Question

3£®¸ßÈýij°àÓÐŮͬѧ15Ãû£¬ÄÐͬѧ30Ãû£¬ÀÏʦ°´ÕÕ·Ö²ã³éÑùµÄ·½·¨×齨һ¸ö6È˵ĿÎÍâÐËȤС×飮
£¨1£©Çó¿ÎÍâÐËȤС×éÖÐÄС¢Å®Í¬Ñ§¸÷Ó¦³éÈ¡µÄÈËÊý£»
£¨2£©ÔÚÒ»Öܵļ¼ÄÜÅàѵºó´ÓÕâ6ÈËÖÐÑ¡³öA¡¢BÁ½Ãûͬѧ×öijÏîʵÑ飬ʵÑé½áÊøºó£¬AͬѧµÃµ½µÄʵÑéÊý¾ÝΪ1.6¡¢2¡¢1.9¡¢1.5¡¢2£¬BͬѧµÃµ½µÄʵÑéÊý¾ÝÊÇ2.1¡¢18¡¢1.9¡¢2¡¢2.2£¬ÇëÎÊÄÄλͬѧµÄʵÑé¸üÎȶ¨£¿²¢ËµÃ÷ÀíÓÉ£®
²Î¿¼¹«Ê½£º${s^2}=\frac{1}{n}[{{{£¨{{x_1}-\overline x}£©}^2}+{{£¨{{x_2}-\overline x}£©}^2}+¡­+{{£¨{{x_n}-\overline x}£©}^2}}]$£®

Answer 1

·ÖÎö £¨1£©°´ÕÕ·Ö²ã³éÑùµÄ·½·¨ÄÜÇó¿ÎÍâÐËȤС×éÖÐÄС¢Å®Í¬Ñ§¸÷Ó¦³éÈ¡µÄÈËÊý£®
£¨2£©·Ö±ðÇó³öA¡¢BͬѧµÃµ½µÄʵÑéÊý¾ÝµÄƽ¾ùÊý£¬·½²î£¬ÓÉ´ËÄܵõ½BͬѧµÄʵÑé¸üÎȶ¨£®

½â´ð ½â£º£¨1£©¡ß¸ßÈýij°àÓÐŮͬѧ15Ãû£¬ÄÐͬѧ30Ãû£¬ÀÏʦ°´ÕÕ·Ö²ã³éÑùµÄ·½·¨×齨һ¸ö6È˵ĿÎÍâÐËȤС×飬
¡àÄÐÉú³éÈ¡£º$\frac{30}{45}¡Á6=4$£¨ÈË£©£¬
Å®Éú³éÈ¡£º$\frac{15}{45}¡Á6=2$£¨ÈË£©£®
£¨2£©ÉèA¡¢BͬѧµÃµ½µÄʵÑéÊý¾ÝµÄƽ¾ùÊý·Ö±ðΪ$\overline{x_A}$£¬$\overline{x_B}$£¬·½²î·Ö±ðΪ$S_A^2£¬S_B^2$£¬
$\overline{x_A}=\frac{1.6+2+1.9+2.5+2}{5}=2$£¬
$\overline{x_B}=\frac{2.1+1.8+1.9+2+2.2}{5}=2$£¬
¡àS²_A=$\frac{1}{5}$[£¨1.6-2£©²+£¨2-2£©²+£¨1.9-2£©²+£¨2.5-2£©²+£¨2-2£©²]=0.084£¬
S²_B=$\frac{1}{5}$[£¨2.1-2£©²+£¨1.8-2£©²+£¨1.9-2£©²+£¨2-2£©²+£¨2.2-2£©²]=0.02£¬
$S_A^2=0.084£¬S_B^2=0.02$£¬
¡ß$S_A^2£¾S_B^2$£¬¡àBͬѧµÄʵÑé¸üÎȶ¨£®

µãÆÀ ±¾Ì⿼²é·Ö²ã³éÑùµÄÓ¦Ó㬿¼²éƽ¾ùÊý¡¢·½²îµÄ¼ÆËã¼°Ó¦Óã¬ÊÇ»ù´¡Ì⣬½âÌâʱҪÈÏÕæÉóÌ⣬עÒâ·½²î¹«Ê½µÄºÏÀíÔËÓã®