Machine Learning (PDF)

‫ﻣﺘﺮﺟﻢ ﻣﻦ ﺍﻹﻧﺠﻠﻴﺰﻳﺔ ﺇﻟﻰ ﺍﻟﻌﺮﺑﻴﺔ ‪www.onlinedoctranslator.com -‬‬ ‫ﺍﻟﺘﻌﻠﻢﺍﻵﻟﻲ‬ ‫‪1‬‬  ‫ﻛﻴﻒﻳﺘﻌﻠﻢ ﺍﻟﺒﺸﺮ؟‬ ‫ﺍﻟﺘﻌﻠﻢﺗﺤﺖ ﺇﺷﺮﺍﻑ ﺍﻟﺨﺒﺮﺍء‬ ‫ﻥ‬ ‫ﻳﺘﻌﻠﻢﺍﻟﻄﻔﻞ ﺃﺷﻴﺎء ﻣﻦ ﻭﺍﻟﺪﻳﻪ )ﻫﺬﻩ ﻫﻲ ﺍﻟﻴﺪ‪ ،‬ﺍﻟﻤﺎء‪ ،‬ﺍﻟﻄﻌﺎﻡ‪...

‫ﻣﺘﺮﺟﻢ ﻣﻦ ﺍﻹﻧﺠﻠﻴﺰﻳﺔ ﺇﻟﻰ ﺍﻟﻌﺮﺑﻴﺔ ‪www.onlinedoctranslator.com -‬‬ ‫ﺍﻟﺘﻌﻠﻢﺍﻵﻟﻲ‬ ‫‪1‬‬  ‫ﻛﻴﻒﻳﺘﻌﻠﻢ ﺍﻟﺒﺸﺮ؟‬ ‫ﺍﻟﺘﻌﻠﻢﺗﺤﺖ ﺇﺷﺮﺍﻑ ﺍﻟﺨﺒﺮﺍء‬ ‫ﻥ‬ ‫ﻳﺘﻌﻠﻢﺍﻟﻄﻔﻞ ﺃﺷﻴﺎء ﻣﻦ ﻭﺍﻟﺪﻳﻪ )ﻫﺬﻩ ﻫﻲ ﺍﻟﻴﺪ‪ ،‬ﺍﻟﻤﺎء‪ ،‬ﺍﻟﻄﻌﺎﻡ‪ ،‬ﺍﻟﺴﻤﺎء ﺯﺭﻗﺎ‬ ‫ﺃ‬ ‫ء……(‬ ‫ﺃﻋﻨﺪﻣﺎ ﻳﺒﺪﺃ ﺍﻟﻄﻔﻞ ﺑﺎﻟﺬﻫﺎﺏ ﺇﻟﻰ ﺍﻟﻤﺪﺭﺳﺔ‪ ،‬ﻳﺒﺪﺃ ﺍﻟﻤﻌﻠﻤﻮﻥ‬ ‫ﺍﻷﺑﺠﺪﻳﺎﺕ‪،‬ﺍﻷﺭﻗﺎﻡ‪ ،‬ﺍﻟﻌﻠﻮﻡ……‪.‬‬ ‫ﺃ ﻓﻲﺟﻤﻴﻊ ﻣﺮﺍﺣﻞ ﺣﻴﺎﺓ ﺍﻹﻧﺴﺎﻥ‪ ،‬ﻳﺘﻢ ﺍﻟﺘﻌﻠﻢ ﻣﻦ ﻗﺒﻞ ﺷﺨﺺ ﻟﺪﻳﻪ‬ ‫ﺍﻟﺨﺒﺮﺓﻓﻲ ﻫﺬﺍ ﺍﻟﻤﺠﺎﻝ‪.‬‬ ‫ﻥﺍﻟﺘﻌﻠﻢ ﺑﻨﺎء ﻋﻠﻰ ﺍﻟﻤﻌﺮﻓﺔ ﺍﻟﻤﻜﺘﺴﺒﺔ ﻣﻦ ﺍﻟﺨﺒﺮﺍء‬ ‫ﻳﺴﺘﻄﻴﻊﺍﻟﻄﻔﻞ ﺃﻥ ﻳﺠﻤﻊ ﻛﻞ ﺍﻷﺷﻴﺎء ﺍﻟﺘﻲ ﻟﻬﺎ ﻧﻔﺲ ﺍﻟﻠﻮﻥ ﻣﻌﺎً ﺣﺘﻰ ﻟﻮ ﻟﻢ‬ ‫ﺃ‬ ‫ﻳﻌﻠﻤﻪﻭﺍﻟﺪﺍﻩ ﺫﻟﻚ‪.‬ﻓﻬﻮ ﻗﺎﺩﺭ ﻋﻠﻰ ﺫﻟﻚ ﻷﻧﻪ ﻓﻲ ﻭﻗﺖ ﻣﺎ ﺃﺧﺒﺮﻩ ﻭﺍﻟﺪﺍﻩ ﺃﻱ‬ ‫ﺍﻷﻟﻮﺍﻥﺃﺯﺭﻕ ﻭﺃﻳﻬﺎ ﺃﺣﻤﺮ ﻭﺃﻳﻬﺎ ﺃﺧﻀﺮ‪ ،‬ﺇﻟﺦ‪.‬‬ ‫‪2‬‬  ‫ﻓﻲﻣﺮﺣﻠﺔ ﺍﻟﺪﺭﺍﺳﺎﺕ ﺍﻟﻌﻠﻴﺎ‪ ،‬ﻳﻘﻮﻡ ﺍﻟﺒﺎﺣﺜﻮﻥ ﺑﺤﻞ ﺍﻟﻤﺸﺎﻛﻞ ﺍﻟﺘﻲ ﻟﻢ‬ ‫ﺃ‬ ‫ﻳﺘﻢﺣﻠﻬﺎ ﻣﻦ ﻗﺒﻞ ﺑﻨﺎء ًﻋﻠﻰ ﻣﻌﺮﻓﺘﻬﻢ ﺍﻟﺴﺎﺑﻘﺔ‪.‬‬ ‫ﻥﺍﻟﺘﻌﻠﻢ ﺍﻟﺬﺍﺗﻲ‬ ‫ﻋﻨﺪﻣﺎﻳﺘﻌﻠﻢ ﺍﻟﻄﻔﻞ ﺍﻟﻤﺸﻲ ﻋﺒﺮ ﺍﻟﻌﻮﺍﺉﻖ‪ ،‬ﻓﺈﻧﻪ ﻳﺼﻄﺪﻡ ﺑﺎﻟﻌﻮﺍﺉﻖ‬ ‫ﺃ‬ ‫ﻭﻳﺴﻘﻂﻋﺪﺓ ﻣﺮﺍﺕ ﺣﺘﻰ ﻳﺘﻌﻠﻢ ﺃﻧﻪ ﻛﻠﻤﺎ ﻛﺎﻧﺖ ﻫﻨﺎﻙ ﻋﻘﺒﺔ‪ ،‬ﻓﺈﻧﻪ ﻳﺤﺘﺎﺝ‬ ‫ﺇﻟﻰﻋﺒﻮﺭﻫﺎ‪.‬‬ ‫ﻻﻳﺘﻢ ﺗﻌﻠﻴﻢ ﻛﻞ ﺍﻷﺷﻴﺎء ﻣﻦ ﻗﺒﻞ ﺍﻵﺧﺮﻳﻦ‪ ،‬ﻓﻬﻨﺎﻙ ﺍﻟﻜﺜﻴﺮ ﻣﻦ ﺍﻷﺷﻴﺎء ﺍﻟﺘﻲ‬ ‫ﺃ‬ ‫ﻳﺠﺐﺗﻌﻠﻤﻬﺎ ﻓﻘﻂ ﻣﻦ ﺧﻼﻝ ﺍﻟﻤﺤﺎﻭﻻﺕ ﺍﻟﺘﻲ ﻗﻤﻨﺎ ﺑﻬﺎ ﻓﻲ ﺍﻟﻤﺎﺿﻲ‪.‬ﻧﻤﻴﻞ‬ ‫ﺇﻟﻰﺗﻜﻮﻳﻦ ﻗﺎﺉﻤﺔ ﻣﺮﺍﺟﻌﺔ ﻟﻸﺷﻴﺎء ﺍﻟﺘﻲ ﻳﺠﺐ ﻋﻠﻴﻨﺎ ﺍﻟﻘﻴﺎﻡ ﺑﻬﺎ‪ ،‬ﻭﺍﻷﺷﻴﺎء ﺍﻟﺘﻲ‬ ‫ﻻﻳﺠﺐ ﻋﻠﻴﻨﺎ ﺍﻟﻘﻴﺎﻡ ﺑﻬﺎ‪ ،‬ﺑﻨﺎء ًﻋﻠﻰ ﺗﺠﺎﺭﺑﻨﺎ‪.‬‬ ‫‪3‬‬  ‫ﻣﺎﻫﻮ ﺍﻟﺘﻌﻠﻢ ﺍﻵﻟﻲ؟‬ ‫'ﻳﻘﺎﻝ ﺃﻥ ﺑﺮﻧﺎﻣﺞ ﻛﻤﺒﻴﻮﺗﺮ ﻳﺘﻌﻠﻢ ﻣﻦ ﺍﻟﺘﺠﺮﺑﺔ ‪ E‬ﻓﻴﻤﺎ ﻳﺘﻌﻠﻖ ﺑﺒﻌﺾ ﻓﺉﺎﺕ‬ ‫ﺍﻟﻤﻬﺎﻡ‪ T‬ﻭﻣﻘﻴﺎﺱ ﺍﻷﺩﺍء ‪ ،P‬ﺇﺫﺍ ﻛﺎﻥ ﺃﺩﺍءﻩ ﻓﻲ ﺍﻟﻤﻬﺎﻡ ﻓﻲ ‪ ،T‬ﻛﻤﺎ ﺗﻢ ﻗﻴﺎﺳﻪ‬ ‫ﺑﻮﺍﺳﻄﺔ‪ ،P‬ﻳﺘﺤﺴﻦ ﻣﻊ ﺍﻟﺘﺠﺮﺑﺔ ‪'.E‬‬ ‫]ﺗﻮﻡ ﻣﻴﺘﺸﻞ[‬ ‫‪4‬‬  ‫ﺃﻧﻮﺍﻉﺍﻟﺘﻌﻠﻢ ﺍﻵﻟﻲ‬ ‫ﻳﻤﻜﻦﺗﺼﻨﻴﻒ ﺍﻟﺘﻌﻠﻢ ﺍﻵﻟﻲ ﺇﻟﻰ ﺛﻼﺙ ﻓﺉﺎﺕ ﻋﺮﻳﻀﺔ‪:‬‬ ‫ﻥ‬ ‫ﺍﻟﺘﻲﻫﻲ ‪ms‬‬ ‫ﻥ‬ ‫ﻣﻜﻮﻥ‬ ‫ﺧﻮﺍﺭﺯﻣﻴﺎﺕﺍﻟﺘﻌﻠﻢ ﻏﻴﺮ ﺍﻟﺨﺎﺿﻌﺔ ﻟﻺﺷﺮﺍﻑﻫﻲ ﺧﻮﺍﺭﺯﻣﻴﺎﺕ ﻳﺘﻢ‬ ‫ﻥ‬ ‫ﺗﺪﺭﻳﺒﻬﺎﻋﻠﻰ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺑﺪﻭﻥ ﺗﺴﻤﻴﺎﺕ‪ ،‬ﻭﺍﻟﻬﺪﻑ ﻫﻮ ﺍﻟﻌﺜﻮﺭ ﻋﻠﻰ‬ ‫ﺍﻟﻌﻼﻗﺎﺕﻓﻲ ﺍﻟﺒﻴﺎﻧﺎﺕ‪.‬‬ ‫‪5‬‬  ‫ﺧﻮﺍﺭﺯﻣﻴﺎﺕﺍﻟﺘﻌﻠﻢ ﺍﻟﺘﻌﺰﻳﺰﻱﻫﻲ ﺧﻮﺍﺭﺯﻣﻴﺎﺕ ﻳﺘﻢ ﺗﻌﻠﻤﻬﺎ ﻣﻦ ﺧﻼﻝ‬ ‫ﻥ‬ ‫ﻣﺮﺍﻗﺒﺔﺍﻟﺒﻴﺉﺔ‪ ،‬ﻭﺍﺧﺘﻴﺎﺭ ﺍﻹﺟﺮﺍءﺍﺕ ﻭﺗﻨﻔﻴﺬﻫﺎ‪ ،‬ﻭﻓﻲ ﺍﻟﻤﻘﺎﺑﻞ ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ‬ ‫ﺍﻟﻤﻜﺎﻓﺂﺕﺃﻭﺍﻟﻌﻘﻮﺑﺎﺕﻓﻲ ﺷﻜﻞ ﻣﻜﺎﻓﺂﺕ ﺳﻠﺒﻴﺔ‪.‬‬ ‫ﺃﻣﺜﻠﺔﻋﻠﻰ ﺍﻟﺘﻌﻠﻢ ﺍﻟﺘﻌﺰﻳﺰﻱ‪ :‬ﺍﻟﺴﻴﺎﺭﺍﺕ ﺫﺍﺗﻴﺔ ﺍﻟﻘﻴﺎﺩﺓ‪ ،‬ﻭﺍﻟﺮﻭﺑﻮﺗﺎﺕ ﺍﻟﺬﻛﻴﺔ‪ ،‬ﻭﻣﺎ‬ ‫ﻥ‬ ‫ﺇﻟﻰﺫﻟﻚ‪.‬ﻟﻘﺪ ﺗﻐﻠﺒﺖ ﺷﺮﻛﺔ ‪ DeepMind‬ﺍﻟﺘﺎﺑﻌﺔ ﻟﺸﺮﻛﺔ ‪ Google‬ﻋﻠﻰ‬ ‫‪6‬‬ ‫ﻻﻋﺐ‪ Go‬ﺍﻟﻤﺼﻨﻒ ﺍﻷﻭﻝ ﻓﻲ ﺍﻟﻌﺎﻟﻢ ‪ Ke Jie‬ﻓﻲ ﻋﺎﻡ ‪.2017‬‬  ‫ﻥﺑﻌﺾ ﺍﻷﻣﺜﻠﺔ ﻋﻠﻰ ﺍﻟﺘﻌﻠﻢ ﺍﻟﺨﺎﺿﻊ ﻟﻺﺷﺮﺍﻑ ﻫﻲ‬ ‫ﺍﻟﺘﻨﺒﺆﺑﻨﺘﺎﺉﺞ ﻣﺒﺎﺭﺍﺓ ﻛﺮﺓ ﺍﻟﻘﺪﻡ‪.‬ﺍﻟﺘﻨﺒﺆ ﺑﻤﺎ ﺇﺫﺍ ﻛﺎﻥ ﺍﻟﻮﺭﻡ ﺧﺒﻴﺜﺎً ﺃﻡ‬ ‫ﺃ‬ ‫ﺣﻤﻴﺪﺍً‪.‬ﺍﻟﺘﻨﺒﺆ ﺑﺴﻌﺮ ﺍﻟﻤﻨﺎﺯﻝ‪.‬‬ ‫ﺃ‬ ‫ﺃ‬ ‫ﺗﺼﻨﻴﻒﺭﺳﺎﺉﻞ ﺍﻟﺒﺮﻳﺪ ﺍﻹﻟﻜﺘﺮﻭﻧﻲ ﻛﺮﺳﺎﺉﻞ ﻏﻴﺮ ﻣﺮﻏﻮﺏ ﻓﻴﻬﺎ ﺃﻭ ﻏﻴﺮ ﻣﺮﻏﻮﺏ ﻓﻴﻬﺎ‬ ‫ﺃ‬ ‫ﻋﻨﺪﻣﺎﻧﺤﺎﻭﻝ ﺍﻟﺘﻨﺒﺆ ﺑﻔﺉﺔ ﻋﻴﻨﺔ ﺑﻴﺎﻧﺎﺕ ﺟﺪﻳﺪﺓ‪ ،‬ﺗﻌُﺮﻑ ﺍﻟﻤﺸﻜﻠﺔ ﺑﺎﺳﻢ‬ ‫ﻥ‬ ‫ﺗﺼﻨﻴﻒﺗﺘﻀﻤﻦ ﺑﻌﺾ ﻣﺸﻜﻼﺕ ﺍﻟﺘﺼﻨﻴﻒ ﺍﻟﻨﻤﻮﺫﺟﻴﺔ ﻣﺎ ﻳﻠﻲ‪:‬‬ ‫ﺗﺼﻨﻴﻒﺍﻟﺼﻮﺭ‬ ‫ﺃ‬ ‫ﺍﻟﺘﻨﺒﺆﺑﺎﻟﻤﺮﺽ‬ ‫ﺃ‬ ‫ﺍﻟﺘﻨﺒﺆﺑﺎﻟﻔﻮﺯ ﻭﺍﻟﺨﺴﺎﺭﺓ ﻓﻲ ﺍﻟﻤﺒﺎﺭﻳﺎﺕ‬ ‫ﺃ‬ ‫ﺍﻟﺘﻨﺒﺆﺑﺎﻟﻜﻮﺍﺭﺙ ﺍﻟﻄﺒﻴﻌﻴﺔ ﻣﺜﻞ ﺍﻟﺰﻻﺯﻝ ﻭﺍﻟﻔﻴﻀﺎﻧﺎﺕ ﻭﻣﺎ ﺇﻟﻰ ﺫﻟﻚ‪.‬‬ ‫ﺃ‬ ‫ﺍﻟﺘﻌﺮﻑﻋﻠﻰ ﺍﻟﻜﺘﺎﺑﺔ ﺍﻟﻴﺪﻭﻳﺔ‬ ‫ﺃ‬ ‫ﺍﻟﺘﻌﺮﻑﻋﻠﻰ ﺭﻗﻢ ﻟﻮﺣﺔ ﺍﻟﺴﻴﺎﺭﺓ‬ ‫ﺃ‬ ‫‪7‬‬  ‫ﻓﻲﺣﻴﻦ ﺃﻧﻪ ﻋﻨﺪﻣﺎ ﻧﺤﺎﻭﻝ ﺍﻟﺘﻨﺒﺆ ﺑﻘﻴﻤﺔ ﺣﻘﻴﻘﻴﺔ ﻟﻌﻴﻨﺔ ﺑﻴﺎﻧﺎﺕ ﺟﺪﻳﺪﺓ‪،‬‬ ‫ﻥ‬ ‫ﺗﻌُﺮﻑﺍﻟﻤﺸﻜﻠﺔ ﺑﺎﺳﻢﺍﻻﻧﺤﺪﺍﺭ‪.‬ﺗﺘﻀﻤﻦ ﺑﻌﺾ ﻣﺸﺎﻛﻞ ﺍﻻﻧﺤﺪﺍﺭ‬ ‫ﺍﻟﻨﻤﻮﺫﺟﻴﺔﻣﺎ ﻳﻠﻲ‪:‬‬ ‫ﺍﻟﺘﻨﺒﺆﺑﺎﻟﻄﻠﺐ ﻓﻲ ﺗﺠﺎﺭﺓ ﺍﻟﺘﺠﺰﺉﺔ‬ ‫ﺃ‬ ‫ﺍﻟﺘﻨﺒﺆﺑﺎﻟﻤﺒﻴﻌﺎﺕ ﻟﻠﻤﺪﻳﺮﻳﻦ ﺍﻟﺘﻨﺒﺆ‬ ‫ﺃ‬ ‫ﺑﺎﻷﺳﻌﺎﺭﻓﻲ ﺍﻟﻌﻘﺎﺭﺍﺕ ﺗﻮﻗﻌﺎﺕ ﺍﻟﻄﻘﺲ‬ ‫ﺃ‬ ‫ﺃ‬ ‫ﺗﻮﻗﻌﺎﺕﺍﻟﻄﻠﺐ ﻋﻠﻰ ﺍﻟﻤﻬﺎﺭﺍﺕ ﻓﻲ ﺳﻮﻕ ﺍﻟﻌﻤﻞ‬ ‫ﺃ‬ ‫ﺍﻟﺘﺠﻤﻴﻊﻫﻮ ﺍﻟﻨﻮﻉ ﺍﻟﺮﺉﻴﺴﻲ ﻣﻦ ﺍﻟﺘﻌﻠﻢ ﻏﻴﺮ ﺍﻟﺨﺎﺿﻊ ﻟﻺﺷﺮﺍﻑ‪.‬ﻭﻳﻬﺪﻑ‬ ‫ﻥ‬ ‫ﺇﻟﻰﺗﺠﻤﻴﻊ ﺃﻭ ﺗﺠﻤﻴﻊ ﺍﻟﻜﺎﺉﻨﺎﺕ ﺍﻟﻤﺘﺸﺎﺑﻬﺔ ﻣﻌﺎً ﺩﺍﺧﻞ ﺍﻟﺒﻴﺎﻧﺎﺕ‪.‬ﻭﻟﻬﺬﺍ‬ ‫ﺍﻟﺴﺒﺐ‪،‬ﺗﻜﻮﻥ ﺍﻟﻜﺎﺉﻨﺎﺕ ﺍﻟﺘﻲ ﺗﻨﺘﻤﻲ ﺇﻟﻰ ﻧﻔﺲ ﺍﻟﻤﺠﻤﻮﻋﺔ ﻣﺘﺸﺎﺑﻬﺔ‬ ‫ﺗﻤﺎﻣﺎًﻣﻊ ﺑﻌﻀﻬﺎ ﺍﻟﺒﻌﺾ ﺑﻴﻨﻤﺎ ﺗﻜﻮﻥ ﺍﻟﻜﺎﺉﻨﺎﺕ ﺍﻟﺘﻲ ﺗﻨﺘﻤﻲ ﺇﻟﻰ‬ ‫ﻣﺠﻤﻮﻋﺎﺕﻣﺨﺘﻠﻔﺔ ﻣﺨﺘﻠﻔﺔ ﺗﻤﺎﻣﺎً‪.‬ﺗﺘﻀﻤﻦ ﺑﻌﺾ ﻣﺸﻜﻼﺕ ﺍﻻﻧﺤﺪﺍﺭ‬ ‫ﺍﻟﻨﻤﻮﺫﺟﻴﺔﻣﺎ ﻳﻠﻲ‪:‬‬ ‫ﺗﺼﻨﻴﻒﺍﻟﺠﺮﺍﺉﻢ ﻓﻲ ﺍﻟﻴﻤﻦ ﺣﺴﺐ )ﺍﻟﻌﻤﺮ‪ ،‬ﺍﻟﺘﻌﻠﻴﻢ‪ ،‬ﺍﻟﻤﻨﻄﻘﺔ(‪ ،‬ﺗﺼﻨﻴﻒ ﻣﺸﺘﺮﻛﻲ‬ ‫ﺃ‬ ‫ﺧﺪﻣﺔﺍﻟﺒﺚ‬ ‫ﺃ‬ ‫‪8‬‬ ‫ﻧﻴﻨﻎ‬ ‫ﺃﻧﻮﺍﻉﺍﻟﺪﺍ‬ ‫ﺍﻟﺤﺒﺎﻝ‪.