Question

2£®Ò»°ãÀ´Ëµ£¬Ò»¸öÈ˽ÅÕÆÔ½³¤£¬ËûµÄÉí¸ßÔ½¸ß£¬ÏÖ¶Ô10Ãû³ÉÄêÈ˵ĽÅÕƳ¤xÓëÉí¸ßy½øÐвâÁ¿£¬µÃµ½Êý¾Ý£¨µ¥Î»¾ùΪcm£©×÷Ϊһ¸öÑù±¾ÈçϱíËùʾ£º

½ÅÕƳ¤£¨x£©	20	21	22	23	24	25	26	27	28	29
Éí¸ß£¨y£©	141	146	154	160	169	176	181	188	197	203

£¨1£©ÔÚÉϱíÊý¾ÝÖУ¬ÒÔ¡°½ÅÕƳ¤¡±Îªºá×ø±ê£¬¡°Éí¸ß¡±Îª×Ý×ø±ê£¬×÷³öÉ¢µãͼºó£¬·¢ÏÖÈýµãÔÚÒ»ÌõÖ±Ï߸½½ü£¬ÊÔÇó¡°Éí¸ß¡±Óë¡°½ÅÕƳ¤¡±Ö®¼äµÄÏßÐԻع鷽³Ì$\stackrel{¡Ä}{y}$=$\stackrel{¡Ä}{b}$x+a
£¨2£©ÈôijÈ˵ĽÅÕƳ¤Îª26cm£¬ÊÔ¹À¼Æ´ËÈ˵ÄÉý¸ß£»
£¨3£©ÔÚÑù±¾ÖУ¬´ÓÉí¸ß180cmÒÔÉϵÄ4ÈËÖÐËæ»ú³éÈ¡2ÈË×÷½øÒ»²½µÄ·ÖÎö£¬ÇóËù³éÈ¡µÄ2ÈËÖÐÖÁÉÙÓÐ1ÈËÔÚ190cmÒÔÉϵĸÅÂÊ£® 
²Î¿¼Êý¾Ý£º$\sum_{i=1}^{10}$£¨x_i-$\overline{x}$£©£¨y_i-$\overline{y}$£©=577.5£¬$\sum_{i=1}^{10}$£¨x_i-$\overline{x}$£©²=82.5£©
¸½£º»Ø¹éÖ±ÏßµÄбÂʺͽؾàµÄ×îС¶þ³Ë·¨¹À¼Æ¹«Ê½·Ö±ðΪ£º$\overline{b}$=$\frac{\sum_{i=1}^{n}{x}_{i}{y}_{1}-n\overline{xy}}{\sum_{i=1}^{n}{{x}_{i}}^{2}-n£¨\overline{x}£©^{2}}$=$\frac{\sum_{i=1}^{n}£¨{x}_{i}-\overline{x}£©£¨{y}_{i}-\overline{y}£©}{\sum_{i=1}^{n}£¨{x}_{i}-\overline{x}£©^{2}}$£¬$\stackrel{¡Ä}{a}$=$\overline{y}$-$\stackrel{¡Ä}{b}$$\overline{x}$£®

Answer 1

·ÖÎö £¨1£©Çó³öÑù±¾ÖÐÐĵ㣨$\overline{x}$£¬$\overline{y}$£©£¬ÀûÓù«Ê½Çó³ö$\stackrel{¡Ä}{b}$Óë$\stackrel{¡Ä}{a}$µÄÖµ£¬¼´¿Éд³öÏßÐԻع鷽³Ì£»
£¨2£©¸ù¾ÝÏßÐԻع鷽³ÌÇó³öx=26.5ʱ$\stackrel{¡Ä}{y}$µÄÖµ¼´¿É£»
£¨3£©ÓÃÁоٷ¨Çó³ö´ÓÉí¸ß180cmÒÔÉÏ4ÈËÖÐËæ»ú³éÈ¡2È˵Ļù±¾Ê¼þÊý£¬¼ÆËãËùÇóµÄ¸ÅÂÊÖµ£®

½â´ð ½â£º£¨1£©¼ÇÑù±¾ÖÐ10È˵ġ°½ÅÕƳ¤¡±Îªx_i£¨i=1£¬2£¬3£¬¡­£¬10£©£¬
¡°Éí¸ß¡±Îªy_i£¨i=1£¬2£¬3£¬¡­£¬10£©£¬
Ôò$\overline{x}$=$\frac{1}{10}$¡Á£¨20+21+¡­+29£©=24.5£¬
$\overline{y}$=$\frac{1}{10}$¡Á£¨141+146+¡­+203£©=171.5£»
¡ß$\sum_{i=1}^{10}$£¨x_i-$\overline{x}$£©£¨y_i-$\overline{y}$£©=577.5£¬$\sum_{i=1}^{10}$£¨x_i-$\overline{x}$£©²=82.5£¬
¡à$\stackrel{¡Ä}{b}$=$\frac{\sum_{i=1}^{n}£¨{x}_{i}-\overline{x}£©£¨{y}_{i}-\overline{y}£©}{\sum_{i=1}^{n}£¨{x}_{i}-\overline{x}£©^{2}}$=$\frac{577.5}{82.5}$=7£»---£¨3·Ö£©
¡à$\stackrel{¡Ä}{a}$=$\overline{y}$-$\stackrel{¡Ä}{b}$$\overline{x}$=171.5-7¡Á24.5=0£¬--£¨4·Ö£©
ËùÇóµÄÏßÐԻع鷽³ÌΪ$\stackrel{¡Ä}{y}$=7x---£¨5·Ö£©
£¨2£©ÓÉ£¨1£©Öª$\stackrel{¡Ä}{y}$=7x£¬--------£¨6·Ö£©
µ±x=26.5ʱ£¬$\stackrel{¡Ä}{y}$=7¡Á26.5=185.5£¬
¹Ê¹À¼Æ´ËÈ˵ÄÉí¸ßΪ185.5£»---£¨7·Ö£©
£¨3£©½«Éí¸ßΪ181¡¢188¡¢197¡¢203£¨cm£©µÄ4ÈË·Ö±ð¼ÇΪA¡¢B¡¢C¡¢D£¬---£¨8·Ö£©
¼Ç¡°´ÓÉí¸ß180cmÒÔÉÏ4ÈËÖÐËæ»ú³éÈ¡2ÈË£¬
Ëù³éµÄ2ÈËÖÐÖÁÉÙÓÐ1¸öÉí¸ßÔÚ190cmÒÔÉÏ¡±ÎªÊ¼þA£¬
Ôò»ù±¾Ê¼þÓУºAB¡¢AC¡¢AD¡¢BC¡¢BD¡¢CD£¬×ÜÊýΪ6£¬---£¨10·Ö£©
A°üº¬µÄ»ù±¾Ê¼þÓУºAC¡¢AD¡¢BC¡¢BD¡¢CD£¬¸öÊýΪ5£¬
ËùÒÔP£¨A£©=$\frac{5}{6}$£®---£¨12·Ö£©

µãÆÀ ±¾Ì⿼²éÁËÏßÐԻع鷽³ÌµÄÇó·¨ÓëÓ¦ÓÃÎÊÌ⣬Ҳ¿¼²éÁËÓÃÁоٷ¨Çó¹Åµä¸ÅÐ͵ĸÅÂÊÎÊÌ⣬ÊÇ»ù´¡ÌâÄ¿£®