{"id":1236,"date":"2023-07-27T04:34:55","date_gmt":"2023-07-27T04:34:55","guid":{"rendered":"https:\/\/statorials.org\/pl\/normalizuj-dane-w-zakresie-od-0-do-100\/"},"modified":"2023-07-27T04:34:55","modified_gmt":"2023-07-27T04:34:55","slug":"normalizuj-dane-w-zakresie-od-0-do-100","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/normalizuj-dane-w-zakresie-od-0-do-100\/","title":{"rendered":"Jak normalizowa\u0107 dane od 0 do 100"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Aby znormalizowa\u0107 warto\u015bci w zbiorze danych od 0 do 100, mo\u017cesz u\u017cy\u0107 nast\u0119puj\u0105cej formu\u0142y:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>z <sub>i<\/sub> = (x <sub>i<\/sub> \u2013 min(x)) \/ (max(x) \u2013 min(x)) * 100<\/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>min(x)<\/strong> : Minimalna warto\u015b\u0107 w zbiorze danych<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>max(x):<\/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:<br \/><\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12259 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normaliser1.png\" alt=\"\" width=\"90\" height=\"300\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Minimalna warto\u015b\u0107 w zbiorze danych to 12, a maksymalna warto\u015b\u0107 to 68.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Aby znormalizowa\u0107 pierwsz\u0105 warto\u015b\u0107 <strong>12<\/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> = (x <sub>i<\/sub> \u2013 min(x)) \/ (max(x) \u2013 min(x)) *<\/strong> <strong>100<\/strong> = (12 \u2013 12) \/ (68 \u2013 12) * 100 = <strong>0<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Aby znormalizowa\u0107 drug\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> = (x <sub>i<\/sub> \u2013 min(x)) \/ (max(x) \u2013 min(x)) *<\/strong> <strong>100<\/strong> = (19 \u2013 12) \/ (68 \u2013 12) * 100 = <strong>12,5<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Aby znormalizowa\u0107 trzeci\u0105 warto\u015b\u0107 <strong>21<\/strong> , u\u017cyliby\u015bmy tego samego wzoru:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>z <sub>i<\/sub> = (x <sub>i<\/sub> \u2013 min(x)) \/ (max(x) \u2013 min(x)) *<\/strong> <strong>100<\/strong> = (21 \u2013 12) \/ (68 \u2013 12) * 100 = <strong>16,07<\/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 w zakresie od 0 do 100:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12260 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normaliser2.png\" alt=\"Normalizuj dane w zakresie od 0 do 100\" width=\"167\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Jak normalizowa\u0107 dane w dowolnym zakresie<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">W rzeczywisto\u015bci mo\u017cemy u\u017cy\u0107 tej formu\u0142y do normalizacji zbioru danych od 0 do dowolnej liczby:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>z <sub>i<\/sub> = (x <sub>i<\/sub> \u2013 min(x)) \/ (max(x) \u2013 min(x)) * Q<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">gdzie <strong>Q<\/strong> jest maksymaln\u0105 liczb\u0105 wymagan\u0105 dla znormalizowanych warto\u015bci danych.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W poprzednim przyk\u0142adzie wybrali\u015bmy Q na 100, ale mogliby\u015bmy \u0142atwo znormalizowa\u0107 zakres warto\u015bci danych od 0 do 1000, wybieraj\u0105c Q na 1000:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Aby znormalizowa\u0107 pierwsz\u0105 warto\u015b\u0107 <strong>12<\/strong> , zastosowaliby\u015bmy wz\u00f3r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>z <sub>i<\/sub> = (x <sub>i<\/sub> \u2013 min(x)) \/ (max(x) \u2013 min(x)) *<\/strong> <strong>1000<\/strong> = (12 \u2013 12) \/ (68 \u2013 12) * 100 = <strong>0<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Aby znormalizowa\u0107 drug\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> = (x <sub>i<\/sub> \u2013 min(x)) \/ (max(x) \u2013 min(x)) *<\/strong> <strong>1000<\/strong> = (19 \u2013 12) \/ (68 \u2013 12) * 100 = <strong>125<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Aby znormalizowa\u0107 trzeci\u0105 warto\u015b\u0107 <strong>21<\/strong> , u\u017cyliby\u015bmy tego samego wzoru:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>z <sub>i<\/sub> = (x <sub>i<\/sub> \u2013 min(x)) \/ (max(x) \u2013 min(x)) *<\/strong> <strong>1000<\/strong> = (21 \u2013 12) \/ (68 \u2013 12) * 100 = <strong>160,7<\/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 w zakresie od 0 do 1000:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12261 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normaliser3.png\" alt=\"Normalizuj dane mi\u0119dzy dwiema liczbami\" width=\"174\" height=\"288\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Kiedy normalizowa\u0107 dane<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Czasami standaryzujemy zmienne, gdy przeprowadzamy pewien rodzaj analizy, 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 niepo\u017c\u0105danego wp\u0142ywu, zw\u0142aszcza je\u015bli jest ona mierzona w r\u00f3\u017cnych jednostkach (tzn. je\u015bli jedna zmienna jest mierzona w calach, a druga w jardach).<\/span><\/p>\n<p> <span style=\"color: #000000;\">Warto r\u00f3wnie\u017c zauwa\u017cy\u0107, \u017ce w tym samouczku zastosowali\u015bmy metod\u0119 znan\u0105 jako <strong>normalizacja min-max,<\/strong> aby znormalizowa\u0107 warto\u015bci danych.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Dwie najpopularniejsze metody normalizacji to:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Normalizacja Min-Max<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><b>Cel:<\/b> Konwertuje ka\u017cd\u0105 warto\u015b\u0107 danych na warto\u015b\u0107 z zakresu od 0 do 100.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Wz\u00f3r:<\/strong> Nowa warto\u015b\u0107 = (warto\u015b\u0107 \u2013 min) \/ (max \u2013 min) * 100<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>2. \u015arednia normalizacja<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><b>Cel:<\/b> Skaluje warto\u015bci w taki spos\u00f3b, aby \u015brednia wszystkich warto\u015bci wynosi\u0142a 0 i std. rozw. jest 1.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Wz\u00f3r:<\/strong> Nowa warto\u015b\u0107 = (warto\u015b\u0107 \u2013 \u015brednia) \/ (odchylenie standardowe)<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pl\/normalizuj-dane-od-0-do-1\/\">Jak normalizowa\u0107 dane mi\u0119dzy 0 a 1<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/normalizowac-dane-excela\/\" target=\"_blank\" rel=\"noopener noreferrer\">Jak normalizowa\u0107 dane w programie Excel<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/jak-normalizowac-dane-w-r\/\" target=\"_blank\" rel=\"noopener noreferrer\">Jak normalizowa\u0107 dane w R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/normalizuj-kolumny-ramki-danych-pand\/\" target=\"_blank\" rel=\"noopener noreferrer\">Jak normalizowa\u0107 kolumny w Pythonie<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aby znormalizowa\u0107 warto\u015bci w zbiorze danych od 0 do 100, mo\u017cesz u\u017cy\u0107 nast\u0119puj\u0105cej formu\u0142y: z i = (x i \u2013 min(x)) \/ (max(x) \u2013 min(x)) * 100 Z\u0142oto: z i : i-ta znormalizowana warto\u015b\u0107 w zbiorze danych x i : i-ta warto\u015b\u0107 zbioru danych min(x) : Minimalna warto\u015b\u0107 w zbiorze danych max(x): Maksymalna warto\u015b\u0107 w [&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-1236","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - 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