‬‬ ‫ﻥﻣﺠﻤﻮﻋﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ ﻫﻲ ﻋﺒﺎﺭﺓ ﻋﻦ ﻣﺠﻤﻮﻋﺔ‬ ‫ﺱ‪:‬‬ ‫ﻥﺩ‬ ‫ﺃ‬ ‫ﺃ‬ ‫‪9‬‬  ‫ﺍﻟﺒﻴﺎﻧﺎﺕﺍﻟﻨﻮﻋﻴﺔﻫﻲ ﻣﻌﻠﻮﻣﺎﺕ ﺣﻮﻝ ﺟﻮﺩﺓ ﺍﻟﻜﺎﺉﻦ ﻭﺍﻟﺘﻲ ﻻ ﻳﻤﻜﻦ‬ ‫ﻥ‬ ‫ﻗﻴﺎﺳﻬﺎ‪.‬‬ ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﺍﺳﻢ ﺃﻭ ﺭﻗﻢ ﻗﻴﺪ ﺍﻟﻄﻼﺏ‪.‬ﻭﺇﺫﺍ ﻧﻈﺮﻧﺎ ﺇﻟﻰ ﺃﺩﺍء ﺍﻟﻄﻼﺏ‬ ‫ﺃ‬ ‫)ﻣﻦ ﺣﻴﺚ "ﺟﻴﺪ" ﻭ"ﻣﺘﻮﺳﻂ" ﻭ"ﺿﻌﻴﻒ"(‪ ،‬ﻓﻬﺬﻩ ﻣﻌﻠﻮﻣﺎﺕ ﻻ ﻳﻤﻜﻦ‬ ‫ﻗﻴﺎﺳﻬﺎﺑﺎﺳﺘﺨﺪﺍﻡ ﻣﻘﻴﺎﺱ ﻣﺎ‪.‬‬ ‫ﻳﻤﻜﻦﺗﻘﺴﻴﻢ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻨﻮﻋﻴﺔ ﺇﻟﻰ ﻧﻮﻋﻴﻦ ﻋﻠﻰ ﺍﻟﻨﺤﻮ ﺍﻟﺘﺎﻟﻲ‪:‬‬ ‫ﻥ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕﺍﻹﺳﻤﻴﺔ‬ ‫ﺃ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕﺍﻟﺘﺮﺗﻴﺒﻴﺔ‬ ‫ﺃ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕﺍﻹﺳﻤﻴﺔﻫﻲ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺘﻲ ﻟﻴﺲ ﻟﻬﺎ ﻗﻴﻤﺔ ﻋﺪﺩﻳﺔ‪ ،‬ﻭﻟﻜﻦ ﻟﻬﺎ‬ ‫ﻥ‬ ‫ﻗﻴﻤﺔﻣﺴﻤﺎﺓ‪.‬ﻭﻣﻦ ﺃﻣﺜﻠﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻻﺳﻤﻴﺔ‪:‬‬ ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﻓﺼﻴﻠﺔ ﺍﻟﺪﻡ‪ ،A، B، O، AB :‬ﺇﻟﺦ‪.‬ﺍﻟﺠﻨﺴﻴﺔ‪:‬‬ ‫ﺃ‬ ‫ﻳﻤﻨﻴﺔ‪،‬ﻫﻨﺪﻳﺔ‪ ،‬ﺃﻣﺮﻳﻜﻴﺔ‪ ،‬ﺑﺮﻳﻄﺎﻧﻴﺔ‪ ،‬ﺇﻟﺦ‪.‬ﺍﻟﺠﻨﺲ‪ :‬ﺫﻛﺮ‪ ،‬ﺃﻧﺜﻰ‬ ‫ﺃ‬ ‫ﺃ‬ ‫‪10‬‬  ‫ﻣﻦﺍﻟﻮﺍﺿﺢ ﺃﻧﻪ ﻻ ﻳﻤﻜﻦ ﺇﺟﺮﺍء ﺍﻟﻌﻤﻠﻴﺎﺕ ﺍﻟﺤﺴﺎﺑﻴﺔ )ﺍﻟﺠﻤﻊ ﻭﺍﻟﻄﺮﺡ‬ ‫ﻥ‬ ‫ﻭﺍﻟﻀﺮﺏﻭﻣﺎ ﺇﻟﻰ ﺫﻟﻚ( ﻋﻠﻰ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻻﺳﻤﻴﺔ‪.‬ﻭﻟﻬﺬﺍ ﺍﻟﺴﺒﺐ‪ ،‬ﻻ‬ ‫ﻳﻤﻜﻦﺃﻳﻀﺎً ﺗﻄﺒﻴﻖ ﺍﻟﻮﻇﺎﺉﻒ ﺍﻹﺣﺼﺎﺉﻴﺔ ﻣﺜﻞ ﺍﻟﻤﺘﻮﺳﻂ ﻭﺍﻟﺘﺒﺎﻳﻦ‬ ‫ﻭﻣﺎﺇﻟﻰ ﺫﻟﻚ ﻋﻠﻰ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻻﺳﻤﻴﺔ‪.‬ﻭﻣﻊ ﺫﻟﻚ‪ ،‬ﻣﻦ ﺍﻟﻤﻤﻜﻦ ﺇﺟﺮﺍء ﻋﺪ‬ ‫ﺃﺳﺎﺳﻲ‪.‬ﻭﺑﺎﻟﺘﺎﻟﻲ ﻳﻤﻜﻦ ﺗﺤﺪﻳﺪ ﺍﻟﻤﻨﻮﺍﻝ ﻟﻠﺒﻴﺎﻧﺎﺕ ﺍﻻﺳﻤﻴﺔ‪.‬‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕﺍﻟﺘﺮﺗﻴﺒﻴﺔ‪ ،‬ﻫﻮ ﺍﻟﺬﻱ ﻟﺪﻳﻪﻻﻗﻴﻤﺔ ﻋﺪﺩﻳﺔﻟﻜﻦ ﻳﻤﻜﻦ ﺗﺮﺗﻴﺒﻬﺎ‬ ‫ﻥ‬ ‫ﺑﺸﻜﻞﻃﺒﻴﻌﻲ )ﻳﻤﻜﻨﻨﺎ ﺃﻥ ﻧﻘﻮﻝ ﻣﺎ ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﻘﻴﻤﺔ ﺃﻓﻀﻞ ﺃﻭ ﺃﻛﺒﺮ ﻣﻦ‬ ‫ﻗﻴﻤﺔﺃﺧﺮﻯ(‬ ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﺭﺿﺎ ﺍﻟﻌﻤﻼء‪" :‬ﺳﻌﻴﺪ ﺟﺪﺍً"‪" ،‬ﺳﻌﻴﺪ"‪" ،‬ﻏﻴﺮ‬ ‫ﺃ‬ ‫ﺳﻌﻴﺪ"‪،‬‬ ‫ﺍﻟﺪﺭﺟﺎﺕ‪':‬ﻣﻤﺘﺎﺯ'‪' ،‬ﺟﻴﺪ ﺟﺪﺍً'‪' ،‬ﺟﻴﺪ'‪' ،‬ﺭﺩﻱء' ﻭ'ﺭﺍﺳﺐ' ﺻﻼﺑﺔ ﺍﻟﻤﻌﺪﻥ‪' :‬‬ ‫ﺃ‬ ‫ﺻﻌﺐﺟﺪﺍً'‪' ،‬ﺻﻠﺐ'‪' ،‬ﻧﺎﻋﻢ'‪ ،‬ﺇﻟﺦ‪.‬‬ ‫ﺃ‬ ‫ﻣﺜﻞﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻻﺳﻤﻴﺔ‪ ،‬ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻷﺳﺎﺳﻴﺔﻭﺿﻊﻳﻤﻜﻦ ﺗﻄﺒﻴﻖ ﺫﻟﻚ‪.‬‬ ‫ﻥ‬ ‫ﻧﻈﺮﺍًﻷﻥ ﺍﻟﺘﺮﺗﻴﺐ ﻣﻤﻜﻦ ﻓﻲ ﺣﺎﻟﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺘﺮﺗﻴﺒﻴﺔ‪،‬ﻣﺘﻮﺳﻂ‪ ،‬ﻭ‬ ‫ﺍﻷﺭﺑﺎﻉﻳﻤﻜﻦ ﺗﻄﺒﻴﻘﻬﺎ ﺃﻳﻀﺎً‪.‬ﻻ ﻳﺰﺍﻝ ﻣﻦ ﻏﻴﺮ ﺍﻟﻤﻤﻜﻦ ﺣﺴﺎﺏ‬ ‫‪11‬‬ ‫ﺍﻟﻤﺘﻮﺳﻂﻭﺍﻟﺘﺒﺎﻳﻦ‪.‬‬  ‫ﺍﻟﺒﻴﺎﻧﺎﺕﺍﻟﻜﻤﻴﺔﻫﻲ ﻣﻌﻠﻮﻣﺎﺕ ﺣﻮﻝ ﻛﻤﻴﺔ ﺷﻲء ﻣﺎ ﻳﻤﻜﻦ ﻗﻴﺎﺳﻬﺎ )‬ ‫ﻥ‬ ‫ﻣﺮﺗﺒﺔﺑﺸﻜﻞ ﻭﺍﺿﺢ(‬ ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﻳﻤﻜﻦ ﻗﻴﺎﺱ ﺳﻤﺔ "ﺍﻟﻌﻼﻣﺎﺕ" ﺑﺎﺳﺘﺨﺪﺍﻡ ﻣﻘﻴﺎﺱ‬ ‫ﺃ‬ ‫ﺍﻟﻘﻴﺎﺱ‪.‬‬ ‫ﻫﻨﺎﻙﻧﻮﻋﺎﻥ ﻣﻦ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻜﻤﻴﺔ‪:‬‬ ‫ﻥ‬ ‫ﺑﻴﺎﻧﺎﺕﺍﻟﻔﺎﺻﻞ ﺍﻟﺰﻣﻨﻲ‬ ‫ﺃ‬ ‫ﺑﻴﺎﻧﺎﺕﺍﻟﻨﺴﺒﺔ‬ ‫ﺃ‬ ‫ﺑﻴﺎﻧﺎﺕﺍﻟﻔﺎﺻﻞ ﺍﻟﺰﻣﻨﻲﻫﻲ ﺑﻴﺎﻧﺎﺕ ﻛﻤﻴﺔ ﺣﻴﺚ ﻳﻜﻮﻥ ﺍﻟﻔﺮﻕ‬ ‫ﻥ‬ ‫ﺍﻟﺪﻗﻴﻖﺑﻴﻦ ﻗﻴﻤﻬﺎ ﻣﻌﺮﻭﻓﺎً ﺃﻳﻀﺎً‪.‬ﻟﻜﻦﻻ ﻳﻮﺟﺪ ﻟﺪﻱﺻﻔﺮ ﻣﻄﻠﻖ')‬ ‫ﻧﻘﻄﺔﺍﻟﺼﻔﺮ ﺫﺍﺕ ﺍﻟﻤﻌﻨﻰ(‪.‬‬ ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﺩﺭﺟﺔ ﺍﻟﺤﺮﺍﺭﺓ ﻋﺒﺎﺭﺓ ﻋﻦ ﺑﻴﺎﻧﺎﺕ ﻓﺎﺻﻠﺔ‪.‬ﺍﻟﻔﺮﻕ ﺑﻴﻦ ‪12‬‬ ‫ﺃ‬ ‫ﺩﺭﺟﺔﻣﺉﻮﻳﺔ ﻭ‪ 18‬ﺩﺭﺟﺔ ﻣﺉﻮﻳﺔ ﻫﻮ ‪ 6‬ﺩﺭﺟﺎﺕ ﻣﺉﻮﻳﺔ ﻣﺜﻞ ﺍﻟﻔﺮﻕ ﺑﻴﻦ ‪15.5‬‬ ‫ﺩﺭﺟﺔﻣﺉﻮﻳﺔ ﻭ‪ 21.5‬ﺩﺭﺟﺔ ﻣﺉﻮﻳﺔ‪.‬‬ ‫ﺩﺭﺟﺔﺣﺮﺍﺭﺓ ﺻﻔﺮ ﺩﺭﺟﺔ ﻻ ﺗﻌﻨﻲ ﺃﻧﻪ ﻻ ﺗﻮﺟﺪ ﺩﺭﺟﺔ ﺣﺮﺍﺭﺓ )ﺃﻭ ﻻ ﺗﻮﺟﺪ ﺣﺮﺍﺭﺓ‬ ‫ﺃ‬ ‫ﻋﻠﻰﺍﻹﻃﻼﻕ( ‪ -‬ﺑﻞ ﺗﻌﻨﻲ ﻓﻘﻂ ﺃﻥ ﺩﺭﺟﺔ ﺍﻟﺤﺮﺍﺭﺓ ﺃﻗﻞ ﺑـ ‪ 10‬ﺩﺭﺟﺎﺕ ﻣﻦ‬ ‫‪.10‬‬ ‫‪12‬‬ ‫ﻭﺗﺸﻤﻞﺍﻷﻣﺜﻠﺔ ﺍﻷﺧﺮﻯ ﺍﻟﺘﺎﺭﻳﺦ ﻭﺍﻟﻮﻗﺖ ﻭﻣﺎ ﺇﻟﻰ ﺫﻟﻚ‪.‬‬ ‫ﺃ‬ ‫ﺑﺎﻟﻨﺴﺒﺔﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻔﻮﺍﺻﻞ ﺍﻟﺰﻣﻨﻴﺔ‪ ،‬ﻣﻦ ﺍﻟﻤﻤﻜﻦ ﺇﺟﺮﺍء ﻋﻤﻠﻴﺎﺕ ﺣﺴﺎﺑﻴﺔ ﻣﺜﻞ‬ ‫ﻥ‬ ‫ﺍﻟﺠﻤﻊﻭﺍﻟﻄﺮﺡ‪.‬ﻭﻟﻬﺬﺍ ﺍﻟﺴﺒﺐ‪ ،‬ﺑﺎﻟﻨﺴﺒﺔ ﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻔﻮﺍﺻﻞ ﺍﻟﺰﻣﻨﻴﺔ‪ ،‬ﻣﻦ‬ ‫ﺍﻟﻤﻤﻜﻦﻗﻴﺎﺱ ﺍﻟﻤﺘﻮﺳﻂ ﺍﻟﺤﺴﺎﺑﻲ ﻭﺍﻟﻮﺳﻴﻂ ﻭﺍﻟﻤﻨﻮﺍﻝ ﻭﺍﻻﻧﺤﺮﺍﻑ‬ ‫ﺍﻟﻤﻌﻴﺎﺭﻱﻭﻣﺎ ﺇﻟﻰ ﺫﻟﻚ‪.‬‬ ‫ﺑﻴﺎﻧﺎﺕﺍﻟﻨﺴﺒﺔﻫﻲ ﺑﻴﺎﻧﺎﺕ ﻛﻤﻴﺔ ﺣﻴﺚ ﻳﻜﻮﻥ ﺍﻟﻔﺮﻕ ﺍﻟﺪﻗﻴﻖ ﺑﻴﻦ‬ ‫ﻥ‬ ‫ﺍﻟﻘﻴﻢﻣﻌﺮﻭﻓﺎً ﻭﻟﻬﺎ ﺃﻳﻀﺎً "ﺻﻔﺮ ﻣﻄﻠﻖ' ‪.