{"id":4064,"date":"2023-07-13T20:27:06","date_gmt":"2023-07-13T20:27:06","guid":{"rendered":"https:\/\/statorials.org\/pl\/normalizuj-dane-pomiedzy-1-a-1\/"},"modified":"2023-07-13T20:27:06","modified_gmt":"2023-07-13T20:27:06","slug":"normalizuj-dane-pomiedzy-1-a-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/normalizuj-dane-pomiedzy-1-a-1\/","title":{"rendered":"Jak normalizowa\u0107 dane mi\u0119dzy -1 a 1"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Aby znormalizowa\u0107 warto\u015bci w zbiorze danych od -1 do 1, mo\u017cesz u\u017cy\u0107 nast\u0119puj\u0105cej formu\u0142y:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>z <sub>ja<\/sub> = 2 * ((x <sub>i<\/sub> \u2013 x <sub>min<\/sub> ) \/ (x <sub>max<\/sub> \u2013 x <sub>min<\/sub> )) \u2013 1<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>z <sub>i<\/sub> :<\/strong> <sup>i-ta<\/sup> znormalizowana warto\u015b\u0107 w zbiorze danych<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>i<\/sub> :<\/strong> <sup>i-ta<\/sup> warto\u015b\u0107 zbioru danych<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>min<\/sub><\/strong> : Minimalna warto\u015b\u0107 w zbiorze danych<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>max<\/sub> :<\/strong> Maksymalna warto\u015b\u0107 w zbiorze danych<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy na przyk\u0142ad, \u017ce mamy nast\u0119puj\u0105cy zestaw danych:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-16491 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normaliser01.png\" alt=\"\" width=\"94\" height=\"341\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Minimalna warto\u015b\u0107 w zbiorze danych to 13, a maksymalna warto\u015b\u0107 to 71.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Aby znormalizowa\u0107 pierwsz\u0105 warto\u015b\u0107 <strong>13<\/strong> , zastosowaliby\u015bmy udost\u0119pnion\u0105 wcze\u015bniej formu\u0142\u0119:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>z <sub>i<\/sub> = 2 * ((x <sub>i<\/sub> \u2013 x <sub>min<\/sub> ) \/ (x <sub>max<\/sub> \u2013 x <sub>min<\/sub> )) \u2013 1<\/strong> = 2 * ((13 \u2013 13) \/ (71 \u2013 13)) \u2013 1 = <strong>-1<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Aby znormalizowa\u0107 drug\u0105 warto\u015b\u0107 <strong>16<\/strong> , u\u017cyliby\u015bmy tego samego wzoru:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>z <sub>i<\/sub> = 2 * ((x <sub>i<\/sub> \u2013 x <sub>min<\/sub> ) \/ (x <sub>max<\/sub> \u2013 x <sub>min<\/sub> )) \u2013 1<\/strong> = 2 * ((16 \u2013 13) \/ (71 \u2013 13)) \u2013 1 = <strong>-0,897<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Aby znormalizowa\u0107 trzeci\u0105 warto\u015b\u0107 <strong>19<\/strong> , u\u017cyliby\u015bmy tego samego wzoru:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>z <sub>i<\/sub> = 2 * ((x <sub>i<\/sub> \u2013 x <sub>min<\/sub> ) \/ (x <sub>max<\/sub> \u2013 x <sub>min<\/sub> )) \u2013 1<\/strong> = 2 * ((19 \u2013 13) \/ (71 \u2013 13)) \u2013 1 = <strong>-0,793<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Mo\u017cemy u\u017cy\u0107 dok\u0142adnie tego samego wzoru, aby znormalizowa\u0107 ka\u017cd\u0105 warto\u015b\u0107 w oryginalnym zbiorze danych pomi\u0119dzy -1 a 1:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-32397 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normbet1.png\" alt=\"\" width=\"202\" height=\"364\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ka\u017cda warto\u015b\u0107 w znormalizowanym zbiorze danych mie\u015bci si\u0119 teraz w przedziale od -1 do 1.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Stosuj\u0105c t\u0119 metod\u0119 normalizacji, nast\u0119puj\u0105ce stwierdzenia b\u0119d\u0105 zawsze prawdziwe:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Znormalizowana warto\u015b\u0107 minimalnej warto\u015bci w zbiorze danych b\u0119dzie zawsze wynosi\u0107 -1.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Znormalizowana warto\u015b\u0107 maksymalnej warto\u015bci w zbiorze danych b\u0119dzie zawsze wynosi\u0107 1.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Znormalizowane warto\u015bci dla wszystkich pozosta\u0142ych warto\u015bci w zbiorze danych b\u0119d\u0105 wynosi\u0107 od -1 do 1.<\/span><\/li>\n<\/ul>\n<h2> <span style=\"color: #000000;\"><strong>Kiedy normalizowa\u0107 dane<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Cz\u0119sto standaryzujemy zmienne, gdy przeprowadzamy analiz\u0119, w kt\u00f3rej mamy wiele zmiennych mierzonych w r\u00f3\u017cnych skalach i chcemy, aby ka\u017cda ze zmiennych mia\u0142a ten sam zakres.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Zapobiega to wywieraniu przez jedn\u0105 zmienn\u0105 zbyt du\u017cego wp\u0142ywu, zw\u0142aszcza je\u015bli jest mierzona w r\u00f3\u017cnych jednostkach (tj. je\u015bli jedna zmienna jest mierzona w calach, a druga w jardach).<\/span><\/p>\n<p> <span style=\"color: #000000;\">Nale\u017cy r\u00f3wnie\u017c pami\u0119ta\u0107, \u017ce zastosowana tutaj metoda normalizacji jest tylko jedn\u0105 z mo\u017cliwych opcji.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W niekt\u00f3rych przypadkach sensowne jest normalizowanie zmiennych z zakresu od 0 do 1, a nawet od 0 do 100.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Poni\u017csze samouczki wyja\u015bniaj\u0105, jak wykonywa\u0107 inne typy normalizacji:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pl\/normalizuj-dane-od-0-do-1\/\" target=\"_blank\" rel=\"noopener\">Jak normalizowa\u0107 dane mi\u0119dzy 0 a 1<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/normalizuj-dane-w-zakresie-od-0-do-100\/\" target=\"_blank\" rel=\"noopener\">Jak normalizowa\u0107 dane od 0 do 100<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aby znormalizowa\u0107 warto\u015bci w zbiorze danych od -1 do 1, mo\u017cesz u\u017cy\u0107 nast\u0119puj\u0105cej formu\u0142y: z ja = 2 * ((x i \u2013 x min ) \/ (x max \u2013 x min )) \u2013 1 Z\u0142oto: z i : i-ta znormalizowana warto\u015b\u0107 w zbiorze danych x i : i-ta warto\u015b\u0107 zbioru danych x min : Minimalna [&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-4064","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 normalizowa\u0107 dane pomi\u0119dzy -1 i 1 - Statologia<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, na przyk\u0142adzie, jak normalizowa\u0107 warto\u015bci w zestawie danych od -1 do 1.\" \/>\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\/normalizuj-dane-pomiedzy-1-a-1\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" 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