Givet en m\303\246ngde p\303\245 n punkter i planen med koordianeter 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vil vi gerne finde den retning hvor variationen er minimal.Dvs faktisk er det den minimale variationen kontra den maksimale variation vi vil g\303\245 efter her.I det f\303\270lgende t\303\246nker vi os at vi har fundet middelv\303\246rdien af x og y-kordinaterne og trukket den fra alle v\303\246rdierne. dvs middelv\303\246rdien af LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImlGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic= og LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImlGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic=-erne er nu begge 0.N\303\245r man har et konkret datas\303\246t m\303\245 man alts\303\245 selv begynde med at finde middelv\303\246rdierne og tr\303\246kke dem fra.Projektionen af stedvektoren for et punkt 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 p\303\245 en given retning 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 er prikproduktet af de to: 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 i den aktuelle retning for hele punktskyen er middelv\303\246rdien af summen over alle punkter af kvadraterne p\303\245 disse prikprodukter, 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Det ses at cos, sin og cossin er det samme for alle led og derfor kan rykkes uden for summationstegnet. For at skrive det mere overskueligt indf\303\270rer vi: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St\303\270rrelserne 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 er alts\303\245 alle blot tal der kan beregnes ud fra punkternes koordinater.L\303\230SNING SOM EGENV\303\206RDIPROBLEMBenytter vi generel teori for et egenv\303\246rdiproblem med vilk\303\245rligt mange dimensioner, ved vi at de \303\270nskede varianser er egenv\303\246rdierne, dvs l\303\270sninger til ligningenLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEoJiM5MzE7dkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSgmIzk1NTt2RidGL0YyLyUrZXhlY3V0YWJsZUdGPUY5 hvor \316\243 st\303\245r for kovariansmatricen. I 2D Ligingen kan ogs\303\245 skrives som 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udfoldet giver det karakteristiske polynomium:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkobWZlbmNlZEdGJDYkLUYjNictSSVtc3VwR0YkNiUtSSNtaUdGJDYlUSJYRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYkUSIyRicvRjtRJ25vcm1hbEYnRjdGOi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSgmbWludXM7RidGQy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGTi8lKXN0cmV0Y2h5R0ZOLyUqc3ltbWV0cmljR0ZOLyUobGFyZ2VvcEdGTi8lLm1vdmFibGVsaW1pdHNHRk4vJSdhY2NlbnRHRk4vJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0Znbi1GNDYlUScmIzk1NTtGJy9GOEZORkMvJStleGVjdXRhYmxlR0ZORkNGQy1GSTYtUScmc2RvdDtGJ0ZDRkxGT0ZRRlNGVUZXRlkvRmZuUSYwLjBlbUYnL0ZpbkZkby1GLDYkLUYjNictRjE2JS1GNDYlUSJZRidGN0Y6Rj1GRUZIRmpuRl5vRkNGQ0ZILUYxNiUtRjQ2JVEjWFlGJ0Y3RjpGPUZFLUZJNi1RIj1GJ0ZDRkxGT0ZRRlNGVUZXRlkvRmZuUSwwLjI3Nzc3NzhlbUYnL0ZpbkZocC1GQDYkRkdGQ0Zeb0ZDLUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JS1JI21vR0YkNi9RJyZyYXJyO0YnLyUrZXhlY3V0YWJsZUdRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JJm10ZXh0R0YkNiZRMXNvbHZlfmZvcn5sYW1iZGFGJ0YvRjJGNUZFLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY2LUkjbWlHRiQ2KVEmc29sdmVGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYxUSIoRidGL0YyRjhGOy9GPlEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjE2NjY2NjdlbUYnLyUncnNwYWNlR0ZWLUZBNjFRIn5GJ0YvRjJGOEY7RkQvRkdGNEZIL0ZLRjRGTEZORlBGUi9GVVEmMC4wZW1GJy9GWEZpbi1GQTYxUSJ8ZnJGJ0YvRjJGOEY7RkRGRkZIRkpGTEZORlBGUkZURldGWS1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUWNxLywmKiYsJiokKUkiWEc2IiIiIyIiIiIiIkknbGFtYmRhRzYiISIiIiIiLCYqJClJIllHNiIiIiMiIiIiIiJJJ2xhbWJkYUc2IiEiIiIiIiIiIiokKUkjWFlHNiIiIiMiIiIhIiIiIiFGJy8lK2FjdGlvbnR5cGVHUTptYXBsZXNvZnQuY29tOmxhYmVsKEwyOTApRicvJSV2aWV3R1EmbGFiZWxGJ0ZZLUZBNjFRInxockYnRi9GMkY4RjtGREZGRkhGSkZMRk5GUEZSRlQvRlhRLDAuMTExMTExMWVtRictRkE2MVEiLEYnRi9GMkY4RjtGREZmbi9GSUY3RmduRkxGTkZQRlJGaG4vRlhRLDAuMzMzMzMzM2VtRidGWS1GQTYxUSJbRidGL0YyRjhGO0ZERkZGSEZKRkxGTkZQRlJGVEZXLUYsNilRJyYjOTU1O0YnRi9GMi9GNkY0RjhGO0ZELUZBNjFRIl1GJ0YvRjJGOEY7RkRGRkZIRkpGTEZORlBGUkZURl5wRlktRkE2MVEiKUYnRi9GMkY4RjtGREZGRkhGSkZMRk5GUEZSRlRGV0YvRjJGOEY7RkQ=JSFHVi ser alts\303\245 at det er muligt direkte at finde en l\303\270sninger der kan opskrives meget simplere.Det ses at udtrykket under kvadratroden kan omskrives: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S\303\245 den mindste l\303\270sning kan ogs\303\245 skrives:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUkjbWlHRiQ2JlEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZm9yZWdyb3VuZEdRKlsyNTUsMCwwXUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi5RKSZlcXVhbHM7RidGMkY1LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJm1mcmFjR0YkNiktSSNtbkdGJDYlUSIxRidGMkY1LUYjNiYtRlM2JVEiMkYnRjJGNS9GMFEldHJ1ZUYnRjIvRjZRJ2l0YWxpY0YnLyUubGluZXRoaWNrbmVzc0dGVS8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zdby8lKWJldmVsbGVkR0YxRjItRjk2LlEiKEYnRjJGNS9GPUZmbkY+L0ZBRmZuRkJGREZGRkgvRktRLDAuMTY2NjY2N2VtRicvRk5GaG8tSSVtc3VwR0YkNiUtRiw2JlEiWEYnRmVuRjJGZ25GWC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjk2LlEnJnBsdXM7RidGMkY1RjxGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GZ3AtRltwNiUtRiw2JlEiWUYnRmVuRjJGZ25GWEZgcEZjcC1JJm1zcXJ0R0YkNiQtRiM2KS1GIzYqLUYsNiNRIUYnLUZbcDYlLUkobWZlbmNlZEdGJDYmLUYjNictRltwNiUtRiw2J0ZfcEZlbkYyLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0Znbi1GIzYlLUZTNiZGWkYyRmNyRjVGMkY1RmBwLUY5Ni9RKCZtaW51cztGJ0YyRmNyRjVGPEY+RkBGQkZERkZGSEZmcEZocC1GW3A2JS1GLDYnRl1xRmVuRjJGY3JGZ25GZnJGYHBGMkY1RjJGY3JGNUZmckZgcC1GOTYvUSIrRidGMkZjckY1RjxGPkZARkJGREZGRkhGZnBGaHAtRlM2JlEiNEYnRjJGY3JGNS1GOTYvUSJ+RidGMkZjckY1RjxGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GW3QtRltwNiUtRiw2J1EjWFlGJ0ZlbkYyRmNyRmduRmZyRmBwRjJGNUZlcUYyLyUrZXhlY3V0YWJsZUdGMS8lKXJlYWRvbmx5R0Zmbi9GZHJRKjJEfk91dHB1dEYnRjVGMkYyRmJ0RmR0RmZ0RjU=Teorien