‬‬ ‫ﺑﺎﻟﻨﺴﺒﺔﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻨﺴﺒﺔ‪ ،‬ﻣﻦ ﺍﻟﻤﻤﻜﻦ ﺇﺟﺮﺍء ﻋﻤﻠﻴﺎﺕ ﺣﺴﺎﺑﻴﺔ ﻣﺜﻞ‬ ‫ﻥ‬ ‫ﺍﻟﺠﻤﻊﻭﺍﻟﻄﺮﺡ‪.‬ﻭﻳﻤﻜﻦ ﻗﻴﺎﺱ ﺍﻟﻤﺘﻮﺳﻂ ﻭﺍﻟﻮﺳﻴﻂ ﻭﺍﻟﻤﻨﻮﺍﻝ‬ ‫ﻭﺍﻻﻧﺤﺮﺍﻑﺍﻟﻤﻌﻴﺎﺭﻱ‪.‬‬ ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﺍﻟﺴﻤﺎﺕ ﻣﺜﻞ ﺍﻟﻄﻮﻝ ﻭﺍﻟﻮﺯﻥ ﻭﺍﻟﻌﻤﺮ ﻭﺍﻟﺮﺍﺗﺐ ﻭﻣﺎ‬ ‫ﺃ‬ ‫ﺇﻟﻰﺫﻟﻚ ﻫﻲ ﺑﻴﺎﻧﺎﺕ ﻧﺴﺒﻴﺔ‪.‬‬ ‫‪13‬‬ 14  ‫ﺍﺳﺘﻜﺸﺎﻑﺑﻨﻴﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﺍﺳﺘﻜﺸﺎﻑﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻜﻤﻴﺔ‬ ‫ﻓﻬﻢﺍﻻﺗﺠﺎﻩ ﺍﻟﻤﺮﻛﺰﻱ‬ ‫ﺗﺴﺎﻋﺪﻣﻘﺎﻳﻴﺲ ﺍﻻﺗﺠﺎﻩ ﺍﻟﻤﺮﻛﺰﻱ ﻋﻠﻰ ﻓﻬﻢ ﺍﻟﻨﻘﻄﺔ ﺍﻟﻤﺮﻛﺰﻳﺔ‬ ‫ﻥ‬ ‫ﻟﻤﺠﻤﻮﻋﺔﻣﻦ ﺍﻟﺒﻴﺎﻧﺎﺕ‪.‬‬ ‫ﻳﻘﺼﺪ‪ :‬ﻫﻮ ﻣﺠﻤﻮﻉ ﻛﻞ ﻗﻴﻢ ﺍﻟﺒﻴﺎﻧﺎﺕ ﻣﻘﺴﻮﻣﺎً ﻋﻠﻰ ﻋﺪﺩ ﻋﻨﺎﺻﺮ‬ ‫ﺃ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﻣﺘﻮﺳﻂ‪:‬ﻋﻠﻰ ﺍﻟﻌﻜﺲ ﻣﻦ ﺫﻟﻚ‪ ،‬ﻓﺈﻥ ﺍﻟﻮﺳﻴﻂ ﻫﻮ ﻗﻴﻤﺔ ﺍﻟﻌﻨﺼﺮ ﺍﻟﺬﻱ‬ ‫ﺃ‬ ‫ﻳﻈﻬﺮﻓﻲ ﻣﻨﺘﺼﻒ ﻗﺎﺉﻤﺔ ﻣﺮﺗﺒﺔ ﻣﻦ ﻋﻨﺎﺻﺮ ﺍﻟﺒﻴﺎﻧﺎﺕ‪.‬‬ ‫ﻗﺪﻳﻜﻮﻥ ﻫﻨﺎﻙ ﺗﺴﺎﺅﻝ ﺣﻮﻝ ﺳﺒﺐ ﻣﺮﺍﺟﻌﺔ ﻣﻘﻴﺎﺳﻴﻦ ﻟﻼﺗﺠﺎﻩ ﺍﻟﻤﺮﻛﺰﻱ‪.‬‬ ‫ﻥ‬ ‫ﻭﺍﻟﺴﺒﺐﻫﻮ ﺃﻥ ﺍﻟﻤﺘﻮﺳﻂ ﻭﺍﻟﻮﺳﻴﻂ ﻳﺘﺄﺛﺮﺍﻥ ﺑﺸﻜﻞ ﻣﺨﺘﻠﻒ ﺑﻘﻴﻢ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕﺍﻟﺘﻲ ﺗﻈﻬﺮ ﻓﻲ ﺑﺪﺍﻳﺔ ﺍﻟﻨﻄﺎﻕ ﺃﻭ ﻧﻬﺎﻳﺘﻪ‪.‬‬ ‫‪15‬‬  ‫ﺍﻟﻤﺘﻮﺳﻂﺣﺴﺎﺱ ﻟﻠﻐﺎﻳﺔ ﻟﻠﻘﻴﻢ ﺍﻟﻤﺘﻄﺮﻓﺔ )ﺍﻟﻘﻴﻢ ﺍﻟﺘﻲ ﺗﻜﻮﻥ ﻣﺮﺗﻔﻌﺔ‬ ‫ﻥ‬ ‫ﺃﻭﻣﻨﺨﻔﻀﺔ ﺑﺸﻜﻞ ﻏﻴﺮ ﻋﺎﺩﻱ‪ ،‬ﻣﻘﺎﺭﻧﺔ ﺑﺎﻟﻘﻴﻢ ﺍﻷﺧﺮﻯ(‪.‬‬ ‫ﺇﺫﺍﻻﺣﻈﻨﺎ ﺃﻧﻪ ﺑﺎﻟﻨﺴﺒﺔ ﻟﺒﻌﺾ ﺍﻟﺴﻤﺎﺕ‪،‬ﺍﻧﺤﺮﺍﻑ ﺇﺫﺍ ﻛﺎﻧﺖ ﻗﻴﻢ‬ ‫ﻥ‬ ‫ﺍﻟﻤﺘﻮﺳﻂﻭﺍﻟﻮﺳﻴﻂ ﻣﺮﺗﻔﻌﺔ ﺟﺪﺍً‪ ،‬ﻓﻴﺠﺐ ﻋﻠﻴﻨﺎ ﺍﻟﺘﺤﻘﻴﻖ ﻓﻲ ﻫﺬﻩ‬ ‫ﺍﻟﺴﻤﺎﺕﺑﺸﻜﻞ ﺃﻛﺒﺮ‪.‬‬ ‫‪Auto-MPG‬ﺍﻟﺴﻴﺎﺭﺍﺕ‪16‬‬ ‫ﺃﺩﺍءﺍﺳﺘﻬﻼﻙ ﺍﻟﻮﻗﻮﺩ ﻟﻜﻞ ﺟﺎﻟﻮﻥ ﻣﻦ ﺍﻟﺴﻴﺎﺭﺍﺕ ﺍﻟﻤﺨﺘﻠﻔﺔ ﺣﺴﺐ ﻧﻈﺎﻡ‬  ‫‪%‬‬ ‫ﺍﻻﻧﺤﺮﺍﻑﻣﻬﻢ ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﺴﻤﺎﺕ "ﺍﻷﺳﻄﻮﺍﻧﺎﺕ" ﻭ"ﺍﻹﺯﺍﺣﺔ" ﻭ"ﺍﻷﺻﻞ"‪.‬‬ ‫ﻥ‬ ‫ﻟﺬﺍ‪،‬ﻧﺤﺘﺎﺝ ﺇﻟﻰ ﺇﻟﻘﺎء ﻧﻈﺮﺓ ﺃﻋﻤﻖ ﻋﻠﻰ ﺑﻌﺾ ﺍﻹﺣﺼﺎﺉﻴﺎﺕ ﺍﻹﺿﺎﻓﻴﺔ‬ ‫ﻟﻬﺬﻩﺍﻟﺴﻤﺎﺕ‪.‬‬ ‫ﻫﻨﺎﻙﺃﻳﻀﺎً ﺑﻌﺾ ﺍﻟﻤﺸﺎﻛﻞ ﻓﻲ ﻗﻴﻢ ﺳﻤﺔ "ﻗﻮﺓ ﺍﻟﺤﺼﺎﻥ" ﻭﺍﻟﺘﻲ ﺑﺴﺒﺒﻬﺎ‬ ‫ﻥ‬ ‫ﻻﻳﻤﻜﻦ ﺣﺴﺎﺏ ﺍﻟﻤﺘﻮﺳﻂ ﻭﺍﻟﻮﺳﻴﻂ‪.‬‬ ‫‪17‬‬  ‫ﻓﻬﻢﺍﻧﺘﺸﺎﺭ ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﺍﻵﻥ‪،‬ﻟﺪﻳﻨﺎ ﻓﻜﺮﺓ ﻭﺍﺿﺤﺔ ﻋﻦ ﺍﻟﺴﻤﺎﺕ ﺍﻟﺘﻲ ﻳﻮﺟﺪ ﺑﻬﺎ ﺍﻧﺤﺮﺍﻑ ﻛﺒﻴﺮ‬ ‫ﻥ‬ ‫ﺑﻴﻦﺍﻟﻤﺘﻮﺳﻂ ﻭﺍﻟﻮﺳﻴﻂ‪.‬ﺩﻋﻮﻧﺎ ﻧﻨﻈﺮ ﻋﻦ ﻛﺜﺐ ﺇﻟﻰ ﺗﻠﻚ ﺍﻟﺴﻤﺎﺕ‬ ‫ﻓﻲﺷﻜﻞ‬ ‫ﺗﺸﺘﺖﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﺃ‬ ‫ﻣﻮﺿﻊﻗﻴﻢ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻤﺨﺘﻠﻔﺔ‬ ‫ﺃ‬ ‫ﺗﺸﺘﺖﺍﻟﺒﻴﺎﻧﺎﺕ‪:‬‬ ‫ﻥﺧﺬ ﻓﻲ ﺍﻻﻋﺘﺒﺎﺭ ﻗﻴﻢ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺨﺎﺻﺔ ﺑﺨﺎﺻﻴﺘﻴﻦ‪:‬‬ ‫ﺍﻟﻤﺘﻮﺳﻂ= ‪46‬‬ ‫ﻗﻴﻢﺍﻟﺴﻤﺔ ‪ ،45 ،48 ،46 ،44 :1‬ﻭ‪ 47‬ﻗﻴﻢ ﺍﻟﺴﻤﺔ ‪:2‬‬ ‫ﻥ‬ ‫ﺍﻟﻤﺘﻮﺳﻂ= ‪46‬‬ ‫‪ ،39 ،59 ،46،34‬ﻭ‪52‬‬ ‫ﻥ‬ ‫ﻭﻣﻊﺫﻟﻚ‪ ،‬ﻓﺈﻥ ﻣﺠﻤﻮﻋﺔ ﻗﻴﻢ ﺍﻟﺴﻤﺔ ‪ 1‬ﺗﺘﺮﻛﺰ ﺑﺸﻜﻞ ﺃﻛﺒﺮ ﺣﻮﻝ ﺍﻟﻘﻴﻤﺔ‬ ‫ﺍﻟﻤﺘﻮﺳﻄﺔﺑﻴﻨﻤﺎ ﺍﻟﻤﺠﻤﻮﻋﺔ ﺍﻟﺜﺎﻧﻴﺔ ﻣﻦ ﻗﻴﻢ ﺍﻟﺴﻤﺔ ‪ 2‬ﻣﻨﺘﺸﺮﺓ ﺃﻭ ﻣﺸﺘﺘﺔ‬ ‫ﺇﻟﻰﺣﺪ ﻛﺒﻴﺮ‪.‬‬ ‫‪18‬‬  ‫ﻟﻤﻌﺮﻓﺔﻣﺪﻯ ﺍﻧﺘﺸﺎﺭ ﺍﻟﻘﻴﻢ ﺍﻟﻤﺨﺘﻠﻔﺔ ﻟﻠﺒﻴﺎﻧﺎﺕ‪ ،‬ﻳﺘﻢ ﻗﻴﺎﺱ ﺗﺒﺎﻳﻦ‬ ‫ﻥ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕﻋﻠﻰ ﺍﻟﻨﺤﻮ ﺍﻟﺘﺎﻟﻲ‪:‬‬ ‫)‬ ‫!=‬ ‫" ∑‪,+*%('&%‬‬ ‫‪-‬‬ ‫ﺣﻴﺚ ‪.‬ﻫﻮ ﻣﺘﻮﺳﻂ ﻋﻨﺎﺻﺮ ﺍﻟﺒﻴﺎﻧﺎﺕ‪ / ،‬ﻫﻮ ﻋﺪﺩﻫﺎ‬ ‫ﺗﺸﻴﺮﺍﻟﻘﻴﻤﺔ ﺍﻷﻛﺒﺮ ﻟﻠﺘﺒﺎﻳﻦ ﺇﻟﻰ ﻣﺰﻳﺪ ﻣﻦ ﺍﻟﺘﺸﺘﺖ ﻓﻲ ﺍﻟﺒﻴﺎﻧﺎﺕ ﻭﺍﻟﻌﻜﺲ‬ ‫ﻥ‬ ‫ﺻﺤﻴﺢ‪.‬ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﻤﺜﺎﻝ ﺃﻋﻼﻩ‪،‬‬ ‫" =)‪,(28*22)5,(27*22)5,(26*22)5,(23*23)5,(23*22‬‬ ‫=‪6‬‬ ‫ﺃ !‪0‬‬ ‫‪7‬‬ ‫‪7)5,(23*23‬؛*‪:)5,(26‬؛*‪,(28*"7)5,(27‬‬ ‫)‪5 ( ),23*2:‬‬ ‫= ‪65.2‬‬ ‫!" "=‬ ‫ﺃ‬ ‫‪7‬‬ ‫ﻟﺬﺍﻓﻤﻦ ﺍﻟﻮﺍﺿﺢ ﺗﻤﺎﻣﺎً ﻣﻦ ﺍﻟﻘﻴﺎﺱ ﺃﻥ ﻗﻴﻢ ﺍﻟﺴﻤﺔ ‪ 1‬ﺗﺘﺮﻛﺰ ﺗﻤﺎﻣﺎً‬ ‫ﻥ‬ ‫ﺣﻮﻝﺍﻟﻤﺘﻮﺳﻂ ﺑﻴﻨﻤﺎ ﻗﻴﻢ ﺍﻟﺴﻤﺔ ‪ 2‬ﻣﺘﺒﺎﻋﺪﺓ ﻟﻠﻐﺎﻳﺔ‪.‬‬ ‫‪19‬‬  ‫ﻗﻴﺎﺱﻣﻮﺿﻊ ﻗﻴﻤﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ‪:‬‬ ‫ﻳﺘﻢﺗﺮﺗﻴﺐ ﻗﻴﻢ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺨﺎﺻﺔ ﺑﺨﺎﺻﻴﺔ ﻣﺎ ﺑﺘﺮﺗﻴﺐ ﺗﺼﺎﻋﺪﻱ ﺛﻢ‬ ‫ﻥ‬ ‫ﺗﻘﺴﻴﻤﻬﺎﺇﻟﻰ ﻧﺼﻔﻴﻦ‪.‬ﻳﺘﻢ ﺗﻘﺴﻴﻢ ﻛﻞ ﻧﺼﻒ ﺇﻟﻰ ﻧﺼﻔﻴﻦ‪.‬‬ ‫ﺍﻟﺤﺪﺍﻷﻗﺼﻰ‬ ‫ﺱ‪2‬‬ ‫ﺍﻟﻤﺘﻮﺳﻂ)ﺍﻟﺮﺑﻊ ﺍﻟﺜﺎﻧﻲ(‬ ‫ﺱ‪1‬‬ ‫ﺍﻟﺤﺪﺍﻷﺩﻧﻰ‬ ‫ﻧﺤﻦﻧﻨﻈﺮ ﺇﻟﻰ ﺍﻟﻔﺮﻕ ﺑﻴﻦ ﺍﻷﺭﺑﺎﻉ )ﺍﻟﺤﺪ ﺍﻷﺩﻧﻰ ﻭ‪ Q1، Q1‬ﻭﺍﻟﻮﺳﻴﻂ‪،‬‬ ‫ﻥ‬ ‫ﺍﻟﻮﺳﻴﻂﻭ‪ Q2، Q2‬ﻭﺍﻟﺤﺪ ﺍﻷﻗﺼﻰ( ﺍﻟﻘﻴﻢ ﺍﻷﻛﺒﺮ ﺃﻛﺜﺮ ﺍﻧﺘﺸﺎﺭﺍً ﻣﻦ ﺍﻟﻘﻴﻢ‬ ‫ﺍﻷﺻﻐﺮ‪.‬‬ ‫ﻳﺴﺎﻋﺪﻫﺬﺍ ﻓﻲ ﻓﻬﻢ ﺳﺒﺐ ﻛﻮﻥ ﻗﻴﻤﺔ ﺍﻟﻤﺘﻮﺳﻂ ﺃﻋﻠﻰ ﺑﻜﺜﻴﺮ ﻣﻦ‬ ‫ﻥ‬ ‫ﻗﻴﻤﺔﺍﻟﻮﺳﻴﻂ ﻟﺨﺎﺻﻴﺔ "ﺍﻹﺯﺍﺣﺔ"‪.‬‬ ‫ﻭﻣﻊﺫﻟﻚ‪ ،‬ﻻ ﻳﺰﺍﻝ ﻣﻦ ﻏﻴﺮ ﺍﻟﻤﻤﻜﻦ ﺍﻟﺘﺄﻛﺪ ﻣﻦ ﻭﺟﻮﺩ ﺃﻱ ﻗﻴﻤﺔ ﺷﺎﺫﺓ ﻓﻲ‬ ‫ﻥ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕ‪.