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#1
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⨷ÂìàÃ×èͧʶԵԤÃѺ¼Á
¹Ñ¡àÃÕ¹¤¹Ë¹Ö觤ӹdzËÒ¤èÒÊèǹàºÕè§ູÁҵðҹ¢Í§¤Ðá¹¹ÊͺÇÔªÒ¤³ÔµÈÒʵÃì¢Í§à¾×è͹·Ñé§ËÁ´ã¹Ëéͧä´éà·èҡѺ 7 áµè¾ºÇèҤӹdz¼Ô´ à¹×èͧ¨Ò¡¹Ó¤èÒÁѸ°ҹÁÒãªéá·¹¤èÒà©ÅÕèÂàÅ¢¤³Ôµ ¶éÒ¤èÒÁѸ°ҹÁÕ¤èÒà·èҡѺ 53 áÅФèÒà©ÅÕèÂàÅ¢¤³ÔµÁÕ¤èÒà·èҡѺ 57 áÅéǤèÒÊèǹàºÕè§ູÁҵðҹ·Õè¶Ù¡µéͧ¤ÇÃÁÕ¤èÒà·èÒã´
ú¡Ç¹·èÒ¹¼ÙéÃÙéªèÇÂ͸ԺÒÂÇÔ¸Õ·ÓãËé˹èͤÃѺ ¢Íº¤Ø³¤ÃѺ |
#2
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ÊÇÑÊ´Õ¤èÐ
Assumption ¢Í§´Ô©Ñ¹¹Ð¤Ð :¢éÍÁÙŪش¹Õéà»ç¹¢éÍÁÙÅ»ÃЪҡà ãËé à¾×è͹ã¹ËéͧÁÕ N ¤¹ áµèÅФ¹ ä´é¤Ðá¹¹ $x_1,x_2,x_3,...,x_N$ µÍ¹¤Ó¹Ç³¼Ô´ $\sqrt{\frac{\sum_{i = 1}^{N} (x_i-53)^2}{N}}=7$ $\sum_{i = 1}^{N} (x_i-53)^2=49N$ $\sum_{i = 1}^{N} (x_i^2-106x_i+2809)=49N$ $\sum_{i = 1}^{N} x_i^2-106\sum_{i =1}^{N} x_i+2809N=49N$ $\sum_{i = 1}^{N} x_i^2-106\sum_{i =1}^{N} x_i=-2760N$ áµè·ÇèÒ ¤èÒà©ÅÕèÂàÅ¢¤³Ôµ¤×Í 57 ¹Ñ蹤×Í $\sum_{i =1}^{N} x_i=57N$ àÍÒä»á·¹¤èÒ¡ÅѺ·Õèà´ÔÁ $\sum_{i = 1}^{N} x_i^2-106(57N)=-2760N$ $\sum_{i = 1}^{N} x_i^2=-2760N+106(57N)=3282N$ µÍ¹¤Ó¹Ç³¶Ù¡ $ANS=\sqrt{\frac{\sum_{i = 1}^{N} (x_i-57)^2}{N}}$ =$\sqrt{\frac{\sum_{i = 1}^{N} (x_i^2-114x_i+3249)}{N}}$ =$\sqrt{\frac{\sum_{i = 1}^{N} (x_i^2)-114 \sum_{i = 1}^{N} (x_i)+3249N}{N}}$ =$\sqrt{\frac{3282N-114(57N)+3249N}{N}}$ =$\sqrt{33}$ Personal Comment: ÇèÒáÅéÇ¡ç·Óà»ç¹ general case ãËé˹èÍÂÅСѹ ¶éÒà»ÅÕè¹⨷Âìà»ç¹µÑÇá»ÃãËéËÁ´ ¹Ñ¡àÃÕ¹¤¹Ë¹Ö觤ӹdzËÒ¤èÒÊèǹàºÕè§ູÁҵðҹ¢Í§¤Ðá¹¹ÊͺÇÔªÒ¤³ÔµÈÒʵÃì¢Í§à¾×è͹·Ñé§ËÁ´ã¹Ëéͧä´éà·èҡѺ a áµè¾ºÇèҤӹdz¼Ô´ à¹×èͧ¨Ò¡¹Ó¤èÒÁѸ°ҹÁÒãªéá·¹¤èÒà©ÅÕèÂàÅ¢¤³Ôµ ¶éÒ¤èÒÁѸ°ҹÁÕ¤èÒà·èҡѺ b áÅФèÒà©ÅÕèÂàÅ¢¤³ÔµÁÕ¤èÒà·èҡѺ c áÅéǤèÒÊèǹàºÕè§ູÁҵðҹ·Õè¶Ù¡µéͧ¤ÇÃÁÕ¤èÒà·èÒã´ ¤ÓµÍº·Õèä´é¤ÇèÐà»ç¹ $\sqrt{a^2-(b-c)^2}$ àªè¹ã¹¡Ã³Õ¹Õé a=7,b=53,c=57 ¤ÓµÍº¨Ðà»ç¹ $\sqrt{7^2-(53-57)^2}=\sqrt{7^2-4^2}=\sqrt{49-16}=\sqrt{33}$ ÊÇÑÊ´Õ¤èÐ edit 1 à¾ÔèÁ Personal Comment 15 ¾ÄȨԡÒ¹ 2014 10:52 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Scylla_Shadow |
#3
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àÃÒãªéÊٵõÒÁÃÙ» äÁèä´éàËÃͤÃѺ ¼ÁÅͧ´ÙáÅéÇÁѹäÁèÍÍ¡¤ÃѺ
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#4
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ÊٵùÕéãªé¡Ñº ¤èÒ¡ÅÒ§·Õèà»ç¹¤èÒà©ÅÕèÂàÅ¢¤³Ôµ à·èÒ¹Ñ鹤ÃѺ |
#5
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à¾ÃÒÐà˵عÕéàͧ ¼Á¡çà¾Ô觷ÃÒº ¢Íº¾ÃФس¤ÃѺ
15 ¾ÄȨԡÒ¹ 2014 17:17 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ g_boy |
#6
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ÊٵõÒÁÃÙ»ãªéä´é¡ÑºµÍ¹¤Ó¹Ç³¢éÍÁÙŶ١¤èÐ ¶éÒãªé¡ÑºµÍ¹¤Ó¹Ç³¢éÍÁÙÅ·ÕèãÊèÁÒ¼Ô´µÍ¹áá ¡çäÁèä´é¤èÐ à˵ؼÅÍÂÙè¢éÒ§ÅèÒ§¤èÐ ÊÇÑÊ´Õ¤èÐ ÍéÒ§ÍÔ§:
¼Ô´µÑé§áµèºÃ÷ѴááàŤèÐ ÍéÒ§ÍÔ§:
͹Öè§ ¡Ó˹´¡ÒÃãªéÊÑÅѡɳìµÒÁ¹Õé¹Ð¤Ð (µÒÁ¸ÃÃÁà¹ÕÂÁÂÖ´¶×Í»¯ÔºÑµÔÍÂèÒ§à¤Ã觤ÃÑ´¤èÐ) ÊèǹàºÕè§ູÁҵðҹ ¨Ðãªé $\sigma $ ÊÓËÃѺ¢éÍÁÙÅ»ÃЪҡà áÅÐ S.D. ÊÓËÃѺ¢éÍÁÙÅ¡ÅØèÁµÑÇÍÂèÒ§ ¨Ó¹Ç¹¢éÍÁÙÅ ¨Ðãªé N ÊÓËÃѺ¢éÍÁÙÅ»ÃЪҡà áÅÐ n ÊÓËÃѺ¢éÍÁÙÅ¡ÅØèÁµÑÇÍÂèÒ§ ¤èÒà©ÅÕèÂàÅ¢¤³Ôµ ¨Ðãªé $\mu $ ÊÓËÃѺ¢éÍÁÙÅ»ÃЪҡà áÅÐ $\bar x $ ÊÓËÃѺ¢éÍÁÙÅ¡ÅØèÁµÑÇÍÂèÒ§ ¡ÃسÒÍÂèÒãªéÊÅѺ¡Ñ¹¤èÐ ¡ÒäӹdzÊèǹàºÕè§ູÁҵðҹ¹Ñé¹àÃÔèÁ¨Ò¡ÊٵùÕé¤èÐ $\sqrt{\frac{\sum_{i = 1}^{N} (x_i-\mu )^2}{N}}$ ÊÓËÃѺ¢éÍÁÙÅ»ÃЪҡà $\sqrt{\frac{\sum_{i = 1}^{n} (x_i-\bar x )^2}{n-1}}$ ÊÓËÃѺ¢éÍÁÙÅ¡ÅØèÁµÑÇÍÂèÒ§ ÊèǹÊÙµÃÍ×è¹ ¶×Íà»ç¹ Corollary ·ÕèµÒÁÁÒ¤èР͹Öè§ ¤Ô´ÇèÒ¤ÇÃÃÐÅÖ¡Êٵ÷Õèà»ç¹·ÕèÁҢͧÊÙµÃäÇé à¾ÃÒÐÇèҵ͹·Õè¨Ð¢ÂÒ¼Å仨Ðä´éäÁèÅÓºÒ¡¤èÐ ÊÇÑÊ´Õ¤èÐ |
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