og det matematiske abstraktionsniveau er imidlertid uden for r\303\246kkevide p\303\245 gymnasieniveau.I det f\303\270lgende ser vi p\303\245 hvordan det kan g\303\270res med mere basale v\303\246rkt\303\270jer.L\303\270sning i 2D med simple v\303\246rkt\303\270jer.Den st\303\270rrelse vi skal minimere, ved at v\303\246lge den optimale vinkel v er 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er at differentiere st\303\270rrelsen mht v, s\303\246tte den lig 0, l\303\270se ligningen mht til v OG inds\303\246tte det funde v i L(v).L\303\230SNING I MAPLEVi definerer: 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l\303\270ser s\303\245: 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inds\303\246tter den f\303\270rste l\303\270sning i 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er er l\303\270sning og maple har endda kunnet simplificere via omskrivning af kombinationer af trigonemetriske og inversetrigonometriske.Men det er lidt voldsomt og faktisk kan det reduceres betydeligt Maple kan bare ikke.SUBSTITUTION OG MANUEL L\303\230SNINGDet viser sig hensigtsm\303\246ssigt at indf\303\270re en substitutionen : 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 f\303\270r vi g\303\245r i gang. Det medf\303\270rer LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JJW1zdXBHRiQ2JS1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInZGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHRjFGMkYyLUYjNiUtSSNtbkdGJDYkUSIyRidGMkZARkIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiPUYnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Zdby1GSTYkUSIxRidGMi1GUDYtUSgmbWludXM7RidGMkZTRlVGV0ZZRmVuRmduRmluL0Zcb1EsMC4yMjIyMjIyZW1GJy9GX29GZ28tRiw2JVEidEYnRkBGQkZERjI= og 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 . Vi f\303\245r s\303\245 ligningen: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Vi dividerer nu igennem med 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 i alle led og indf\303\270rer betegnelsen 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Dermed har vi ligningen: 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 der har l\303\270sningerne 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.Nu er vi s\303\245dan set f\303\246rdige. Vi har beregnet 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 kan beregne a, derefter t og inds\303\246tte den funde v\303\246rdi for t i udtrykket for L: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.Det hele kan fx g\303\270res i et regneark.JSFHMANUEL REDUKTIONDet kan lade sig g\303\270re at samle det hele det ovenst\303\245ende i et udtryk og f\303\245 det reduceret. Det er en teoretisk \303\270velse, en gang bogstavregning. Lad os se p\303\245 det.F\303\270rst ser vi p\303\245 st\303\270rrelsen 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 med v\303\246rdien for t