‬ﻭﻟﺘﺤﻘﻴﻖ ﻫﺬﻩ ﺍﻟﻐﺎﻳﺔ‪ ،‬ﻳﻤﻜﻨﻨﺎ ﺍﺳﺘﺨﺪﺍﻡ ﺑﻌﺾ ﺍﻟﻮﺳﺎﺉﻞ‬ ‫‪20‬‬ ‫ﻟﺘﺼﻮﺭﺍﻟﺒﻴﺎﻧﺎﺕ‪.‬‬  ‫ﺭﺳﻢﻭﺍﺳﺘﻜﺸﺎﻑ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺮﻗﻤﻴﺔ ﻣﺨﻄﻄﺎﺕ‬ ‫ﺍﻟﺼﻨﺪﻭﻕ‪:‬‬ ‫ﻳﻌﻄﻲﺍﻟﺮﺳﻢ ﺍﻟﺒﻴﺎﻧﻲ ﺍﻟﺼﻨﺪﻭﻗﻲ )ﻳﺴُﻤﻰ ﺃﻳﻀﺎً ﺍﻟﺮﺳﻢ ﺍﻟﺒﻴﺎﻧﻲ‬ ‫ﻥ‬ ‫ﺍﻟﺼﻨﺪﻭﻗﻲﻭﺍﻟﺸﺎﺭﺏ( ﺗﺼﻮﺭﺍً ﻗﻴﺎﺳﻴﺎً ﻹﺣﺼﺎﺉﻴﺎﺕ ﺍﻟﻤﻠﺨﺺ ﺍﻟﻤﻜﻮﻧﺔ‬ ‫ﻣﻦﺧﻤﺴﺔ ﺃﺭﻗﺎﻡ ﻟﻤﺠﻤﻮﻋﺔ ﺑﻴﺎﻧﺎﺕ‪ ،‬ﻭﻫﻲ‪ :‬ﺍﻟﺤﺪ ﺍﻷﺩﻧﻰ‪ ،‬ﻭﺍﻟﺮﺑﻊ ﺍﻷﻭﻝ‬ ‫)‪ ،(Q1‬ﻭﺍﻟﻮﺳﻴﻂ )‪ ،(Q2‬ﻭﺍﻟﺮﺑﻊ ﺍﻟﺜﺎﻟﺚ )‪ ،(Q3‬ﻭﺍﻟﺤﺪ ﺍﻷﻗﺼﻰ‪.‬ﻓﻴﻤﺎ ﻳﻠﻲ‬ ‫ﺗﻔﺴﻴﺮﻣﻔﺼﻞ ﻟﻠﺮﺳﻢ ﺍﻟﺒﻴﺎﻧﻲ ﺍﻟﺼﻨﺪﻭﻗﻲ‪.‬‬ ‫‪21‬‬  ‫ﻳﺒﺪﻭﺍﻟﺮﺳﻢ ﺍﻟﺒﻴﺎﻧﻲ ﻟﻠﺼﻨﺪﻭﻕ ﺍﻟﺨﺎﺹ ﺑﺨﺎﺻﻴﺔ "ﺍﻷﺳﻄﻮﺍﻧﺎﺕ" ﻏﺮﻳﺒﺎً‬ ‫ﻥ‬ ‫ﺟﺪﺍًﻓﻲ ﺍﻟﺸﻜﻞ‪.‬ﻓﺎﻟﺸﺎﺭﺏ ﺍﻟﻌﻠﻮﻱ ﻣﻔﻘﻮﺩ‪ ،‬ﻭﺍﻟﻮﺳﻂ ﻳﻘﻊ ﻓﻲ ﺃﺳﻔﻞ‬ ‫ﺍﻟﺼﻨﺪﻭﻕ‪،‬ﻭﺣﺘﻰ ﺍﻟﺸﺎﺭﺏ ﺍﻟﺴﻔﻠﻲ ﺻﻐﻴﺮ ﺟﺪﺍً ﻣﻘﺎﺭﻧﺔ ﺑﻄﻮﻝ ﺍﻟﺼﻨﺪﻭﻕ!‬ ‫ﻫﻞﻛﻞ ﺷﻲء ﻋﻠﻰ ﻣﺎ ﻳﺮﺍﻡ؟‬ ‫ﺍﻟﺠﻮﺍﺏﻫﻮ ﻛﺒﻴﺮﻧﻌﻢ‪.‬ﺍﻟﺨﺎﺻﻴﺔ "ﺍﻷﺳﻄﻮﺍﻧﺎﺕ" ﻣﻨﻔﺼﻠﺔ ﺑﻄﺒﻴﻌﺘﻬﺎ‬ ‫ﻥ‬ ‫‪22‬‬ ‫ﻭﺗﺘﺮﺍﻭﺡﻗﻴﻤﻬﺎ ﻣﻦ ‪ 3‬ﺇﻟﻰ ‪.8‬‬  ‫ﺍﻟﻬﻴﺴﺘﻮﺟﺮﺍﻡ‪:‬‬ ‫ﻫﻮﺭﺳﻢ ﺑﻴﺎﻧﻲ ﻳﻮﺿﺢ ﺗﺮﺩﺩ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺮﻗﻤﻴﺔ ﺑﺎﺳﺘﺨﺪﺍﻡ ﻣﺴﺘﻄﻴﻼﺕ‬ ‫ﻣﺴﺎﺣﺘﻬﺎﻣﺘﻨﺎﺳﺒﺔ ﻣﻊ ﺗﺮﺩﺩ ﺍﻟﺒﻴﺎﻧﺎﺕ ﻭﻋﺮﺿﻬﺎ ﻳﺴﺎﻭﻱ ﻓﺘﺮﺓ ﺍﻟﺒﻴﺎﻧﺎﺕ‪.‬‬ ‫ﻗﺪﺗﻜﻮﻥ ﺍﻟﻬﺴﺘﻮﺟﺮﺍﻣﺎﺕ ﺫﺍﺕ ﺃﺷﻜﺎﻝ ﻣﺨﺘﻠﻔﺔ ﺍﻋﺘﻤﺎﺩﺍً ﻋﻠﻰ ﻃﺒﻴﻌﺔ‬ ‫ﻥ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫‪23‬‬  ‫ﺕ‬ ‫ﻥ‬ ‫ﺕ‬ ‫ﺍﻧﺖ‬ ‫ﺃ‬ ‫ﻡ‬  ‫ﺍﺳﺘﻜﺸﺎﻑﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻨﻮﻋﻴﺔ‬ ‫ﻻﺗﻮﺟﺪ ﻫﻨﺎ ﺍﻟﻌﺪﻳﺪ ﻣﻦ ﺍﻟﺨﻴﺎﺭﺍﺕ ﻻﺳﺘﻜﺸﺎﻑ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﻨﻮﻋﻴﺔ‪.‬‬ ‫ﻥ‬ ‫ﺳﻨﻮﺿﺢﻋﺪﺩ ﺍﻟﻘﻴﻢ ﺍﻟﻔﺮﻳﺪﺓ ﺍﻟﻤﺘﺎﺣﺔ ﻟﻠﺴﻤﺔ‪.‬‬ ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﺑﺎﻟﻨﺴﺒﺔ ﻟﺨﺎﺻﻴﺔ 'ﺍﺳﻢ ﺍﻟﺴﻴﺎﺭﺓ'‬ ‫ﻥ‬ ‫‪.1‬ﺷﻴﻔﺮﻭﻟﻴﻪ ﺷﻴﻔﻴﻠﻲ ﻣﺎﻟﻴﺒﻮ‬ ‫‪.2‬ﺑﻴﻮﻙ ﺳﻜﺎﻱ ﻻﺭﻙ ‪320‬‬ ‫‪.3‬ﻗﻤﺮ ﺻﻨﺎﻋﻲ ﺑﻠﻴﻤﻮﺙ‬ ‫‪4. AMC Rebel SST‬‬ ‫‪.5‬ﻓﻮﺭﺩ ﺗﻮﺭﻳﻨﻮ‬ ‫‪.6‬ﻓﻮﺭﺩ ﺟﻼﻛﺴﻲ ‪500‬‬ ‫‪.7‬ﺷﻴﻔﺮﻭﻟﻴﻪ ﺇﻣﺒﺎﻻ‬ ‫‪.8‬ﺑﻠﻴﻤﻮﺙ ﻓﻴﻮﺭﻱ ‪3‬‬ ‫‪.9‬ﺑﻮﻧﺘﻴﺎﻙ ﻛﺎﺗﺎﻟﻴﻨﺎ‬ ‫‪.10‬ﺳﻔﻴﺮ ‪AMC dpl‬‬ ‫‪25‬‬  ‫ﻳﻤﻜﻨﻨﺎﺃﻳﻀﺎً ﺍﻟﺒﺤﺚ ﻋﻦ ﻣﺰﻳﺪ ﻣﻦ ﺍﻟﺘﻔﺎﺻﻴﻞ ﻭﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ ﺟﺪﻭﻝ‬ ‫ﻥ‬ ‫ﻳﺤﺘﻮﻱﻋﻠﻰ ﻋﺪﺩ ﻋﻨﺎﺻﺮ ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﻗﺪﻧﻜﻮﻥ ﻣﻬﺘﻤﻴﻦ ﺃﻳﻀﺎً ﺑﻤﻌﺮﻓﺔ ﻧﺴﺒﺔ )ﺃﻭ ﻧﺴﺒﺔ ﻣﺉﻮﻳﺔ( ﻋﺪﺩ ﻋﻨﺎﺻﺮ‬ ‫ﻥ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫‪26‬‬  ‫ﺍﺳﺘﻜﺸﺎﻑﺍﻟﻌﻼﻗﺔ ﺑﻴﻦ ﺍﻟﺴﻤﺎﺕ‬ ‫ﻣﺨﻄﻂﺍﻟﺘﺸﺘﺖ‪:‬‬ ‫ﺭﺳﻢﺑﻴﺎﻧﻲ ﺛﻨﺎﺉﻲ ﺍﻷﺑﻌﺎﺩ ﻳﺴﺎﻋﺪ ﻋﻠﻰ ﺗﺼﻮﺭ ﺍﻟﻌﻼﻗﺔ ﺑﻴﻦ ﺳﻤﺘﻴﻦ )‬ ‫ﻥ‬ ‫ﻣﺘﻐﻴﺮﻳﻦ(‪.‬‬ ‫ﺍﻟﺸﺎﺫ‬ ‫‪27‬‬ 28  ‫ﺟﻮﺩﺓﺍﻟﺒﻴﺎﻧﺎﺕ ﻭﻣﻌﺎﻟﺠﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﺟﻮﺩﺓﺍﻟﺒﻴﺎﻧﺎﺕ‪:‬‬ ‫ﻳﻌﺘﻤﺪﻧﺠﺎﺡ ﺍﻟﺘﻌﻠﻢ ﺍﻵﻟﻲ ﺇﻟﻰ ﺣﺪ ﻛﺒﻴﺮ ﻋﻠﻰ ﺟﻮﺩﺓ ﺍﻟﺒﻴﺎﻧﺎﺕ‪.‬ﺗﺴﺎﻋﺪ‬ ‫ﻥ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕﺫﺍﺕ ﺍﻟﺠﻮﺩﺓ ﺍﻟﻤﻨﺎﺳﺒﺔ ﻓﻲ ﺗﺤﻘﻴﻖ ﺩﻗﺔ ﺃﻓﻀﻞ ﻓﻲ ﺍﻟﺘﻨﺒﺆ‪.‬‬ ‫ﻟﻘﺪﻭﺍﺟﻬﻨﺎ ﺑﺎﻟﻔﻌﻞ ﻧﻮﻋﻴﻦ ﻋﻠﻰ ﺍﻷﻗﻞ ﻣﻦ ﺍﻟﻤﺸﺎﻛﻞ‪:‬‬ ‫ﻥ‬ ‫ﻋﻨﺎﺻﺮﺍﻟﺒﻴﺎﻧﺎﺕ ﺑﺪﻭﻥ ﻗﻴﻢ ﺃﻭ ﺑﻴﺎﻧﺎﺕ ﺫﺍﺕ ﻗﻴﻢ ﻣﻔﻘﻮﺩﺓ‬ ‫ﺃ‬ ‫ﻋﻨﺎﺻﺮﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺘﻲ ﻟﻬﺎ ﻗﻴﻤﺔ ﻣﺨﺘﻠﻔﺔ ﻋﻦ ﺍﻟﻌﻨﺎﺻﺮ ﺍﻷﺧﺮﻯ‪،‬‬ ‫ﺃ‬ ‫ﻭﺍﻟﺘﻲﻧﻄﻠﻖ ﻋﻠﻴﻬﺎ "ﺍﻟﻘﻴﻢ ﺍﻟﻤﺘﻄﺮﻓﺔ"‪.‬‬ ‫‪29‬‬  ‫ﻣﻌﺎﻟﺠﺔﺍﻟﺒﻴﺎﻧﺎﺕ‪:‬‬ ‫ﺇﻥﺍﻟﻘﻀﺎﻳﺎ ﺍﻟﻤﺘﻌﻠﻘﺔ ﺑﺠﻮﺩﺓ ﺍﻟﺒﻴﺎﻧﺎﺕ‪ ،‬ﺍﻟﻤﺬﻛﻮﺭﺓ ﺃﻋﻼﻩ‪ ،‬ﺗﺤﺘﺎﺝ ﺇﻟﻰ‬ ‫ﻥ‬ ‫ﻣﻌﺎﻟﺠﺔﻟﺘﺤﻘﻴﻖ ﺍﻟﻘﺪﺭ ﺍﻟﻤﻨﺎﺳﺐ ﻣﻦ ﺍﻟﻜﻔﺎءﺓ‪.‬‬ ‫‪ (1‬ﺍﻟﻘﻴﻢ ﺍﻟﻤﺘﻄﺮﻓﺔ‬ ‫ﺍﻟﻘﻴﻢﺍﻟﻤﺘﻄﺮﻓﺔ ﻫﻲ ﻋﻨﺎﺻﺮ ﺑﻴﺎﻧﺎﺕ ﺫﺍﺕ ﻗﻴﻤﺔ ﻋﺎﻟﻴﺔ ﺑﺸﻜﻞ ﻏﻴﺮ ﻃﺒﻴﻌﻲ‬ ‫ﻥ‬ ‫ﻣﻤﺎﻗﺪ ﻳﺆﺛﺮ ﻋﻠﻰ ﺩﻗﺔ ﺍﻟﺘﻨﺒﺆ‪.‬‬ ‫ﺍﻛﺘﺸﺎﻑﺍﻟﻘﻴﻢ ﺍﻟﻤﺘﻄﺮﻓﺔ‪:‬‬ ‫ﻫﻨﺎﻙﻋﺪﺩ ﻣﻦ ﺍﻟﺘﻘﻨﻴﺎﺕ ﻟﻠﻜﺸﻒ ﻋﻦ ﺍﻟﻘﻴﻢ ﺍﻟﻤﺘﻄﺮﻓﺔ‪ ،‬ﻭﺳﻮﻑ‬ ‫ﻥ‬ ‫ﻧﻨﺎﻗﺶﺑﻌﻀﺎً ﻣﻨﻬﺎ‪:‬‬ ‫ﺭﺳﻢﺑﻴﺎﻧﻲ ﻟﻠﺼﻨﺪﻭﻕ‬ ‫ﺃ‬ ‫ﻣﺨﻄﻂﺍﻟﺘﺸﺘﺖ‬ ‫ﺃ‬ ‫ﺃﺳﻮﺍﺭﺗﻮﻛﻲ‬ ‫ﺃ‬ ‫ﺍﻟﻨﺘﻴﺠﺔ‪Z‬‬ ‫ﺃ‬ ‫‪30‬‬  ‫ﻃﺮﻳﻘﺔﺳﻴﺎﺝ ﺗﻮﻛﻲ‬ ‫ﻳﻌﺘﻤﺪﻋﻠﻰ ﺍﻟﻨﻄﺎﻕ ﺍﻟﺮﺑﻌﻲ ‪)IQR‬ﺍﻟﺮﺑﻊ ﺍﻟﺮﺍﺑﻊ=ﺍﻟﺮﺑﻊ ﺍﻟﺜﺎﻟﺚ‪-‬ﺍﻟﺮﺑﻊ ﺍﻷﻭﻝ(‬ ‫ﻥ‬ ‫ﻓﻲ‪ ،Tukey Fences‬ﺍﻟﻘﻴﻢ ﺍﻟﻤﺘﻄﺮﻓﺔ ﻫﻲ ﺍﻟﻘﻴﻢ ﺍﻟﺘﻲ‪:‬‬ ‫ﻥ‬ ‫ﺃﻗﻞﻣﻦ (‪ ،Q1 – )1.5 × IQR‬ﺃﻭ ﺃﻛﺜﺮ‬ ‫ﺃ‬ ‫ﻣﻦ (‪Q3 + )1.5 × IQR‬‬ ‫ﺃ‬ ‫ﻃﺮﻳﻘﺔﺍﻟﺪﺭﺟﺔ ﺍﻟﻤﻌﻴﺎﺭﻳﺔ‬ ‫ﺗﺸﻴﺮﺍﻟﺪﺭﺟﺔ ﺍﻟﻤﻌﻴﺎﺭﻳﺔ ﺇﻟﻰ ﻋﺪﺩ ﺍﻻﻧﺤﺮﺍﻓﺎﺕ ﺍﻟﻤﻌﻴﺎﺭﻳﺔ ﺍﻟﺘﻲ ﺗﻔﺼﻞ ﻧﻘﻄﺔ‬ ‫ﻥ‬ ‫ﺑﻴﺎﻧﺎﺕﻋﻦ ﺍﻟﻤﺘﻮﺳﻂ‪.‬ﺗﺤﺘﻮﻱ ﺍﻟﺪﺭﺟﺔ ﺍﻟﻤﻌﻴﺎﺭﻳﺔ ﻋﻠﻰ ﺍﻟﺼﻴﻐﺔ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫‪/‬‬ ‫ﺃﻧﺎ‬ ‫ﺱ‬ ‫ﺃﻳﻦ‪x‬ﺃﻧﺎﻫﻲ ﻧﻘﻄﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ‪ ،‬ﻭ‪ μ‬ﻫﻲ ﻣﺘﻮﺳﻂ ﻣﺠﻤﻮﻋﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ‪ ،‬ﻭ‪ σ‬ﻫﻲ‬ ‫ﺍﻻﻧﺤﺮﺍﻑﺍﻟﻤﻌﻴﺎﺭﻱ‪.