-24T21:01:52+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/frequencemoyenne1.png\" \/>\n<meta name=\"author\" content=\"Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuta\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/srednia-z-tabeli-czestotliwosci\/\",\"url\":\"https:\/\/statorials.org\/pl\/srednia-z-tabeli-czestotliwosci\/\",\"name\":\"Jak obliczy\u0107 \u015bredni\u0105 z tabeli cz\u0119sto\u015bci (z przyk\u0142adami)\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-24T21:01:52+00:00\",\"dateModified\":\"2023-07-24T21:01:52+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 \u015bredni\u0105 warto\u015b\u0107 z tabeli cz\u0119sto\u015bci, podaj\u0105c kilka przyk\u0142ad\u00f3w.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/srednia-z-tabeli-czestotliwosci\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/srednia-z-tabeli-czestotliwosci\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/srednia-z-tabeli-czestotliwosci\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak obliczy\u0107 \u015bredni\u0105 z tabeli cz\u0119sto\u015bci (z przyk\u0142adami)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pl\/#website\",\"url\":\"https:\/\/statorials.org\/pl\/\",\"name\":\"Statorials\",\"description\":\"Tw\u00f3j przewodnik po kompetencjach statystycznych!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pl-PL\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\",\"name\":\"Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pl-PL\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin Anderson\"},\"description\":\"Cze\u015b\u0107, jestem Benjamin i jestem emerytowanym profesorem statystyki, kt\u00f3ry zosta\u0142 oddanym nauczycielem Statorials. 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