indsat: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkmbXNxcnRHRiQ2Iy1GIzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GOFEnbm9ybWFsRictRjE2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0Y6Vi husker at: 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 Vi kan ogs\303\245 skrive dette som LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkmbWZyYWNHRiQ2KC1JJW1zdXBHRiQ2JS1JI21pR0YkNiVRI1hZRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYkUSIyRicvRjlRJ25vcm1hbEYnRjVGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRiM2JS1GMjYlUSJiRidGNUY4RjVGOC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGUC8lKWJldmVsbGVkR1EmZmFsc2VGJy1GMjYjUSFGJy8lK2V4ZWN1dGFibGVHRlVGQQ== i det: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsyNTUsMCwyNTVdRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi9RIj1GJ0YyRjUvRjlRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZDLyUpc3RyZXRjaHlHRkMvJSpzeW1tZXRyaWNHRkMvJShsYXJnZW9wR0ZDLyUubW92YWJsZWxpbWl0c0dGQy8lJ2FjY2VudEdGQy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlItRiM2KC1GLDYjUSFGJy1GIzYqLUklbXN1cEdGJDYlLUkobWZlbmNlZEdGJDYmLUYjNictRmduNiUtRiw2J1EiWEYnRi9GMkY1RjgtRiM2JS1JI21uR0YkNiZRIjJGJ0YyRjVGP0YyRj8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUY8Ni9RKiZ1bWludXMwO0YnRjJGNUY/RkFGREZGRkhGSkZMRk4vRlFRLDAuMjIyMjIyMmVtRicvRlRGYHAtRmduNiUtRiw2J1EiWUYnRi9GMkY1RjhGY29GaW9GMkY/RjJGNUY/RmNvRmlvLUY8Ni9RIitGJ0YyRjVGP0ZBRkRGRkZIRkpGTEZORl9wRmFwLUZmbzYmUSI0RidGMkY1Rj8tRjw2L1EifkYnRjJGNUY/RkFGREZGRkhGSkZMRk4vRlFRJjAuMGVtRicvRlRGYXEtRmduNiUtRiw2J1EjWFlGJ0YvRjJGNUY4RmNvRmlvRjIvJStleGVjdXRhYmxlR0ZDRj9GV0YvRjVGOEZXRmhxRj8=Dermed hav vi 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Herefter ser vi p\303\245 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inds\303\246ttes dette samt t og a i 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=(Vi ser at denne l\303\270sning er identisk med den egenv\303\246rdiproblemet gav.)ET ENDELIGT M\303\205L FOR RETLINETHEDVi har set hvordan variansen i den retning hvor den er henholdsvis minimal og maksimal kan beregnes.Et godt bud p\303\245 "retlinethed" vil v\303\246re forholdet mellem disse to. Det afh\303\246nger naturligvis men ofte vil den realtive variation (i forhold til linjestykkets l\303\246ngde) p\303\245 tv\303\246rs v\303\246re et godt bud.Det er blot forholdet mellem de to vairationer:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkmbWZyYWNHRiQ2KC1GIzYpLUYsNigtSSNtbkdGJDYlUSIxRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYkLUYzNiVRIjJGJ0Y2RjlGOS8lLmxpbmV0aGlja25lc3NHRjUvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRS8lKWJldmVsbGVkR1EmZmFsc2VGJy1JKG1mZW5jZWRHRiQ2JS1GIzYnLUkjbW9HRiQ2LlEifkYnRjZGOS8lJmZlbmNlR0ZKLyUqc2VwYXJhdG9yR0ZKLyUpc3RyZXRjaHlHRkovJSpzeW1tZXRyaWNHRkovJShsYXJnZW9wR0ZKLyUubW92YWJsZWxpbWl0c0dGSi8lJ2FjY2VudEdGSi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRl5vLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnRjYvRjpRJ2l0YWxpY0YnRjwvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUZRNi5RIitGJ0Y2RjlGVEZWRlhGWkZmbkZobkZqbi9GXW9RLDAuMjIyMjIyMmVtRicvRmBvRmRwLUZibzYlLUZlbzYmUSJZRidGaG9GNkZbcEY8Rl1wRjlGNkY5LUZRNi5RKiZ1bWludXMwO0YnRjZGOUZURlZGWEZaRmZuRmhuRmpuRmNwRmVwRjAtSSZtc3FydEdGJDYjLUYjNiktRmJvNiUtRkw2JS1GIzYmRmFvRltxRmZwRjlGNkY5RjxGXXBGYHAtRjM2JVEiNEYnRjZGOUZQLUZibzYlLUZlbzYmUSNYWUYnRmhvRjZGW3BGPEZdcC1GZW82I1EhRidGOS8lK2V4ZWN1dGFibGVHRkpGOS1GIzYoRmFyLUYjNilGMEZLRmBwRjBGYXJGXnFGOUZhckZob0Y2RltwRkFGQ0ZGRkgtRlE2LlEiPUYnRjZGOUZURlZGWEZaRmZuRmhuRmpuL0Zdb1EsMC4yNzc3Nzc4ZW1GJy9GYG9GXnMtRiw2KS1GIzYqLUZRNi9GUy8lK2ZvcmVncm91bmRHUSpbMjU1LDAsMF1GJ0Y2RjlGVEZWRlhGWkZmbkZobkZqbkZcb0Zfby1GYm82JS1GZW82J0Znb0Zob0Zmc0Y2RltwLUYjNiUtRjM2JkZARmZzRjZGOUZmc0Y5Rl1wLUZRNi9GYnBGZnNGNkY5RlRGVkZYRlpGZm5GaG5Gam5GY3BGZXAtRmJvNiUtRmVvNidGanBGaG9GZnNGNkZbcEZddEZdcC1GUTYvRl1xRmZzRjZGOUZURlZGWEZaRmZuRmhuRmpuRmNwRmVwLUZfcTYkLUYjNiUtRmVvNidRIkRGJy9GaW9GSkZmc0Y2RjlGZnNGOUZmc0Zmc0Y5LUYjNipGZHNGaXNGYXRGY3RGYXRGaXRGZnNGOUZBRkNGRkZIRmZzLUZRNi5RIixGJ0Y2RjlGVC9GV0Zqb0ZYRlpGZm5GaG5Gam5GXG8vRmBvUSwwLjMzMzMzMzNlbUYnRlAtRmVvNiZRJWh2b3JGJ0Zob0Y2RltwRlAtRmVvNiZGX3VGYHVGNkY5RmpyLUYjNihGY3FGYHBGaXFGUEZcckY5RmFyRmRyRjk=Det bem\303\246rkes at i dette resultat er antallet af punkter n forkortet ud, s\303\245 det kan vi tillade os at ignorer i beregningerne.Vi ser ogs\303\245 at den lidt stiltiende omgang af hvilken af de 2 varianser vi egentlig har regnet p\303\245 falder p\303\245 plads.Den minimale varians er den hvor kvadratroden er fratrukker og den maksimale er den anden. S\303\245 forholdet ovenfor er korrekt.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkmbWZyYWNHRiQ2KS1GIzYmLUkjbW9HRiQ2L1EifkYnLyUrZm9yZWdyb3VuZEdRKlsyNTUsMCwwXUYnLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTi1JJW1zdXBHRiQ2JS1JKG1mZW5jZWRHRiQ2Ji1GIzYpLUZSNiUtSSNtaUdGJDYnUSJYRicvJSdpdGFsaWNHUSV0cnVlRidGNEY3L0Y7USdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JlEiMkYnRjRGN0Y6RjovJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYxNi9RIitGJ0Y0RjdGOkY9RkBGQkZERkZGSEZKL0ZNUSwwLjIyMjIyMjJlbUYnL0ZQRltwLUZSNiUtRmZuNidRIllGJ0ZpbkY0RjdGXG9GXm9GZG8tRjE2L1EqJnVtaW51czA7RidGNEY3RjpGPUZARkJGREZGRkhGSkZqb0ZccC1JJm1zcXJ0R0YkNiQtRiM2JS1GZm42J1EiREYnL0ZqbkY/RjRGN0Y6RjRGOkY0RjRGOkY0RjdGOi1GIzYnRmBvRmluRjRGN0Zcb0Zkb0Y0RjotRiM2J0YwLUZVNiYtRiM2KUZZRmdvRl1wRmdvRmVwRjRGOkY0RjdGOkZURjRGOi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGW3IvJSliZXZlbGxlZEdGP0Y0LUYxNi9RIj1GJ0Y0RjdGOkY9RkBGQkZERkZGSEZKL0ZNUSwwLjI3Nzc3NzhlbUYnL0ZQRmRyLUYsNiktRiM2JkYwLUZSNiUtRlU2Ji1GIzYoRllGZ29GXXBGYnBGZXBGOkY0RjdGOkZeb0Zkb0Y0RjotRiM2K0YwLUZSNiUtRlU2Ji1GIzYnRllGZ29GXXBGNEY6RjRGN0Y6Rl5xRmRvLUZmbjYjUSFGJ0Zocy1GMTYvUSgmbWludXM7RidGNEY3RjpGPUZARkJGREZGRkhGSkZqb0ZccC1GIzYoLUZSNiUtRlU2Ji1GIzYmRllGYnBGXXBGOkY0RjdGOkZeb0Zkb0Znby1GYW82JlEiNEYnRjRGN0Y6RjAtRlI2JS1GZm42J1EjWFlGJ0ZpbkY0RjdGXG9GXm9GZG9GOkZoc0Y0RjpGZnFGaXFGXHJGXnJGNEZgci1GLDYpRmhyLUYjNi1GMEZmdEYwLUZSNiVGZW5GXnFGZG8tRlI2JUZfcEZecUZkb0Znb0ZmdEYwRml0RjRGOkZmcUZpcUZcckZeckY0RjRGOg==JSFH