‬‬ ‫ﻥﺗﻌﺘﺒﺮ ﺍﻟﺪﺭﺟﺔ ‪ Z‬ﻗﻴﻤﺔ ﺷﺎﺫﺓ ﺇﺫﺍ‬ ‫ﺃﻛﺒﺮﻣﻦ ‪ 3‬ﺃﻭ ﺃﻗﻞ ﻣﻦ‬ ‫ﺃ‬ ‫‪3-‬‬ ‫ﺃ‬ ‫‪31‬‬  ‫ﺍﻟﺘﻌﺎﻣﻞﻣﻊ ﺍﻟﻘﻴﻢ ﺍﻟﻤﺘﻄﺮﻓﺔ‬ ‫ﺑﻤﺠﺮﺩﺗﺤﺪﻳﺪ ﺍﻟﻘﻴﻢ ﺍﻟﻤﺘﻄﺮﻓﺔ ﻭﺍﺗﺨﺎﺫ ﺍﻟﻘﺮﺍﺭ ﺑﺈﺻﻼﺡ ﺗﻠﻚ ﺍﻟﻘﻴﻢ‪ ،‬ﻳﻤﻜﻨﻚ‬ ‫ﻥ‬ ‫ﺍﻟﺘﻔﻜﻴﺮﻓﻲ ﺃﺣﺪ ﺍﻷﺳﺎﻟﻴﺐ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬ ‫ﺇﺯﺍﻟﺔﺍﻟﻘﻴﻢ ﺍﻟﻤﺘﻄﺮﻓﺔ‪:‬ﺇﺫﺍ ﻟﻢ ﻳﻜﻦ ﻋﺪﺩ ﺍﻟﺴﺠﻼﺕ ﺍﻟﻤﺘﻄﺮﻓﺔ ﻛﺒﻴﺮﺍً‪،‬‬ ‫ﺃ‬ ‫ﻓﻴﻤﻜﻨﻨﺎﺑﺒﺴﺎﻃﺔ ﺇﺯﺍﻟﺘﻬﺎ‪.‬‬ ‫ﺍﻹﺳﻨﺎﺩ‪:‬ﻫﻨﺎﻙ ﻃﺮﻳﻘﺔ ﺃﺧﺮﻯ ﻭﻫﻲ ﺇﺳﻨﺎﺩ ﺍﻟﻘﻴﻤﺔ ﺍﻟﻤﺘﻄﺮﻓﺔ ﺑﺎﺳﺘﺨﺪﺍﻡ‬ ‫ﺃ‬ ‫ﺍﻟﻤﺘﻮﺳﻂﺃﻭ ﺍﻟﻮﺳﻴﻂ ﺃﻭ ﺍﻟﻤﻨﻮﺍﻝ ﻟﺠﻤﻴﻊ ﻗﻴﻢ ﺍﻟﺴﻤﺎﺕ‪.‬‬ ‫ﺍﻟﺘﻐﻄﻴﺔ‪:‬ﻗﺪ ﻳﺆﺩﻱ ﺇﺯﺍﻟﺔ ﺍﻟﻘﻴﻢ ﺍﻟﻤﺘﻄﺮﻓﺔ ﺇﻟﻰ ﺇﺯﺍﻟﺔ ﻋﺪﺩ ﻛﺒﻴﺮ ﻣﻦ ﺍﻟﺴﺠﻼﺕ‬ ‫ﺃ‬ ‫ﻣﻦﻣﺠﻤﻮﻋﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺨﺎﺻﺔ ﺑﻚ ﻭﻫﻮ ﺃﻣﺮ ﻏﻴﺮ ﻣﺮﻏﻮﺏ ﻓﻴﻪ ﻓﻲ ﺑﻌﺾ‬ ‫ﺍﻟﺤﺎﻻﺕ‪.‬ﻧﺴﺘﺨﺪﻡ ﺍﻟﺤﺪ ﺍﻷﻗﺼﻰ ﻻﺳﺘﺒﺪﺍﻝ ﺍﻟﻘﻴﻢ ﺍﻟﻤﺘﻄﺮﻓﺔ ﺑﻘﻴﻢ ﻗﺼﻮﻯ ﺃﻭ‬ ‫ﺩﻧﻴﺎﻣﺤﺪﻭﺩﺓ‪.‬ﻳﻤﻜﻨﻨﺎ ﺍﺳﺘﺨﺪﺍﻡ ﺍﻟﺤﺪ ﺍﻷﻗﺼﻰ ﺍﻟﻤﺉﻮﻱ‪.‬ﺍﻟﻘﻴﻢ > ﺍﻟﻘﻴﻤﺔ ﻋﻨﺪ‬ ‫‪1‬ﺷﺎﺭﻉ‬ ‫ﻳﺘﻢﺍﺳﺘﺒﺪﺍﻝ ﺍﻟﻨﺴﺒﺔ ﺍﻟﻤﺉﻮﻳﺔ ﺑﺎﻟﻘﻴﻤﺔ ﻋﻨﺪ ‪1‬ﺷﺎﺭﻉﺍﻟﻨﺴﺒﺔ ﺍﻟﻤﺉﻮﻳﺔ‪ ،‬ﻭﺍﻟﻘﻴﻢ‬ ‫< ﻣﻦ ﺍﻟﻘﻴﻤﺔ ﻋﻨﺪ ‪99‬ﺫﻳﺘﻢ ﺍﺳﺘﺒﺪﺍﻝ ﺍﻟﻨﺴﺒﺔ ﺍﻟﻤﺉﻮﻳﺔ ﺑﺎﻟﻘﻴﻤﺔ ﺍﻟﻤﻮﺟﻮﺩﺓ‬ ‫ﻋﻨﺪ‪99‬ﺫﺍﻟﻨﺴﺒﺔ ﺍﻟﻤﺉﻮﻳﺔ‪.‬ﺍﻟﺤﺪ ﺍﻷﻗﺼﻰ ﻋﻨﺪ ‪5‬ﺫﻭ ‪95‬ﺫ‬ ‫ﺍﻟﻨﺴﺒﺔﺍﻟﻤﺉﻮﻳﺔ ﺷﺎﺉﻌﺔ ﺃﻳﻀﺎً‪.‬‬ ‫‪32‬‬  ‫‪ (2‬ﺍﻟﻘﻴﻢ ﺍﻟﻤﻔﻘﻮﺩﺓ‬ ‫ﻓﻲﻣﺠﻤﻮﻋﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ‪ ،‬ﻗﺪ ﻳﻜﻮﻥ ﻟﻌﻨﺼﺮ ﺑﻴﺎﻧﺎﺕ ﻭﺍﺣﺪ ﺃﻭ ﺃﻛﺜﺮ ﻗﻴﻢ‬ ‫ﻥ‬ ‫ﻣﻔﻘﻮﺩﺓﻓﻲ ﺳﺠﻼﺕ ﻣﺘﻌﺪﺩﺓ‪.‬‬ ‫ﺗﻮﺟﺪﺍﺳﺘﺮﺍﺗﻴﺠﻴﺎﺕ ﻣﺘﻌﺪﺩﺓ ﻟﻠﺘﻌﺎﻣﻞ ﻣﻊ ﺍﻟﻘﻴﻢ ﺍﻟﻤﻔﻘﻮﺩﺓ ﻟﻌﻨﺎﺻﺮ‬ ‫ﻥ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕ‪.‬ﻭﻣﻦ ﺑﻴﻦ ﻫﺬﻩ ﺍﻻﺳﺘﺮﺍﺗﻴﺠﻴﺎﺕ‪:‬‬ ‫ﺃ ﺇﺯﺍﻟﺔﺍﻟﺴﺠﻼﺕ ﺍﻟﺘﻲ ﺗﺤﺘﻮﻱ ﻋﻠﻰ ﻗﻴﻤﺔ ﻣﻔﻘﻮﺩﺓ‬ ‫ﺃ ﺇﺩﺧﺎﻝﺍﻟﺴﺠﻼﺕ ﺍﻟﺘﻲ ﺗﺤﺘﻮﻱ ﻋﻠﻰ ﻗﻴﻤﺔ ﻣﻔﻘﻮﺩﺓ‪ :‬ﺃﻳﺘﻢ ﺍﺣﺘﺴﺎﺏ‬ ‫ﺟﻤﻴﻊﺍﻟﻘﻴﻢ ﺍﻟﻤﻔﻘﻮﺩﺓ ﺑﺎﺳﺘﺨﺪﺍﻡ ﺍﻟﻤﺘﻮﺳﻂ ﺃﻭ ﺍﻟﻮﺳﻴﻂ ﺃﻭ ﺍﻟﻤﻨﻮﺍﻝ )‬ ‫ﻗﺪﺭﺍﻹﻣﻜﺎﻥ( ﻟﻠﻘﻴﻢ ﺍﻟﻤﺘﺒﻘﻴﺔ ﻣﻦ ﻧﻔﺲ ﺍﻟﺴﻤﺔ‬ ‫ﺗﻘﺪﻳﺮﺍﻟﻘﻴﻢ ﺍﻟﻤﻔﻘﻮﺩﺓ‪:‬ﺇﺫﺍ ﻛﺎﻧﺖ ﻫﻨﺎﻙ ﺳﺠﻼﺕ ﻣﺸﺎﺑﻬﺔ ﻟﺘﻠﻚ ﺍﻟﺘﻲ‬ ‫ﺃ‬ ‫ﺗﺤﺘﻮﻱﻋﻠﻰ ﻗﻴﻢ ﻣﻔﻘﻮﺩﺓ‪ ،‬ﻓﻴﻤﻜﻦ ﺯﺭﻉ ﻗﻴﻢ ﺍﻟﺴﻤﺎﺕ ﻣﻦ ﺗﻠﻚ ﺍﻟﺴﺠﻼﺕ‬ ‫ﺍﻟﻤﺸﺎﺑﻬﺔﺑﺪﻻ ًﻣﻦ ﺍﻟﻘﻴﻤﺔ ﺍﻟﻤﻔﻘﻮﺩﺓ‪.‬ﻋﻠﻰ ﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﺇﺫﺍ ﻛﺎﻥ ﻭﺯﻥ‬ ‫ﻃﺎﻟﺐﺭﻭﺳﻲ ﻳﺒﻠﻎ ﻣﻦ ﺍﻟﻌﻤﺮ ‪ 12‬ﻋﺎﻣﺎً ﻭﻳﺒﻠﻎ ﻃﻮﻟﻪ ‪ 5‬ﺃﻗﺪﺍﻡ ﻣﻔﻘﻮﺩﺍً‪ ،‬ﻓﻴﻤﻜﻦ‬ ‫ﺍﺳﺘﺨﺪﺍﻡﻭﺯﻥ ﺃﻱ ﻃﺎﻟﺐ ﺭﻭﺳﻲ ﺁﺧﺮ ﻳﺒﻠﻎ ﻣﻦ ﺍﻟﻌﻤﺮ ‪ 12‬ﻋﺎﻣﺎً ﺗﻘﺮﻳﺒﺎً ﻭﻳﺒﻠﻎ‬ ‫ﻃﻮﻟﻪ‪ 5‬ﺃﻗﺪﺍﻡ ﺗﻘﺮﻳﺒﺎً‪.‬‬ ‫‪33‬‬  ‫ﺳﻤﺎﺕ‬ ‫ﻥﻣﺎ ﻫﻲ ﺍﻟﻤﻴﺰﺓ؟‬ ‫ﺍﻟﻤﻴﺰﺓﻫﻲ ﺳﻤﺔ ﻟﻤﺠﻤﻮﻋﺔ ﺑﻴﺎﻧﺎﺕ ﺗﺴُﺘﺨﺪﻡ ﻓﻲ ﻋﻤﻠﻴﺔ ﺍﻟﺘﻌﻠﻢ ﺍﻵﻟﻲ‪.‬‬ ‫ﺿﻊﻓﻲ ﺍﻋﺘﺒﺎﺭﻙ ﻣﺠﻤﻮﻋﺔ ﺑﻴﺎﻧﺎﺕ ‪:Iris‬‬ ‫‪34‬‬  ‫ﻫﻨﺪﺳﺔﺍﻟﻤﻤﻴﺰﺍﺕ‬ ‫ﻥﻣﺎ ﻫﻲ ﻫﻨﺪﺳﺔ ﺍﻟﻤﻴﺰﺍﺕ؟‬ ‫ﻫﻨﺪﺳﺔﺍﻟﻤﻴﺰﺍﺕ ﻫﻲ ﺧﻄﻮﺓ ﻣﻬﻤﺔ ﻓﻲ ﺍﻟﻤﻌﺎﻟﺠﺔ ﺍﻟﻤﺴﺒﻘﺔ ﻟﻠﺘﻌﻠﻢ ﺍﻵﻟﻲ‪.‬‬ ‫ﻫﻨﺪﺳﺔﺍﻟﻤﻴﺰﺍﺕ ﻫﻲ ﻋﻤﻠﻴﺔ ﻣﻌﺎﻟﺠﺔ ﻣﺠﻤﻮﻋﺔ ﺑﻴﺎﻧﺎﺕ ﻟﺘﺸﻜﻴﻞ ﻣﻴﺰﺍﺕ ﺗﻤﺜﻞ‬ ‫ﻣﺠﻤﻮﻋﺔﺍﻟﺒﻴﺎﻧﺎﺕ ﺑﺸﻜﻞ ﺃﻛﺜﺮ ﻓﻌﺎﻟﻴﺔ ﻭﺗﺆﺩﻱ ﺇﻟﻰ ﺃﺩﺍء ﺗﻌﻠﻴﻤﻲ ﺃﻓﻀﻞ‪.‬‬ ‫ﻥﺗﺘﻜﻮﻥ ﻫﻨﺪﺳﺔ ﺍﻟﻤﻴﺰﺍﺕ ﻣﻦ ﻋﻨﺼﺮﻳﻦ ﺭﺉﻴﺴﻴﻴﻦ‪:‬‬ ‫ﺗﺤﻮﻳﻞﺍﻟﻤﻴﺰﺓ‬ ‫ﺃ‬ ‫ﺍﺧﺘﻴﺎﺭﺍﻟﻤﻴﺰﺓ‬ ‫ﺃ‬ ‫‪35‬‬  ‫ﺗﺤﻮﻳﻞﺍﻟﻤﻴﺰﺓ‬ ‫ﺗﺤﻮﻳﻞﺍﻟﻤﻴﺰﺍﺕ ﻫﻲ ﻋﻤﻠﻴﺔ ﺇﻧﺸﺎء ﻣﻴﺰﺍﺕ ﺟﺪﻳﺪﺓ ﻣﻦ ﺍﻟﻤﻴﺰﺍﺕ‬ ‫ﻥ‬ ‫ﺍﻟﻤﻮﺟﻮﺩﺓ‪.‬‬ ‫ﻫﻨﺎﻙﻧﻮﻋﺎﻥ ﻣﻦ ﺗﺤﻮﻳﻞ ﺍﻟﻤﻴﺰﺍﺕ‪:‬‬ ‫ﻥ‬ ‫ﺑﻨﺎءﺍﻟﻤﻴﺰﺓ‬ ‫ﺃ‬ ‫ﺍﺳﺘﺨﺮﺍﺝﺍﻟﻤﻴﺰﺍﺕ‬ ‫ﺃ‬ ‫ﺑﻨﺎءﺍﻟﻤﻴﺰﺓﻫﻲ ﻋﻤﻠﻴﺔ ﺇﻧﺸﺎء ﻣﻴﺰﺍﺕ ﺟﺪﻳﺪﺓ ﺇﺿﺎﻓﻴﺔ ﻣﻦ ﺍﻟﻤﻴﺰﺍﺕ‬ ‫ﻥ‬ ‫ﺍﻟﻤﻮﺟﻮﺩﺓﻣﻦ ﺧﻼﻝ ﺍﻛﺘﺸﺎﻑ ﺍﻟﻤﻌﻠﻮﻣﺎﺕ ﺍﻟﻤﻔﻘﻮﺩﺓ ﺣﻮﻝ ﺍﻟﻌﻼﻗﺎﺕ ﺑﻴﻦ‬ ‫ﺍﻟﻤﻴﺰﺍﺕ‪.‬ﻭﻣﻦ ﺛﻢ ﻓﺈﻥ ﺇﻧﺸﺎء ﺍﻟﻤﻴﺰﺍﺕ ﻳﻌﻤﻞ ﻋﻠﻰ ﺗﻮﺳﻴﻊ ﻣﺴﺎﺣﺔ‬ ‫ﺍﻟﻤﻴﺰﺍﺕ‪.‬ﻋﻠﻰ ﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﺇﺫﺍ ﻛﺎﻥ ﻫﻨﺎﻙ 'ﻥ'ﺍﻟﻤﻴﺰﺍﺕ ﺍﻟﻤﻮﺟﻮﺩﺓ ﻓﻲ‬ ‫ﻣﺠﻤﻮﻋﺔﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺨﺎﻡ‪ ،‬ﺑﻌﺪ ﺇﻧﺸﺎء ﺍﻟﻤﻴﺰﺍﺕ'ﻡ"ﻗﺪ ﺗﺘﻢ ﺇﺿﺎﻓﺔ ﺍﻟﻤﺰﻳﺪ ﻣﻦ‬ ‫ﺍﻟﻤﻴﺰﺍﺕ‪.‬ﻟﺬﺍ ﻓﻲ ﺍﻟﻨﻬﺎﻳﺔ‪ ،‬ﺳﺘﺼﺒﺢ ﻣﺠﻤﻮﻋﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ ""ﻥ‪+‬ﻡ' ﺳﻤﺎﺕ‪.‬‬ ‫‪36‬‬  ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﺗﺤﺘﻮﻱ ﻣﺠﻤﻮﻋﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺘﺎﻟﻴﺔ ﻋﻠﻰ ﺛﻼﺙ‬ ‫ﻥ‬ ‫ﺳﻤﺎﺕ‪:‬ﻃﻮﻝ ﺍﻟﺸﻘﺔ ﻭﻋﺮﺿﻬﺎ ﻭﺳﻌﺮﻫﺎ‪.‬ﻭﺇﺫﺍ ﺗﻢ ﺍﺳﺘﺨﺪﺍﻣﻬﺎ ﻛﻤﺪﺧﻞ‬ ‫ﻟﻤﺸﻜﻠﺔﺍﻻﻧﺤﺪﺍﺭ‪ ،‬ﻓﻴﻤﻜﻦ ﺍﺳﺘﺨﺪﺍﻡ ﻫﺬﻩ ﺍﻟﺒﻴﺎﻧﺎﺕ ﻟﺘﺪﺭﻳﺐ ﻧﻤﻮﺫﺝ‬ ‫ﺍﻻﻧﺤﺪﺍﺭ‪.‬ﻭﻣﻦ ﺍﻷﻧﺴﺐ ﻭﺍﻷﻛﺜﺮ ﻣﻨﻄﻘﻴﺔ ﺍﺳﺘﺨﺪﺍﻡ ﻣﺴﺎﺣﺔ ﺍﻟﺸﻘﺔ‪ ،‬ﻭﻫﻲ‬ ‫ﻟﻴﺴﺖﺳﻤﺔ ﻣﻮﺟﻮﺩﺓ ﻓﻲ ﻣﺠﻤﻮﻋﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ‪.