Statistik 2C: Skillnad mellan sidversioner
Hakan (diskussion | bidrag) |
Hakan (diskussion | bidrag) |
||
Rad 57: | Rad 57: | ||
Övning i att generera egna värden i Excel. | Övning i att generera egna värden i Excel. | ||
Använd [[ | Använd [[File:Generera_summan_av_två_slumptal.xls|följande fil]] till att generera slumptal. | ||
Excel genereerar två slumptal mellan 1-6. Sedan adderas de. Dessa värden ska du undersöka fördelningen av. | Excel genereerar två slumptal mellan 1-6. Sedan adderas de. Dessa värden ska du undersöka fördelningen av. |
Versionen från 16 maj 2012 kl. 10.45
Histogram
Uppgift
Gör uppgiften nedan genom att använda Excel eller GeoGebra.
<ggb_applet width="493" height="620" version="4.0" ggbBase64="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" showResetIcon = "false" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />
Exempel på histogram till uppgiften ovan
Histogrammet i Excel.
Exempeluppgift
Övning
Statistik i GeoGebra
Det går alldeles utmärkt att göra histogram och annat i GGB.
1, 1, 2, 3, 2, 4, 3, 3, 2, 1, 4, 3, 5, 6, 7, 8, 9, 9, 11, 12, 3, 4
Siffrorna ovan kan man exempelvis klippa in i GGB och sedan klicka analysknappen. Ger automatiskt histogram och standardavvikelse och allt man kan begöära. Vi kan ha det som grund för alla undervisning.
Varationsbredd och låddiagram
Några spridningsmått Sidorna 217-221.
Standardavvikelse
<ggb_applet width="523" height="393" version="4.0" ggbBase64="UEsDBBQACAAIABOxrkAAAAAAAAAAAAAAAAAWAAAAZ2VvZ2VicmFfamF2YXNjcmlwdC5qc0srzUsuyczPU0hPT/LP88zLLNHQVKiuBQBQSwcI1je9uRkAAAAXAAAAUEsDBBQACAAIABSxrkAAAAAAAAAAAAAAAAAMAAAAZ2VvZ2VicmEueG1s5VrdbuM2Fr6ePgWhi8UUGNukSP0460wxtjs7A2S6RT1bLPZiAFpibDay5EqU42zbt9k32RfbQ1KSpSib2M00QCdBFInk4fnjOR8PpUy+2W8StBN5IbP03CFD7CCRRlks09W5U6rLQeh88/qryUpkK7HMObrM8g1X5w7TlDI+dyIceRyH/kAESz5gARWDZUjpIGCuR8XlMsSMOAjtC3mWZt/xjSi2PBKLaC02/CKLuDKC10ptz0aj6+vrYS1qmOWr0Wq1HO6L2EGgZlqcO9XDGbDrTLqmhtzFmIz++eHCsh/ItFA8jYSDtAmlfP3Vi8m1TOPsGl3LWK3PHY+CcmshV2ulG76DRppoCw7ZikjJnShgaqtpbFabrWPIeKrHX9gnlDTmOCiWOxmL/NzBQ4YpJpSErh8wMh6DjCyXIlUVLalkjmpuk50U15atfjISgWgnC7lMxLlzyZMCTJLpZQ7ubNqFuknEkudNx0Ed8orCuPw3EBMM62Z9YBqv9OXDxfTAqCuVOUhlWWKYYvTrr8jFLkav9I3Ymws337dD2PZham+uvTF78ywNs9OZJWWWhlkaRltGqrw80cbaQs+lx1voPsqvjVddwvoyXe9umcS/R6i1+xg7iddaSRBlfs3Vk0jvM/O2RNt+nECfPYmJk1GdKpMqTlGx1rRV9CixKXTk0jHyxjoACfIgSv0A4s1DZAy3wEUQl4h4iHnQJCHy9T1ANIABhigKkaYjFJkw9UL4wwLDzEceMNO9AWQHIiCIIY8iYqKbIYhpZDIEssWlQOF5yINJWjxxNQvqI+ZDi4aIgY46OQIChBQmQhvEu4gSRPVkEiDXR77mR5hOOj/UqgNLF/kY+UQzhPyC3LJ5BfQhotqaGtZkui1Vx0XRJq4fVbZt1gKoAY8OqGfxqQOKLyYJX4oE9omFXkmEdjzRGWEEXWapQvUi+rZvlfPtWkbFQigFswr0E9/xC67E/i1QF7VsQxtlafF9nqlZlpSbtEAoyhLc6JwlpPXsNlpDg7YGWHvAaw34refgTrkZjKCyECA/y4uanMfxe01xgAbw5N/T5GaaC361zWTXjMnIbDkTUUaJjCVPf4Rg1VK0X1C9AxlAbnYgd1wrkuXx4qaACEb7f4k80xjjDXHrR0POjR2ihA3HrZ9QA1PEdfJ5uDMJ6y3uphpj486scVitlNg1a8T3ojF/lcu4/fy+mGZJ3DjD2D/jW1XmpngAHXJt1Zt0lQgTIyazYWeOrpbZfmGDg1peH2+20MJW/nJl/I4AG1zPAwK4Y7B2qRGhijCtWEOFDQ02FLiONhn3uOjZHS4Qvla1ylBSW0lwLUYWBtGw08kbE/t6ny9TqS7qhpLR1cFSTf9duVmKJoK6LMlnYjkZ3YqwSbGFgIyLtRDqzpgzW2Qdc9T3rGIw6XImkmTRJg1a0ekGlrDF3iZo7aE6pAN8HyE9EGK3IhSJBpYsRWi9iPIsSQy/Xes5MgxsWNldtlpCfpOVGmzANW+hOC0TPm3tKrr7b63A1e13lu30sNvp3h/v7J2CsELk30NtlnSYWoPegX2iM+EH4G86UQMbSZJdLwA5JU++jaXKDtqZoY+wdX2U2ybPxM8ljP4AN5mLuAMovYWdXIkcNKuwC3K2zMrCQnEL1mKQvYGmHah8znVe/gNizfbGYpWLOkQTU4HbzDCjuA1LvW7D6m2ebd6nu4+Q9LcUmIxqLSdFlMuthha0hP3+6mAeFMwFh3KhY68GW/CJjQwllc4CcFqp1tqHMAd2D7hrjE3EBkpqpAyOpOVG5DJqcmoamHIdtCorxQkBXKxiDxYNZcufIAAPtYid13IhEPwfuIFF3K65LvRJE5Gw+m3/GHYfsrgWXnsNFsWYBjC/tfm9FcIig6oAEW2BncHTljK83MtE8vzG8msBgXXDww7xew7B9Fk7xOs7hDxrh7C+Q553ytDbDhk/74xxn50/9rD7FvpFWeMD4Aq9585ffi4z9dfkv/9JV7F9NpO7HoSTjnJaUz+vp/CRnsKtExoUNvLyUNXUxzV7Nq9I7/fArOuB4komScqP9MHsy/DBm7Djg0W52fDjHAAz/3wOiDKwL41Ral7mgLXO4dUCxxoYzqbVQQEK86Y3tHyq2Q/DS3gbXvzD/nM0cjyQvuNq4aYhGlUvSR5Sa3zPtngCoP0uuJm5tb4uGiBSvQV7QONZD6cHwSkK48coTGuF6QkK9zbaJ1SY1QqzExTulUonRcSj9PVqfb0T9O3Xuk+mr1/r65+gb++wQp9M36DWNzhB3/5p88kCYl5DxMz99NL9+hh15z2AYOOnQrR5DRAzerS6PXh4QnVreJixo9V9HDg8StsaHGbe0do+DhoepW0NDTP/aG17wPB0kVADwyw4Wts7YOEPioWHSrS5ezbvl2jzE0u0ea9Ec3H4mUu0+d3ni0/ucQX2/As5YZCuGxYK1ofnMd/t5JUAtkceN8iX4Y4LWShee+SXqfsKTSlcDC4PLh+u4Le7UjKBic4tLj2HdL7G3OsPUw/8zhcWdW/zAUqtZXSVgqHmnxKadxX64Z2MY5E2LznMhzbzkab9ydX2Hl7ND47IrjfjTlh9ELFIjgyl8Z8wkm7B4vwWKlYB0Tu5EnLi0bVKsxYwesMwDEKGvSDwPBIy/4mqwQY3Xs71Edf7+tNLPPSO2676VvhDxsYh9sk49GkYsj9i6xq1v/mYb+jVv4O9/h9QSwcI918nTu4HAACrJgAAUEsBAhQAFAAIAAgAE7GuQNY3vbkZAAAAFwAAABYAAAAAAAAAAAAAAAAAAAAAAGdlb2dlYnJhX2phdmFzY3JpcHQuanNQSwECFAAUAAgACAAUsa5A918nTu4HAACrJgAADAAAAAAAAAAAAAAAAABdAAAAZ2VvZ2VicmEueG1sUEsFBgAAAAACAAIAfgAAAIUIAAAAAA==" showResetIcon = "false" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />
Tips: Testa standard deviation i WolframAlpha
Normalfördelningen
![](https://upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Normal_distribution.svg/langsv-300px-Normal_distribution.svg.png)
Gemensam övningsuppgift
Testa dessa data i GGB:
85, 87, 150, 100, 100, 90, 70, 72, 75, 70, 85, 143, 100, 121, 92, 66, 70, 69, 75, 80, 140, 92, 130, 83, 70, 68, 67, 75, 83, 149, 95, 130, 80, 68, 85, 75, 73, 78, 140, 90, 124, 86, 69, 70, 75, 77, 110, 165, 110, 150, 110, 115, 80, 75, 75, 98, 172, 110, 145, 110, 95, 52, 80, 96, 110, 168, 110, 145, 110, 80,80, 75, 89, 95, 170, 110, 145, 120, 89, 72, 79, 75, 95, 220, 100, 149, 100, 110,80, 85, 80, 90, 165, 103, 135, 95, 77, 76, 85, 80, 88, 155, 103, 120, 85, 79, 78, 82, 75, 85, 150, 103, 135, 90, 75, 85, 78, 75, 88, 150, 95, 130, 90, 70, 76, 89, 82, 95, 145, 100, 133, 90, 77, 89, 79, 80, 90, 165, 103, 135, 95, 77, 86, 80, 85, 100, 160, 120, 140, 100, 90, 79, 92, 70, 100, 165, 120, 140, 100, 120, 86, 71, 95, 100, 155, 120, 139, 100, 89, 86, 78, 78, 110, 158, 122, 145, 108, 95, 95, 78
Är de normalfördelade?
Skapa värden i Excel
Övning i att generera egna värden i Excel.
Använd Fil:Generera summan av två slumptal.xls till att generera slumptal.
Excel genereerar två slumptal mellan 1-6. Sedan adderas de. Dessa värden ska du undersöka fördelningen av.
- Plocka in dem i GGB för att göra ett histogram.
- Är de normalfördelade?
Hur många värden behöver du för att det ska se bra ut jämfört med normalförelningskurvan?
Testa även att generera slumptal i GGB.