‬ﻟﺬﺍ‬ ‫‪37‬‬ ‫ﺑﻨﺎءﺍﻟﻤﻴﺰﺓ‬  ‫ﺍﺳﺘﺨﺮﺍﺝﺍﻟﻤﻴﺰﺍﺕﻫﻲ ﻋﻤﻠﻴﺔ ﺇﻧﺸﺎء ﻣﻴﺰﺍﺕ ﺟﺪﻳﺪﺓ ﺇﺿﺎﻓﻴﺔ ﻣﻦ‬ ‫ﻥ‬ ‫ﺍﻟﻤﻴﺰﺍﺕﺍﻟﻤﻮﺟﻮﺩﺓ ﺑﺎﺳﺘﺨﺪﺍﻡ ﺑﻌﺾ‬ ‫ﻣﺜﺎﻝﺁﺧﺮ ﻫﻮ ﺗﺤﻮﻳﻞ ﺍﻟﻠﻮﻏﺎﺭﻳﺘﻢ‪.‬ﻳﺘﻢ ﺍﺳﺘﺨﺪﺍﻣﻪ ﻟﺘﺤﻮﻳﻞ ﺍﻟﺒﻴﺎﻧﺎﺕ ﻏﻴﺮ‬ ‫ﻥ‬ ‫ﺍﻟﻤﻮﺯﻋﺔﺑﺸﻜﻞ ﻃﺒﻴﻌﻲ ﺇﻟﻰ ﺍﻟﺘﻮﺯﻳﻊ ﺍﻟﻄﺒﻴﻌﻲ‪.‬‬ ‫(')‪! = log‬‬ ‫‪38‬‬  ‫ﻫﻨﺎﻙﻣﻮﺍﻗﻒ ﻣﻌﻴﻨﺔ ﺣﻴﺚ ﻳﻜﻮﻥ ﺇﻧﺸﺎء ﺍﻟﻤﻴﺰﺓ ﻧﺸﺎﻃﺎً ﺃﺳﺎﺳﻴﺎً ﻗﺒﻞ ﺃﻥ‬ ‫ﻥ‬ ‫ﻧﺘﻤﻜﻦﻣﻦ ﺍﻟﺒﺪء ﻓﻲ ﻣﻬﻤﺔ ﺍﻟﺘﻌﻠﻢ ﺍﻵﻟﻲ‪:‬‬ ‫ﻋﻨﺪﻣﺎﺗﻜﻮﻥ ﻟﻠﻤﻴﺰﺍﺕ ﻗﻴﻤﺔ ﻧﻮﻋﻴﺔ ﻭﻳﺤﺘﺎﺝ ﺍﻟﺘﻌﻠﻢ ﺍﻵﻟﻲ ﺇﻟﻰ ﻗﻴﻤﺔ ﻛﻤﻴﺔ‬ ‫ﺃ‬ ‫ﻋﻨﺪﻣﺎﺗﺤﺘﻮﻱ ﺍﻟﻤﻴﺰﺍﺕ ﻋﻠﻰ ﻗﻴﻢ ﺭﻗﻤﻴﺔ )ﻣﺴﺘﻤﺮﺓ( ﻭﻳﺤﺘﺎﺝ ﺍﻟﺘﻌﻠﻢ‬ ‫ﺃ‬ ‫ﺍﻵﻟﻲﺇﻟﻰ ﻗﻴﻢ ﺗﺮﺗﻴﺒﻴﺔ‬ ‫ﻋﻨﺪﺍﻟﺘﻌﺎﻣﻞ ﻣﻊ ﻣﻴﺰﺓ ﻧﺼﻴﺔ ﻣﺤﺪﺩﺓ‬ ‫ﺃ‬ ‫‪39‬‬  ‫ﺗﺮﻣﻴﺰﺍﻟﻤﻴﺰﺍﺕ ﺍﻻﺳﻤﻴﺔ‬ ‫ﻥﺿﻊ ﻓﻲ ﺍﻋﺘﺒﺎﺭﻙ ﻣﺠﻤﻮﻋﺔ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﺳﺘﻔﺴﺎﺭﺍﺕ‬ ‫ﻭ‬ ‫ﻥ‬ ‫ﻭﻫﻨﺎﻙ‬ ‫ﻥ‬ ‫ﻭ‬ ‫ﺃ‬ ‫ﻻﻳﻜﻮﻥ‬ ‫ﺝ‬ ‫ﺍﻧﺖ‬ ‫‪40‬‬  ‫ﻟﺤﻞﻫﺬﻩ ﺍﻟﻤﺸﻜﻠﺔ‪ ،‬ﻳﻤﻜﻦ ﺍﺳﺘﺨﺪﺍﻡ ﺑﻨﺎء ﺍﻟﻤﻴﺰﺍﺕ ﻹﻧﺸﺎء ﻣﻴﺰﺍﺕ‬ ‫ﻥ‬ ‫ﻭﻫﻤﻴﺔﺟﺪﻳﺪﺓ ﻳﻤﻜﻦ ﺍﺳﺘﺨﺪﺍﻣﻬﺎ ﺑﻮﺍﺳﻄﺔ ﺧﻮﺍﺭﺯﻣﻴﺎﺕ ﺍﻟﺘﻌﻠﻢ ﺍﻵﻟﻲ‪.‬‬ ‫ﻧﻈﺮﺍًﻷﻥ ﻣﻴﺰﺓ "ﺍﻟﻤﺪﻳﻨﺔ ﺍﻷﺻﻠﻴﺔ" ﻟﻬﺎ ﺛﻼﺙ ﻗﻴﻢ ﻓﺮﻳﺪﺓ ﻭﻫﻲ‪:‬ﻣﺪﻳﻨﺔ ﺃ‪,‬‬ ‫ﻥ‬ ‫ﻣﺪﻳﻨﺔﺏ‪ ،‬ﻭﻣﺪﻳﻨﺔ ﺝ‪ ،‬ﺛﻼﺙ ﻣﻴﺰﺍﺕ ﻭﻫﻤﻴﺔ ﻭﻫﻲ‪:‬ﺍﻟﻤﻨﺸﺄ_ﺍﻟﻤﺪﻳﻨﺔ_ﺃ‪,‬‬ ‫ﺍﻟﻤﺪﻳﻨﺔﺍﻷﺻﻠﻴﺔ ﺏ‪ ،‬ﻭﺃﺻﻞ_ﺍﻟﻤﺪﻳﻨﺔ_ﺝﺗﻢ ﺇﻧﺸﺎء ﺍﻟﻤﻴﺰﺍﺕ ﺍﻟﻮﻫﻤﻴﺔ‪.‬ﻟﻬﺎ‬ ‫ﻗﻴﻤﺔ‪ 0‬ﺃﻭ‪ 1‬ﺑﻨﺎء ًﻋﻠﻰ ﺍﻟﻘﻴﻤﺔ ﺍﻟﻨﻮﻋﻴﺔ ﻟﻠﻤﻴﺰﺓ ﺍﻷﺻﻠﻴﺔ ﻓﻲ ﻫﺬﺍ ﺍﻟﺼﻒ‪.‬‬ ‫ﻭﺑﻨﻔﺲﺍﻟﻄﺮﻳﻘﺔ‪ ،‬ﻣﻴﺰﺍﺕ ﻭﻫﻤﻴﺔﻭﺍﻟﺪﺍ_ﺭﻳﺎﺿﻲ_‪Y‬ﻭ ﻭﺍﻟﺪﻳﻦ_ﺭﻳﺎﺿﻴﻴﻦ_ﻥﺗﻢ‬ ‫ﻥ‬ ‫ﺇﻧﺸﺎﺅﻫﺎﻟﻠﻤﻴﺰﺓ 'ﺍﻵﺑﺎء ﺍﻟﺮﻳﺎﺿﻴﻴﻦ' ﻭﻓﺮﺻﺔ ﺍﻟﻔﻮﺯ_‪Y‬ﻭﻓﺮﺻﺔ ﺍﻟﻔﻮﺯ_ﻥﺗﻢ‬ ‫ﺇﻧﺸﺎﺅﻫﺎﻟﻠﻤﻴﺰﺓ 'ﻓﺮﺻﺔ ﺍﻟﻔﻮﺯ"‪.‬‬ ‫‪41‬‬  ‫ﻥ‬ ‫‪2‬‬  ‫ﻝ‬ ‫ﻥ‬ ‫ﺍﻭﻩ‬ ‫‪43‬‬  ‫ﺗﺮﻣﻴﺰﺍﻟﻤﻴﺰﺍﺕ ﺍﻟﺘﺮﺗﻴﺒﻴﺔ‬ ‫ﻟﻨﺄﺧﺬﻣﺜﺎﻻ ًﻟﻤﺠﻤﻮﻋﺔ ﺑﻴﺎﻧﺎﺕ ﺍﻟﻄﻼﺏ‪.‬ﻟﻨﻔﺘﺮﺽ ﺃﻥ ﻫﻨﺎﻙ ﺛﻼﺛﺔ ﻣﺘﻐﻴﺮﺍﺕ‪:‬‬ ‫ﻥ‬ ‫‪،science_marks‬‬ ‫ﻋﻼﻣﺎﺕﺍﻟﺮﻳﺎﺿﻴﺎﺕ ﻭﺍﻟﺪﺭﺟﺔ ﻛﻤﺎ ﻫﻮ ﻣﻮﺿﺢ ﺃﺩﻧﺎﻩ‬ ‫ﻧﺮﻯﺃﻥ ﺍﻟﺪﺭﺟﺔ ﻫﻲ ﺳﻤﺔ ﺗﺮﺗﻴﺒﻴﺔ ﺑﻘﻴﻢ ‪ A‬ﻭ‪ B‬ﻭ‪ C‬ﻭ‪.D‬ﻟﺘﺤﻮﻳﻞ ﻫﺬﻩ ﺍﻟﺴﻤﺔ‬ ‫ﻥ‬ ‫ﺇﻟﻰﺳﻤﺔ ﺭﻗﻤﻴﺔ‪ ،‬ﻧﻘﻮﻡ ﺑﺈﻧﺸﺎء ﺳﻤﺔ ﺟﺪﻳﺪﺓ ‪ num_grade‬ﻟﺘﻌﻴﻴﻦ ﻗﻴﻤﺔ‬ ‫ﺭﻗﻤﻴﺔﻣﻘﺎﺑﻞ ﻛﻞ ﻗﻴﻤﺔ ﺗﺮﺗﻴﺒﻴﺔ‪.‬ﻳﺘﻢ ﺗﻌﻴﻴﻦ ﺍﻟﺪﺭﺟﺎﺕ ‪ A‬ﻭ‪ B‬ﻭ‪ C‬ﻭ‪ D‬ﻓﻲ‬ ‫ﺇﻟﻰﺍﻟﻘﻴﻢ ‪ 1‬ﻭ‪ 2‬ﻭ‪ 3‬ﻭ‪ 4‬ﻓﻲ ﺍﻟﺴﻤﺔ ﺍﻟﺠﺪﻳﺪﺓ ﺍﻟﻤﻮﺿﺤﺔ ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﺘﺎﻟﻲ‪.‬‬ ‫‪45‬‬  ‫ﺗﺤﻮﻳﻞﺍﻟﻤﻴﺰﺍﺕ ﺍﻟﺮﻗﻤﻴﺔ )ﺍﻟﻤﺴﺘﻤﺮﺓ( ﺇﻟﻰ‬ ‫ﻣﻴﺰﺍﺕﺗﺼﻨﻴﻔﻴﺔ‬ ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﻗﺪ ﻧﺮﻏﺐ ﻓﻲ ﻣﻌﺎﻟﺠﺔ ﻣﺸﻜﻠﺔ ﺍﻟﺘﻨﺒﺆ ﺑﺄﺳﻌﺎﺭ‬ ‫ﻥ‬ ‫ﺍﻟﻌﻘﺎﺭﺍﺕ‪،‬ﻭﻫﻲ ﻣﺸﻜﻠﺔ ﺍﻧﺤﺪﺍﺭ‪ ،‬ﺑﺎﻋﺘﺒﺎﺭﻫﺎ ﻣﺸﻜﻠﺔ ﺗﻨﺒﺆ ﺑﻔﺉﺔ ﺃﺳﻌﺎﺭ‬ ‫ﺍﻟﻌﻘﺎﺭﺍﺕ‪،‬ﻭﻫﻲ ﻣﺸﻜﻠﺔ ﺗﺼﻨﻴﻒ‪.‬ﻓﻲ ﻫﺬﻩ ﺍﻟﺤﺎﻟﺔ‪ ،‬ﻳﻤﻜﻨﻨﺎ‬ ‫ﺗﺠﻤﻴﻊﺍﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺮﻗﻤﻴﺔ ﻓﻲ ﻓﺉﺎﺕ ﻣﺘﻌﺪﺩﺓ ﺍﺳﺘﻨﺎﺩﺍً ﺇﻟﻰ‬ ‫ﻧﻄﺎﻕﺍﻟﺒﻴﺎﻧﺎﺕ‪.‬‬ ‫‪46‬‬  ‫ﺩ‬ ‫‪47‬‬  ‫ﺗﺮﻣﻴﺰﻣﻴﺰﺓ ﺍﻟﻨﺺ‬ ‫ﻓﻲﺍﻟﻮﻗﺖ ﺍﻟﺤﺎﺿﺮ‪ ،‬ﻳﻌﺪ ﺍﻟﻨﺺ ﺍﻟﻮﺳﻴﻠﺔ ﺍﻷﻛﺜﺮ ﺍﻧﺘﺸﺎﺭﺍً ﻟﻠﺘﻮﺍﺻﻞ ﺳﻮﺍء‬ ‫ﻥ‬ ‫ﻛﻨﺎﻧﻔﻜﺮ ﻓﻲ ﺧﺪﻣﺎﺕ ﺍﻟﺒﺮﻳﺪ ﺍﻹﻟﻜﺘﺮﻭﻧﻲ ﺃﻭ ﻓﻴﺴﺒﻮﻙ ﺃﻭ ﺗﻮﻳﺘﺮ ﺃﻭ ﻭﺍﺗﺴﺎﺏ‪.‬‬ ‫ﺣﻘﻴﺒﺔﺍﻟﻜﻠﻤﺎﺕ )‪ (BoW‬ﻫﻲ ﻃﺮﻳﻘﺔ ﺑﻨﺎء ﻣﻴﺰﺍﺕ ﻟﺘﺤﻮﻳﻞ ﺑﻴﺎﻧﺎﺕ ﺍﻟﻨﺺ‬ ‫ﻥ‬ ‫ﺇﻟﻰﺗﻤﺜﻴﻞ ﺭﻗﻤﻲ‪.‬‬ ‫ﻥﺧﻄﻮﺍﺕ ﺑﻨﺎء ﺣﻘﻴﺒﺔ ﺍﻟﻜﻠﻤﺎﺕ‬ ‫ﻳﺘﻢﺗﻘﺴﻴﻢ ﺍﻟﻨﺺ ﺇﻟﻰ ﺃﺟﺰﺍء )ﻓﺼﻞ ﺍﻟﻜﻠﻤﺎﺕ ﺑﺎﺳﺘﺨﺪﺍﻡ ﺍﻟﻤﺴﺎﻓﺎﺕ‬ ‫ﺃ‬ ‫ﺍﻟﻔﺎﺭﻏﺔﻭﻋﻼﻣﺎﺕ ﺍﻟﺘﺮﻗﻴﻢ(‪.‬‬ ‫ﺣﺪﺩﺍﻟﻜﻠﻤﺎﺕ ﺍﻟﻔﺮﻳﺪﺓ ﻟﺒﻨﺎء ﺍﻟﻤﻔﺮﺩﺍﺕ‬ ‫ﺃ‬ ‫ﺛﻢﻳﺘﻢ ﺣﺴﺎﺏ ﻋﺪﺩ ﻣﺮﺍﺕ ﻇﻬﻮﺭ ﻛﻞ ﺭﻣﺰ‬ ‫ﺃ‬ ‫‪48‬‬  ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﺿﻊ ﻓﻲ ﺍﻋﺘﺒﺎﺭﻙ ﺍﻟﻨﺺ ]"ﻫﺬﺍ ﻫﺎﺗﻒ ﺟﻴﺪ‪ ،‬ﻫﺬﺍ‬ ‫ﻥ‬ ‫ﻫﺎﺗﻒﺳﻲء‪ ،‬ﺇﻧﻬﺎ ﻗﻄﺔ ﺟﻴﺪﺓ‪ ،‬ﻟﺪﻳﻪ ﻣﺰﺍﺝ ﺳﻴﺊ‪ ،‬ﻫﺬﺍ ﺍﻟﻬﺎﺗﻒ ﺍﻟﻤﺤﻤﻮﻝ‬ ‫ﻟﻴﺲﺟﻴﺪﺍً"[‬ ‫ﻳﺘﻢﺗﻤﻴﻴﺰ ﺍﻟﻨﺺ ﻋﻠﻰ ﺃﻧﻪ‬ ‫ﺃ‬ ‫]"ﻫﺬﺍ"‪" ،‬ﻫﻮ"‪" ،‬ﺃ"‪" ،‬ﺟﻴﺪ"‪" ،‬ﻫﺎﺗﻒ"‪" ،‬ﻫﺬﺍ"‪" ،‬ﻫﻮ"‪" ،‬ﺃ"‪" ،‬ﺳﻲء"‪" ،‬ﻣﺤﻤﻮﻝ"‬ ‫‪"،‬ﻫﻲ"‪" ،‬ﻫﻲ"‪" ،‬ﺃ"‪" ،‬ﺟﻴﺪ"‪" ،‬ﻗﻄﺔ"‪" ،‬ﻫﻮ"‪" ،‬ﻟﺪﻳﻪ"‪" ،‬ﺃ"‪" ،‬ﺳﻲء"‪" ،‬ﻣﺰﺍﺝ"‪" ،‬‬ ‫ﻫﺬﺍ"‪" ،‬ﻣﺤﻤﻮﻝ"‪" ،‬ﻫﺎﺗﻒ"‪" ،‬ﻫﻮ"‪" ،‬ﻟﻴﺲ"‪" ،‬ﺟﻴﺪ"[‬ ‫ﺣﺪﺩﺍﻟﻜﻠﻤﺎﺕ ﺍﻟﻔﺮﻳﺪﺓ ﻟﺒﻨﺎء ﺍﻟﻤﻔﺮﺩﺍﺕ‬ ‫ﺃ‬ ‫]"ﺃ"‪" ،‬ﺳﻴﺊ"‪" ،‬ﻗﻂ"‪" ،‬ﺟﻴﺪ"‪" ،‬ﻟﺪﻳﻪ"‪" ،‬ﻫﻮ"‪" ،‬ﻫﻮ"‪" ،‬ﻣﺤﻤﻮﻝ"‪" ،‬ﻟﻴﺲ‬ ‫"‪" ،‬ﻫﺎﺗﻒ"‪" ،‬ﻫﻲ"‪" ،‬ﻣﺰﺍﺝ"‪" ،‬ﻫﺬﺍ"[‬ ‫ﺍﻵﻥ‪،‬ﻳﺘﻢ ﺗﻤﺜﻴﻞ ﺍﻟﺠﻤﻠﺔ "ﻫﺬﺍ ﻫﺎﺗﻒ ﺟﻴﺪ‪ ،‬ﻫﺬﺍ ﻫﺎﺗﻒ ﻣﺤﻤﻮﻝ ﺟﻴﺪ"‬ ‫ﺃ‬ ‫ﺑﺎﺳﺘﺨﺪﺍﻡﺍﻟﻤﻔﺮﺩﺍﺕ ﻋﻠﻰ ﺍﻟﻨﺤﻮ ﺍﻟﺘﺎﻟﻲ‪:‬‬ ‫ﺃﺃﻭ ﺑﺒﺴﺎﻃﺔ )‪(2 ،0 ،0 ،1 ،0 ،1 ،2 ،0 ،0 ،2 ،0 ،0 ،2‬‬ ‫‪49‬‬  ‫ﺍﺧﺘﻴﺎﺭﺍﻟﻤﻴﺰﺓ‬ ‫ﺍﺧﺘﻴﺎﺭﺍﻟﻤﻴﺰﺓ ﻫﻲ ﻋﻤﻠﻴﺔ ﺍﺧﺘﻴﺎﺭ ﺍﻟﻤﻴﺰﺍﺕ ﺍﻷﻛﺜﺮ ﺃﻫﻤﻴﺔ ﻣﻦ ﻣﺠﻤﻮﻋﺔ‬ ‫ﻥ‬ ‫ﺍﻟﻤﻴﺰﺍﺕﺍﻟﻤﻮﺟﻮﺩﺓ ﻟﻤﻬﻤﺔ ﺍﻟﺘﻌﻠﻢ ﺍﻵﻟﻲ ﻟﺪﻳﻨﺎ‪.‬‬ ‫‪50‬‬  ‫ﺍﻟﻘﻀﺎﻳﺎﺍﻟﻤﺘﻌﻠﻘﺔ ﺑﺎﻟﺒﻴﺎﻧﺎﺕ ﻋﺎﻟﻴﺔ ﺍﻷﺑﻌﺎﺩ‬ ‫ﺗﺸﻴﺮﻋﺒﺎﺭﺓ "ﺍﻟﺒﻴﺎﻧﺎﺕ ﻋﺎﻟﻴﺔ ﺍﻷﺑﻌﺎﺩ" ﺇﻟﻰ ﻣﺠﻤﻮﻋﺔ ﺑﻴﺎﻧﺎﺕ ﺗﺤﺘﻮﻱ‬ ‫ﻥ‬ ‫ﻋﻠﻰﻋﺪﺩ ﻛﺒﻴﺮ ﻣﻦ ﺍﻟﻤﻴﺰﺍﺕ‪).‬ﺍﻟﺒﻌﺪ = ﻋﺪﺩ ﺍﻟﻤﻴﺰﺍﺕ(‬ ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﺗﺤﻠﻴﻞ ﺍﻟﺤﻤﺾ ﺍﻟﻨﻮﻭﻱ‪ ،‬ﻳﻤﻜﻦ ﻟﺒﻴﺎﻧﺎﺕ ﺍﻟﺤﻤﺾ ﺍﻟﻨﻮﻭﻱ ﺃﻥ ﺗﺤﺘﻮﻱ ﻋﻠﻰ‬ ‫ﻥ‬ ‫ﻣﺎﻳﺼﻞ ﺇﻟﻰ ‪ 450‬ﺃﻟﻒ ﺑﻌُﺪ )ﻣﺴﺒﺎﺭﺍﺕ ﺍﻟﺠﻴﻨﺎﺕ(‪.‬‬ ‫ﻭﻓﻲﺑﻴﺎﻧﺎﺕ ﻧﺼﻴﺔ ﻛﺒﻴﺮﺓ ﺃﻳﻀﺎً )ﻣﺜﻞ ﺍﻟﻜﺘﺐ(‪ ،‬ﻳﻤﻜﻦ ﺃﻥ ﻳﺼﻞ ﻋﺪﺩ‬ ‫ﻥ‬ ‫ﺍﻟﻜﻠﻤﺎﺕﺍﻟﻔﺮﻳﺪﺓ )ﺍﻟﺮﻣﻮﺯ( ﺍﻟﺘﻲ ﺗﻤﺜﻞ ﻣﻴﺰﺓ ﻣﺠﻤﻮﻋﺔ ﺑﻴﺎﻧﺎﺕ ﺍﻟﻨﺺ ﺇﻟﻰ‬ ‫ﻋﺸﺮﺍﺕﺍﻵﻻﻑ‪.‬‬ ‫ﻗﺪﺗﺸﻜﻞ ﻣﺜﻞ ﻫﺬﻩ ﺍﻟﺒﻴﺎﻧﺎﺕ ﻋﺎﻟﻴﺔ ﺍﻷﺑﻌﺎﺩ ﺗﺤﺪﻳﺎً ﻛﺒﻴﺮﺍً ﻷﻱ ﺧﻮﺍﺭﺯﻣﻴﺔ‬ ‫ﻥ‬ ‫ﻟﻠﺘﻌﻠﻢﺍﻵﻟﻲ ﺑﺴﺒﺐ‪.‬‬ ‫ﺳﺘﻜﻮﻥﻫﻨﺎﻙ ﺣﺎﺟﺔ ﺇﻟﻰ ﻛﻤﻴﺔ ﻛﺒﻴﺮﺓ ﻣﻦ ﺍﻟﻤﻮﺍﺭﺩ ﺍﻟﺤﺴﺎﺑﻴﺔ ﻭﺳﺘﻜﻮﻥ‬ ‫ﻥ‬ ‫ﻫﻨﺎﻙﺣﺎﺟﺔ ﺇﻟﻰ ﻛﻤﻴﺔ ﻛﺒﻴﺮﺓ ﻣﻦ ﺍﻟﻮﻗﺖ ﺍﻟﺤﺴﺎﺑﻲ‪.‬‬ ‫ﻥ‬ ‫ﻳﻨﺨﻔﺾﺃﺩﺍء ﺍﻟﻨﻤﻮﺫﺝ ﺑﺸﻜﻞ ﺣﺎﺩ ﺑﺴﺒﺐ ﺍﻟﺒﻴﺎﻧﺎﺕ ﻏﻴﺮ ﺍﻟﻀﺮﻭﺭﻳﺔ‪.‬‬ ‫ﻥ‬ ‫‪51‬‬  ‫ﻋﻮﺍﻣﻞﻣﻬﻤﺔ ﻓﻲ ﺍﺧﺘﻴﺎﺭ ﺍﻟﻤﻴﺰﺓ‬ ‫ﻥﻫﻨﺎﻙ ﻋﺎﻣﻼﻥ ﻳﺆﺛﺮﺍﻥ ﻋﻠﻰ ﺍﺧﺘﻴﺎﺭ ﺍﻟﻤﻴﺰﺓ‪:‬‬ ‫‪ (1‬ﺃﻫﻤﻴﺔ ﺍﻟﻤﻴﺰﺓ ‪ (2‬ﺍﻟﺘﻜﺮﺍﺭ ﻓﻲ ﺍﻟﻤﻴﺰﺓ‬ ‫ﺃﻫﻤﻴﺔﺍﻟﻤﻴﺰﺓ‬ ‫ﻗﺪﺗﺴﺎﻫﻢ ﺍﻟﻤﻴﺰﺓ ﺑﻤﻌﻠﻮﻣﺎﺕ ﻏﻴﺮ ﺫﺍﺕ ﺻﻠﺔ ﻓﻲ ﺳﻴﺎﻕ ﻣﻬﻤﺔ ﺍﻟﺘﻌﻠﻢ‬ ‫ﻥ‬ ‫ﺍﻵﻟﻲ‪.‬‬ ‫ﺧﺬﻣﺜﺎﻻ ًﺑﺴﻴﻄﺎً ﻟﻤﺠﻤﻮﻋﺔ ﺑﻴﺎﻧﺎﺕ ﺍﻟﻄﻼﺏ‪.‬ﻓﻲ ﺳﻴﺎﻕ ﺍﻟﻤﻬﻤﺔ ﺍﻟﺨﺎﺿﻌﺔ‬ ‫ﻥ‬ ‫ﻟﻺﺷﺮﺍﻑﺍﻟﻤﺘﻤﺜﻠﺔ ﻓﻲ ﺍﻟﺘﻨﺒﺆ ﺑﺪﺭﺟﺎﺕ ﺍﻟﻄﻼﺏ ﺃﻭ ﺍﻟﻤﻬﻤﺔ ﻏﻴﺮ ﺍﻟﺨﺎﺿﻌﺔ‬ ‫ﻟﻺﺷﺮﺍﻑﺍﻟﻤﺘﻤﺜﻠﺔ ﻓﻲ ﺗﺠﻤﻴﻊ ﺍﻟﻄﻼﺏ ﺫﻭﻱ ﺍﻟﻘﺪﺭﺍﺕ ﺍﻷﻛﺎﺩﻳﻤﻴﺔ‬ ‫ﺍﻟﻤﺘﺸﺎﺑﻬﺔ‪،‬ﻓﺈﻥ ﺧﺎﺻﻴﺔ ﺭﻗﻢ ﺍﻟﻘﻴﺪ ﻏﻴﺮ ﺫﺍﺕ ﺻﻠﺔ ﺗﻤﺎﻣﺎً‪.‬‬ ‫ﺃﻳﺔﻣﻴﺰﺓ ﻏﻴﺮ ﺫﺍﺕ ﺻﻠﺔ ﻓﻲ ﺳﻴﺎﻕ ﻣﻬﻤﺔ ﺍﻟﺘﻌﻠﻢ ﺍﻵﻟﻲ ﻫﻲ ﻣﺮﺷﺤﺔ‬ ‫ﻥ‬ ‫ﻟﻠﺮﻓﺾﻋﻨﺪﻣﺎ ﻧﻘﻮﻡ ﺑﺎﺧﺘﻴﺎﺭ ﻣﺠﻤﻮﻋﺔ ﻓﺮﻋﻴﺔ ﻣﻦ ﺍﻟﻤﻴﺰﺍﺕ‪.‬‬ ‫‪52‬‬  ‫ﻣﻴﺰﺓﺍﻟﺘﻜﺮﺍﺭ‬ ‫ﻗﺪﺗﺴﺎﻫﻢ ﺍﻟﻤﻴﺰﺓ ﺑﻤﻌﻠﻮﻣﺎﺕ ﻣﻤﺎﺛﻠﺔ ﻟﻠﻤﻌﻠﻮﻣﺎﺕ ﺍﻟﺘﻲ ﺗﺴﺎﻫﻢ ﺑﻬﺎ‬ ‫ﻥ‬ ‫ﻣﻴﺰﺓﻭﺍﺣﺪﺓ ﺃﻭ ﺃﻛﺜﺮ ﺃﺧﺮﻯ‪.‬‬ ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﻓﻲ ﻣﺸﻜﻠﺔ ﺍﻟﺘﻨﺒﺆ ﺑﺎﻟﻮﺯﻥ‪ ،‬ﺗﺴﺎﻫﻢ ﻛﻞ ﻣﻦ‬ ‫ﻥ‬ ‫ﺍﻟﺴﻤﺘﻴﻦ‪ Age‬ﻭ‪ High‬ﻓﻲ ﻣﻌﻠﻮﻣﺎﺕ ﻣﻤﺎﺛﻠﺔ‪.‬ﻷﻧﻪ ﻣﻊ ﺯﻳﺎﺩﺓ ‪ ،Age‬ﻣﻦ‬ ‫ﺍﻟﻤﺘﻮﻗﻊﺃﻥ ﻳﺰﻳﺪ ‪.Weight‬ﻭﺑﺎﻟﻤﺜﻞ‪ ،‬ﻣﻊ ﺯﻳﺎﺩﺓ ‪ Height‬ﺃﻳﻀﺎً ﻣﻦ‬ ‫ﺍﻟﻤﺘﻮﻗﻊﺃﻥ ﻳﺰﻳﺪ ‪.Weight‬ﺃﻳﻀﺎً‪ ،‬ﻳﺘﺰﺍﻳﺪ ‪ Age‬ﻭ‪ High‬ﻣﻊ ﺑﻌﻀﻬﻤﺎ‬ ‫ﺍﻟﺒﻌﺾ‪.‬ﻟﺬﺍ‪ ،‬ﻓﻲ ﺳﻴﺎﻕ ﻣﺸﻜﻠﺔ ﺍﻟﺘﻨﺒﺆ ﺑﺎﻟﻮﺯﻥ‪ ،‬ﻳﺴﺎﻫﻢ ‪ Age‬ﻭ‪High‬‬ ‫ﻓﻲﻣﻌﻠﻮﻣﺎﺕ ﻣﻤﺎﺛﻠﺔ‪.‬ﺑﻌﺒﺎﺭﺓ ﺃﺧﺮﻯ‪ ،‬ﺳﻮﺍء ﻛﺎﻧﺖ ﺍﻟﺴﻤﺔ ‪Height‬‬ ‫ﻣﻮﺟﻮﺩﺓﺃﻡ ﻻ ﻛﺠﺰء ﻣﻦ ﻣﺠﻤﻮﻋﺔ ﻓﺮﻋﻴﺔ ﻣﻦ ﺍﻟﻤﻴﺰﺍﺕ‪ ،‬ﻓﺈﻥ ﻧﻤﻮﺫﺝ‬ ‫ﺍﻟﺘﻌﻠﻢﺳﻴﻌﻄﻲ ﻧﻔﺲ ﺍﻟﻨﺘﺎﺉﺞ ﺗﻘﺮﻳﺒﺎً‪.‬ﻧﻔﺲ ﺍﻟﺸﻲء ﺑﺎﻟﻨﺴﺒﺔ ﻟﺨﺎﺻﻴﺔ‬ ‫‪.Age‬‬ ‫‪53‬‬  ‫ﻓﻲﻫﺬﺍ ﺍﻟﻨﻮﻉ ﻣﻦ ﺍﻟﻤﻮﺍﻗﻒ ﻋﻨﺪﻣﺎ ﺗﻜﻮﻥ ﺇﺣﺪﻯ ﺍﻟﻤﻴﺰﺍﺕ ﻣﺸﺎﺑﻬﺔ‬ ‫ﻥ‬ ‫ﻟﻤﻴﺰﺍﺕﺃﺧﺮﻯ‪ ،‬ﻳﻘُﺎﻝ ﺇﻥ ﺍﻟﻤﻴﺰﺓ ﻫﻲﻣﻦ ﺍﻟﻤﺤﺘﻤﻞ ﺃﻥ ﺗﻜﻮﻥ ﺯﺍﺉﺪﺓ‬ ‫ﻋﻦﺍﻟﺤﺎﺟﺔﻓﻲ ﺳﻴﺎﻕ ﻣﺸﻜﻠﺔ ﺍﻟﺘﻌﻠﻢ‪.‬‬ ‫ﺟﻤﻴﻊﺍﻟﻤﻴﺰﺍﺕ ﺍﻟﺘﻲ ﻗﺪ ﺗﻜﻮﻥ ﺯﺍﺉﺪﺓ ﻋﻦ ﺍﻟﺤﺎﺟﺔ ﻫﻲ ﻣﺮﺷﺤﺔ ﻟﻠﺮﻓﺾ‬ ‫ﻥ‬ ‫ﻓﻲﺍﻟﻤﺠﻤﻮﻋﺔ ﺍﻟﻔﺮﻋﻴﺔ ﺍﻟﻨﻬﺎﺉﻴﺔ ﻟﻠﻤﻴﺰﺍﺕ‪.‬ﻳﺘﻢ ﺍﻟﻨﻈﺮ ﻓﻲ ﻋﺪﺩ ﺻﻐﻴﺮ‬ ‫ﻓﻘﻂﻣﻦ ﺍﻟﻤﻴﺰﺍﺕ ﺍﻟﺘﻤﺜﻴﻠﻴﺔ ﻣﻦ ﻣﺠﻤﻮﻋﺔ ﺍﻟﻤﻴﺰﺍﺕ ﺍﻟﺰﺍﺉﺪﺓ ﻋﻦ ﺍﻟﺤﺎﺟﺔ‬ ‫ﺍﻟﻤﺤﺘﻤﻠﺔﺑﺎﻋﺘﺒﺎﺭﻫﺎ ﺟﺰءﺍً ﻣﻦ ﺍﻟﻤﺠﻤﻮﻋﺔ ﺍﻟﻔﺮﻋﻴﺔ ﺍﻟﻨﻬﺎﺉﻴﺔ ﻟﻠﻤﻴﺰﺍﺕ‪.‬‬ ‫ﺑﺒﺴﺎﻃﺔﻳﻤﻜﻨﻨﺎ ﺍﻟﻘﻮﻝ ﺃﻥ ﺍﻟﻬﺪﻑ ﺍﻟﺮﺉﻴﺴﻲ ﻣﻦ ﺍﺧﺘﻴﺎﺭ ﺍﻟﻤﻴﺰﺍﺕ ﻫﻮ‬ ‫ﻥ‬ ‫ﺇﺯﺍﻟﺔﺟﻤﻴﻊ ﺍﻟﻤﻴﺰﺍﺕ ﻏﻴﺮ ﺫﺍﺕ ﺍﻟﺼﻠﺔ ﻭﺍﺧﺘﻴﺎﺭ ﻣﺠﻤﻮﻋﺔ ﻓﺮﻋﻴﺔ ﺗﻤﺜﻴﻠﻴﺔ‬ ‫ﻣﻦﺍﻟﻤﻴﺰﺍﺕ ﺍﻟﺘﻲ ﻗﺪ ﺗﻜﻮﻥ ﺯﺍﺉﺪﺓ ﻋﻦ ﺍﻟﺤﺎﺟﺔ‪.‬‬ ‫ﺍﻵﻥ‪،‬ﺍﻟﺴﺆﺍﻝ ﻫﻮ ﻛﻴﻔﻴﺔ ﻣﻌﺮﻓﺔ ﺃﻱ ﺍﻟﻤﻴﺰﺍﺕ ﻟﻴﺴﺖ ﺫﺍﺕ ﺻﻠﺔ ﺃﻭ ﺃﻱ‬ ‫ﻥ‬ ‫ﺍﻟﻤﻴﺰﺍﺕﻟﻬﺎ ﺇﻣﻜﺎﻧﻴﺔ ﺍﻟﺘﻜﺮﺍﺭ‪.‬‬ ‫‪54‬‬  ‫ﻣﻘﺎﻳﻴﺲﺃﻫﻤﻴﺔ ﺍﻟﻤﻴﺰﺓ‬ ‫ﺍﻟﻤﻌﻠﻮﻣﺎﺕﺍﻟﻤﺘﺒﺎﺩﻟﺔ )‪(MI‬ﻫﻮ ﻣﻘﻴﺎﺱ ﻟﻜﻤﻴﺔ ﺍﻟﻤﻌﻠﻮﻣﺎﺕ ﺍﻟﺘﻲ‬ ‫ﻥ‬ ‫ﻳﻤﻜﻨﻨﺎﻣﻌﺮﻓﺘﻬﺎ ﻣﻦ ﻣﻴﺰﺓ ﻭﺍﺣﺪﺓ ﻣﻦ ﺧﻼﻝ ﻣﻼﺣﻈﺔ ﻗﻴﻢ ﺍﻟﻤﻴﺰﺓ ﺍﻷﺧﺮﻯ‪.‬‬ ‫ﺍﻟﻤﻌﻠﻮﻣﺎﺕﺍﻟﻤﺘﺒﺎﺩﻟﺔ )‪ (MI‬ﺑﻴﻦ ﻣﻴﺰﺗﻴﻦ ﻫﻲ ﻗﻴﻤﺔ ﻏﻴﺮ ﺳﺎﻟﺒﺔ‪ ،‬ﺗﻘﻴﺲ‬ ‫ﻥ‬ ‫ﻣﺪﻯﺍﻟﺼﻠﺔ ﺑﻴﻦ ﺍﻟﻤﻴﺰﺗﻴﻦ‪.‬ﻭﻫﻲ ﺗﺴﺎﻭﻱ ﺻﻔﺮﺍً ﺇﺫﺍ ﻭﻓﻘﻂ ﺇﺫﺍ ﻛﺎﻧﺖ‬ ‫ﺍﻟﻤﻴﺰﺗﺎﻥﻏﻴﺮ ﺫﻱ ﺻﻠﺔ‪ ،‬ﻭﻛﺎﻧﺖ ﺍﻟﻘﻴﻢ ﺍﻷﻋﻠﻰ ﺗﻌﻨﻲ ﺻﻠﺔ ﺃﻋﻠﻰ‪.‬‬ ‫ﻭﻣﻦﺛﻢ‪ ،‬ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﺘﻌﻠﻢ ﺍﻟﺨﺎﺿﻊ ﻟﻺﺷﺮﺍﻑ ﺣﻴﺚ ﻟﺪﻳﻨﺎ ﺗﺴﻤﻴﺔ ﻓﺉﺔ‪،‬‬ ‫ﻥ‬ ‫ﺗﻌﺘﺒﺮﺍﻟﻤﻌﻠﻮﻣﺎﺕ ﺍﻟﻤﺘﺒﺎﺩﻟﺔ )‪ (MI‬ﺑﻤﺜﺎﺑﺔ ﻣﻘﻴﺎﺱ ﺟﻴﺪ ﻟﻠﻌﻼﻗﺔ ﺑﻴﻦ ﺃﻱ‬ ‫ﻣﻴﺰﺓﻭﺗﺴﻤﻴﺔ ﺍﻟﻔﺉﺔ‪.‬‬ ‫‪55‬‬  ‫ﻳﺘﻢﺗﻌﺮﻳﻒ ﺍﻟﻤﻌﻠﻮﻣﺎﺕ ﺍﻟﻤﺘﺒﺎﺩﻟﺔ )‪ (MI‬ﺑﻴﻦ ﺍﻟﻤﻴﺰﺓ ! ﻭﻋﻼﻣﺔ ﺍﻟﻔﺉﺔ‬ ‫ﻥ‬ ‫" ﻋﻠﻰ ﺃﻧﻬﺎ‬ ‫‪(" ,!)/.-,+*(–(")/.-,+*( + (!)/.-,+*( = (" ,!)$ #‬‬ ‫ﺣﻴﺚﺗﻜﻮﻥ ﺇﻧﺘﺮﻭﺑﻴﺎ ﺍﻟﻤﻴﺰﺓ‪2‬ﺗﻢ ﺗﻌﺮﻳﻔﻪ ﺑﻮﺍﺳﻄﺔ‬ ‫( * ‪ ∗65 8 4 − = (2)/. - , +‬ﺳﺠﻞ‪((56)8)2‬‬ ‫‪2∋65‬‬ ‫( * ‪< ,2 /. - , +‬ﻫﻲ ﺍﻹﻧﺘﺮﻭﺑﻴﺎ ﺍﻟﻤﺸﺘﺮﻛﺔ ﻭﻳﺘﻢ ﺗﻌﺮﻳﻔﻬﺎ ﺑﻮﺍﺳﻄﺔ‬ ‫؟)‪/ ،65 8 4 4 –= (< ،2‬ﻑ∗ ﺳﺠﻞ‪/ ،65 8)2‬ﻑ(‬ ‫@ﺃ∋ﻕ‪.‬ﻡﺩ‪∋E‬‬ ‫ﻳﻤﻜﻨﻨﺎﺍﺳﺘﺨﺪﺍﻡ ﻭﻇﻴﻔﺔ ﺟﺎﻫﺰﺓ ﻟﻼﺳﺘﺨﺪﺍﻡ ﻣﻦﺳﻜﻴﺖ‪-‬ﺗﻌﻠﻢ‬ ‫ﻥ‬ ‫ﻣﺴُﻤَﻰًّ‪sklearn.feature_selection.mutual_info_classif‬‬ ‫ﺳﺄﺳﺘﺨﺪﻡﻣﺠﻤﻮﻋﺔ ﺑﻴﺎﻧﺎﺕ ﺳﺮﻃﺎﻥ ﺍﻟﺜﺪﻱ ﺍﻟﺘﻲ ﺗﺄﺗﻲ ﻣﻊ ﺳﻜﻴﺖ‪-‬ﺗﻌﻠﻢ‬ ‫ﻥ‬ ‫ﻟﺮﺅﻳﺔﺍﻟﻤﻌﻠﻮﻣﺎﺕ ﺍﻟﻤﺘﺒﺎﺩﻟﺔ ﻟﺠﻤﻴﻊ ﺍﻟﻤﻴﺰﺍﺕ ﻓﻴﻤﺎ ﻳﺘﻌﻠﻖ ﺑﻌﻼﻣﺔ ﺍﻟﻔﺼﻞ‪.‬‬ ‫‪56‬‬  ‫ ﺗﺤﻤﻴﻞ ﺑﻴﺎﻧﺎﺕ ﺳﺮﻃﺎﻥ ﺍﻟﺜﺪﻱ‬.1‫ﺍﻟﺨﻄﻮﺓ‬ load_breast_cancer ‫ ﺍﺳﺘﻴﺮﺍﺩ‬sklearn.datasets‫ﻣﻦ‬ ( X = cancer]'data'[ =‫ﺍﻟﺴﺮﻃﺎﻥ‬ load_breast_cancer) y = ['‫ﺍﻟﺴﺮﻃﺎﻥ]'ﺍﻟﻬﺪﻑ‬ MI ‫ ﺣﺴﺎﺏ ﻗﻴﻢ‬.2‫ﺍﻟﺨﻄﻮﺓ‬ mutual_info_classif ‫ ﺍﺳﺘﻴﺮﺍﺩ‬sklearn.feature_selection‫ﻣﻦ‬ = mutual_info_classif)X,y( print)mi_values( mi_values :‫ ﻣﺜﻞ ﻫﺬﺍ‬mi_values ‫ﺳﻮﻑﺗﺮﻯ ﻣﺠﻤﻮﻋﺔ‬ 0.37337 0.21318 0.08427 0.36009 0.40294 0.09670 0.37032] 0.33955 0.27600 0.00189 0.24866 0.00276 0.064560.43985 0.45151 0.03802 0.00967 0.12879 0.11825 07603.00.01503 0.43696 0.31469 0.22647 0.09558 0.46426 0.475950.12293 [0.067350.09717.‫ ﻣﻴﺰﺓ‬30 ‫ ﻟـ‬MI ‫ﺭﻗﻤﺎً ﺗﻤﺜﻞ ﺩﺭﺟﺔ‬30 57  ‫ﻣﻘﺎﻳﻴﺲﺍﻟﺘﻜﺮﺍﺭ ﺍﻟﻤﻤﻴﺰ‬ ‫ﻛﻤﺎﺭﺃﻳﻨﺎ‪ ،‬ﻓﺈﻥ ﺍﻟﺘﻜﺮﺍﺭ ﺍﻟﻤﻤﻴﺰ ﻫﻮ ﻣﺴﺎﻫﻤﺔ ﺍﻟﻤﻌﻠﻮﻣﺎﺕ ﺍﻟﻤﺘﺸﺎﺑﻬﺔ ﻣﻦ‬ ‫ﻥ‬ ‫ﺧﻼﻝﻣﻴﺰﺍﺕ ﻣﺘﻌﺪﺩﺓ‪.‬ﻭﻫﻨﺎﻙ ﻣﻘﺎﻳﻴﺲ ﻣﺘﻌﺪﺩﺓ ﻟﺘﺸﺎﺑﻪ ﻣﺴﺎﻫﻤﺔ‬ ‫ﺍﻟﻤﻌﻠﻮﻣﺎﺕ‪:‬‬ ‫ﻣﻘﺎﻳﻴﺲﺗﻌﺘﻤﺪ ﻋﻠﻰ ﺍﻻﺭﺗﺒﺎﻁ‬ ‫ﺃ‬ ‫ﻣﻘﺎﻳﻴﺲﺗﻌﺘﻤﺪ ﻋﻠﻰ ﺍﻟﻤﺴﺎﻓﺔ‬ ‫ﺃ‬ ‫ﻣﻘﺎﻳﻴﺲﺃﺧﺮﻯ ﻟﻠﺘﺸﺎﺑﻪ‬ ‫ﺃ‬ ‫‪ (1‬ﻣﻘﻴﺎﺱ ﺍﻟﺘﺸﺎﺑﻪ ﺍﻟﻘﺎﺉﻢ ﻋﻠﻰ ﺍﻻﺭﺗﺒﺎﻁ‬ ‫ﺍﻻﺭﺗﺒﺎﻁﻫﻮ ﻣﻘﻴﺎﺱ ﻟﻠﻌﻼﻗﺔ ﺍﻟﺨﻄﻴﺔ ﺑﻴﻦ ﻣﻴﺰﺗﻴﻦ‪.‬‬ ‫ﻥ‬ ‫ﻳﻌﺪﻣﻌﺎﻣﻞ ﺍﺭﺗﺒﺎﻁ ﺑﻴﺮﺳﻮﻥ ﺃﺣﺪ ﺃﻛﺜﺮ ﻣﻘﺎﻳﻴﺲ ﺍﻻﺭﺗﺒﺎﻁ ﺷﻴﻮﻋﺎً‪.‬‬ ‫ﻥ‬ ‫‪58‬‬  ‫ﻟﻤﻴﺰﺗﻴﻦﻑ‪ 1‬ﻭﻑ‪ -2‬ﻣﻌﺎﻣﻞ ﺍﺭﺗﺒﺎﻁ ﺑﻴﺮﺳﻮﻥ ﻳﻌﺮﻑ ﻋﻠﻰ‬ ‫ﻥ‬ ‫ﺍﻟﻨﺤﻮﺍﻟﺘﺎﻟﻲ‪:‬‬ ‫ﺗﺘﺮﺍﻭﺡﻗﻴﻢ ﺍﻻﺭﺗﺒﺎﻁ ﺑﻴﻦ ‪ 1+‬ﻭ‪.1-‬ﻳﺸﻴﺮ ﺍﻻﺭﺗﺒﺎﻁ ‪ +) 1‬ﺃﻭ ‪ (-‬ﺇﻟﻰ ﺍﺭﺗﺒﺎﻁ‬ ‫ﻥ‬ ‫ﻣﺜﺎﻟﻲ‪،‬ﺃﻱ ﺃﻥ ﺍﻟﻤﻴﺰﺗﻴﻦ ﻟﻬﻤﺎ ﻋﻼﻗﺔ ﺧﻄﻴﺔ ﻣﺜﺎﻟﻴﺔ‪.‬ﻓﻲ ﺣﺎﻟﺔ ﺃﻥ ﺍﻻﺭﺗﺒﺎﻁ‬ ‫ﻳﺴﺎﻭﻱ‪ ،0‬ﻓﺈﻥ ﺍﻟﻤﻴﺰﺗﻴﻦ ﻟﻴﺲ ﻟﻬﻤﺎ ﻋﻼﻗﺔ ﺧﻄﻴﺔ‪.‬‬ ‫ﺑﺸﻜﻞﻋﺎﻡ‪ ،‬ﻳﺒﺪﻭ ﺃﻥ ﺍﻟﻤﻴﺰﺗﻴﻦ ﺍﻟﻠﺘﻴﻦ ﺗﺮﺑﻄﻬﻤﺎ ﻋﻼﻗﺔ ﺧﻄﻴﺔ‬ ‫ﻥ‬ ‫ﻗﻮﻳﺔﺗﺘﻤﺘﻌﺎﻥ ﺑﺈﻣﻜﺎﻧﻴﺔ ﺍﻟﺘﻜﺮﺍﺭ‪.‬‬ ‫‪59‬‬  ‫‪ (2‬ﻣﻘﻴﺎﺱ ﺍﻟﺘﺸﺎﺑﻪ ﺍﻟﻘﺎﺉﻢ ﻋﻠﻰ ﺍﻟﻤﺴﺎﻓﺔ‬ ‫ﻣﻘﻴﺎﺱﺍﻟﻤﺴﺎﻓﺔ ﺍﻷﻛﺜﺮ ﺷﻴﻮﻋﺎً ﻫﻮﺍﻟﻤﺴﺎﻓﺔ ﺍﻹﻗﻠﻴﺪﻳﺔﻭﺍﻟﺘﻲ ﻳﺘﻢ‬ ‫ﻥ‬ ‫ﺣﺴﺎﺑﻬﺎﺑﻴﻦ ﻣﻴﺰﺗﻴﻦﻑ‪1‬‬ ‫ﻭﻑ‪2‬ﻣﺜﻞ‪:‬‬ ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﺍﻟﻤﺴﺎﻓﺔ ﺍﻹﻗﻠﻴﺪﻳﺔ ﺑﻴﻦ ﺍﻟﻤﻴﺰﺗﻴﻦ ‪) aptitude‬ﻑ‪(1‬‬ ‫ﻥ‬ ‫ﻭﺍﻟﺘﻮﺍﺻﻞ)ﻑ‪ (2‬ﻛﻤﺎ ﻫﻮ ﻣﻮﺿﺢ‪:‬‬ ‫!"‪81.75 =%"،"#‬‬ ‫= ‪9.04‬‬ ‫‪60‬‬  ‫ﺍﻟﻤﺴﺎﻓﺔﻫﻲ‬ ‫ﺟﻴﻦﺃﻛﺜﺮ‬ ‫ﻥ‬ ‫ﻣﻴﻨﻜﻮﻓﺴﻜﻲ‬ ‫ﻣﺘﻰﺭ=‪ ،2‬ﻣﺴﺎﻓﺔ ﻣﻴﻨﻜﻮﻓﺴﻜﻲ ﺗﺄﺧﺬ ﺷﻜﻞ ﺍﻟﻤﺴﺎﻓﺔ ﺍﻹﻗﻠﻴﺪﻳﺔ)‬ ‫ﺃ‬ ‫ﻭﻳﺴﻤﻰﺃﻳﻀﺎﻝ‪2‬ﺍﻟﻘﺎﻋﺪﺓ(‪.‬‬ ‫ﻣﺘﻰﺭ=‪ ،1‬ﻣﺴﺎﻓﺔ ﻣﻴﻨﻜﻮﻓﺴﻜﻲ ﺗﺄﺧﺬ ﺷﻜﻞ ﻣﺴﺎﻓﺔ ﻣﺎﻧﻬﺎﺗﻦ)‬ ‫ﺃ‬ ‫ﻭﻳﺴﻤﻰﺃﻳﻀﺎﻝ‪1‬ﺍﻟﻘﺎﻋﺪﺓ( ﻣﺜﻞ‪:‬‬ ‫ﻣﺜﺎﻝﻋﻤﻠﻲ ﻋﻠﻰ ﻣﺴﺎﻓﺔ ﻣﺎﻧﻬﺎﺗﻦ ﻫﻮ ﻣﺴﺎﻓﺔ ﻫﺎﻣﻴﻨﺞﻭﺍﻟﺘﻲ‬ ‫ﻥ‬ ‫ﺗﺴﺘﺨﺪﻡﺑﺸﻜﻞ ﻣﺘﻜﺮﺭ ﻟﻠﺤﺴﺎﺏ‬ ‫‪61‬‬  ‫‪ (3‬ﺃﻭﺕ‬ ‫ﻣﺆﺷﺮﺟﺎﻛﺎﺭﺩﻳﺘﻢ ﺍﺳﺘﺨﺪﺍﻣﻪ ﻛﻤﻘﻴﺎﺱ ﻟﻠﺘﺸﺎﺑﻪ ﺑﻴﻦ ﻣﻴﺰﺗﻴﻦ‪.‬ﻣﺴﺎﻓﺔ‬ ‫ﻥ‬ ‫ﺟﺎﻛﺎﺭﺩ‪ ،‬ﻭﻫﻮ ﻣﻘﻴﺎﺱ ﻟﻼﺧﺘﻼﻑ ﺑﻴﻦ ﻣﻴﺰﺗﻴﻦ‪ ،‬ﻭﻫﻮ ﻣﻜﻤﻞ ﻟﻤﺆﺷﺮ ﺟﺎﻛﺎﺭﺩ‪.‬‬ ‫ﺑﺎﻟﻨﺴﺒﺔﻟﻤﻴﺰﺗﻴﻦ ﻟﻬﻤﺎ ﻗﻴﻢ ﺛﻨﺎﺉﻴﺔ‪،‬ﻣﺆﺷﺮ ﺟﺎﻛﺎﺭﺩﻳﻜﻮﻥ‬ ‫ﻥ‬ ‫ﺍﻟﻘﻴﻤﺔ‪1‬‬ ‫ﺍﻟﻤﻴﺰﺓﺍﻟﺜﺎﻧﻴﺔ ﻟﻬﺎ ﺍﻟﻘﻴﻤﺔ ‪1‬‬ ‫ﻭﺍﻟﻤﻴﺰﺓﺍﻟﺜﺎﻧﻴﺔ ﻟﻬﺎ ﺍﻟﻘﻴﻤﺔ ‪0‬‬ ‫‪#‬‬ ‫=‪0.4 =#‬‬ ‫ﺝ=‬ ‫&‬ ‫‪#%#%%‬‬ ‫‪ ,‬ﺩﻭﻻﺭ‪0 − 1 =#, ,‬‬ ‫‪62‬‬  ‫ﺗﺸﺎﺑﻪﺟﻴﺐ ﺍﻟﺘﻤﺎﻡﻭﻫﻮ ﺃﺣﺪ ﺃﻛﺜﺮ ﺍﻟﻤﻘﺎﻳﻴﺲ ﺷﻴﻮﻋﺎً ﻓﻲ ﺗﺸﺎﺑﻪ‬ ‫ﻥ‬ ‫ﺍﻟﻨﺼﻮﺹ‪.‬‬ ‫ﻧﺤﻦﻧﻌﻠﻢ ﺃﻥ ﺑﻴﺎﻧﺎﺕ ﺍﻟﻨﺺ ﺗﺤﺘﺎﺝ ﺃﻭﻻ ًﺇﻟﻰ ﺗﺤﻮﻳﻠﻬﺎ ﺇﻟﻰ ﻣﻴﺰﺍﺕ‪ ،‬ﺣﻴﺚ‬ ‫ﻥ‬ ‫ﺗﻜﻮﻥﻛﻠﻤﺔ ﺍﻟﺮﻣﺰ ﻫﻲ ﺍﻟﻤﻴﺰﺓ‪ ،‬ﻭﻳﺄﺗﻲ ﻋﺪﺩ ﺍﻟﻤﺮﺍﺕ ﺍﻟﺘﻲ ﺗﻈﻬﺮ ﻓﻴﻬﺎ ﺍﻟﻜﻠﻤﺔ‬ ‫ﻓﻲﺍﻟﻤﺴﺘﻨﺪ ﻛﻘﻴﻤﺔ ﻓﻲ ﻛﻞ ﺻﻒ‪.‬‬ ‫ﺃﻭﺭﺱ !ﻭ " ﻳﺘﻢ ﺗﻌﺮﻳﻔﻬﺎ‬ ‫ﺗﺸﺎﺑﻪﺟﻴﺐ ﺍﻟﺘﻤﺎﻡ‬ ‫ﻥ‬ ‫ﺑﻮﺍﺳﻄﺔ‪:‬‬ ‫&')!*"*‬ ‫=∑(‬ ‫ﺣﻴﺚ‪ ".! ،‬ﻫﻮ ﺣﺎﺻﻞ ﺿﺮﺏ ﻧﻘﻄﻲ ﻣﺘﺠﻬﻲ ﻟـ ! ﻭ "‬ ‫‪63‬‬  ‫ﻋﻠﻰﺳﺒﻴﻞ ﺍﻟﻤﺜﺎﻝ‪ ،‬ﺩﻋﻨﺎ ﻧﺤﺴﺐ ﺗﺸﺎﺑﻪ ﺟﻴﺐ ﺍﻟﺘﻤﺎﻡ ﻟﻠﺠﻤﻞ ﺍﻟﻤﻘﺴﻤﺔ‬ ‫ﻥ‬ ‫ﺇﻟﻰﺃﺟﺰﺍءﺱﻭﻱ‪ ،‬ﺃﻳﻦﺱ= )‪ (0 ،0 ،3 ،1 ،2 ،0 ،0 ،4 ،2‬ﻭﻱ= )‪،0 ،1 ،2‬‬ ‫‪.(1 ،0 ،1 ،2 ،3،0‬‬ ‫!‪=! 19 = 1∗0 + 0∗0 + 1∗3 + 2∗1 + 3∗2 + 0∗0 + 0∗0 + 1∗4 + 2∗2= #.‬‬ ‫‪5.83 =34‬‬ ‫‪='0 +'0 +'3 +'1 +'2 +'0 +'0 +'4 +'2‬‬ ‫‪4.47 =20‬‬ ‫‪='1 +'0 +'1 +'2 +'3 +'0 +'0 +'1 +'2‬‬ ‫‪=#‬‬ ‫‪19‬‬ ‫!‪#.‬‬ ‫= ‪0.729‬‬ ‫=‬ ‫ﻷﻥ !‪= #,‬‬ ‫‪4.47 ∗5.83‬‬ ‫‪#‬‬ ‫!∗‬ ‫ﻓﻲﺍﻟﻮﺍﻗﻊ‪ ،‬ﻳﻘﻴﺲ ﺗﺸﺎﺑﻪ ﺟﻴﺐ ﺍﻟﺘﻤﺎﻡ ﺍﻟﺰﺍﻭﻳﺔ ﺑﻴﻦ ﺍﻟﻤﺘﺠﻬﻴﻦ ! ﻭ‪.#‬‬ ‫ﻥ‬ ‫ﻭﺑﺎﻟﺘﺎﻟﻲ‪،‬ﺇﺫﺍ ﻛﺎﻧﺖ ﻗﻴﻤﺔ ﺗﺸﺎﺑﻪ ﺟﻴﺐ ﺍﻟﺘﻤﺎﻡ ‪ ،1‬ﻓﻬﺬﺍ ﻳﻌﻨﻲ ﺃﻥ ﺍﻟﺰﺍﻭﻳﺔ‬ ‫ﺑﻴﻦ !ﻭ‪ #‬ﻫﻲ ‪ ،°0‬ﻣﻤﺎ ﻳﻌﻨﻲ ﺃﻥ ! ﻭ‪ #‬ﻣﺘﻤﺎﺛﻼﻥ ﺑﺎﺳﺘﺜﻨﺎء ﺍﻟﻤﻘﺪﺍﺭ‪.‬ﻭﺇﺫﺍ‬ ‫ﻛﺎﻧﺖﻗﻴﻤﺔ ﺗﺸﺎﺑﻪ ﺟﻴﺐ ﺍﻟﺘﻤﺎﻡ ‪ ،0‬ﻓﺈﻥ ﺍﻟﺰﺍﻭﻳﺔ ﺑﻴﻦ ! ﻭ‪ #‬ﻫﻲ ‪.°90‬‬ ‫ﻭﺑﺎﻟﺘﺎﻟﻲ‪،‬ﻻ ﻳﺸﺘﺮﻛﺎﻥ ﻓﻲ ﺃﻱ ﺗﺸﺎﺑﻪ )ﻓﻲ ﺣﺎﻟﺔ ﺑﻴﺎﻧﺎﺕ ﺍﻟﻨﺺ‪ ،‬ﻻ ﺗﻮﺟﺪ‬ ‫ﻛﻠﻤﺔﻣﺸﺘﺮﻛﺔ(‪.‬ﻓﻲ ﺍﻟﻤﺜﺎﻝ ﺃﻋﻼﻩ‪ ،‬ﺗﺼﺒﺢ ﺍﻟﺰﺍﻭﻳﺔ ‪.°43.2‬‬ ‫‪64‬‬