Question

ijУÔ˶¯Ô±Òª´Ó¼×¡¢ÒÒÁ½ÃûÌøÔ¶Ô˶¯Ô±ÖÐÌôÑ¡Ò»È˲μÓÈ«¹ú±ÈÈü£¬ÔÚ×î½üµÄ10´ÎÑ¡°ÎÈüÖУ¬ËûÃǵijɼ¨ÈçÏ£¨µ¥Î»£ºÀåÃ×£©
¼×£º685£¬696£¬710£¬698£¬712£¬697£¬704£¬700£¬713£¬701£®
ÒÒ£º713£¬718£¬680£¬674£¬718£¬693£¬685£¬690£¬698£¬724£®
£¨1£©ËüÃǵÄƽ¾ù³É¼¨·Ö±ðÊǶàÉÙ£¿
£¨2£©¼×¡¢ÒÒÕâ10´Î±ÈÈü³É¼¨µÄ·½²î·Ö±ðÊǶàÉÙ£¿
£¨3£©ÕâÁ½ÃûÔ˶¯Ô±µÄ³É¼¨¸÷ÓÐʲôÌص㣿
£¨4£©Àú½ì±ÈÈü±íÃ÷£¬³É¼¨´ïµ½6.96Ã׾ͿÉÄܶá¹Ú£¬ÄãÈÏΪΪÁ˶á¹ÚӦѡ˭²Î¼ÓÕâ´Î±ÈÈü£¿Èç¹ûÀú½ì³É¼¨±íÃ÷£¬³É¼¨´ïµ½7.10Ã×£¬¾Í¿ÉÆƼͼ£¬ÄÇôÄãÈÏΪΪÁËÆƼͼӦѡ˭²Î¼Ó±ÈÈü£¿

Answer 1

·ÖÎö£º£¨1£©¸ù¾Ýƽ¾ùÊýµÄ¼ÆË㹫ʽ·Ö±ð½øÐмÆËã¼´¿É£»
£¨2£©¸ù¾Ý·½²î¹«Ê½S²=

1

n

[£¨x₁-

.

x

£©²+£¨x₂-

.

x

£©²+¡­+£¨x_n-

.

x

£©²]£¬½øÐмÆËã¼´¿É£»
£¨3£©¸ù¾Ý£¨1£©ºÍ£¨2£©µÃ³öµÄƽ¾ùÊýºÍ·½²î·Ö±ð½øÐзÖÎö¼´¿É£»
£¨4£©¸ù¾Ý³É¼¨´ïµ½6.96Ã׾ͿÉÄܶá¹Ú£¬Êý³ö¸÷´ïµ½6.96Ã׵ĴÎÊý£¬ÔÙ½øÐбȽϵóöӦѡ˭²Î¼ÓÕâ´Î±ÈÈü£»¸ù¾Ý³É¼¨´ïµ½7.10Ã×£¬¾Í¿ÉÆƼͼ£¬´Ó10´ÎÖзֱðÊý³ö´ïµ½7.10Ã×ÓжàÉٴΣ¬½øÐбȽϼ´¿ÉµÃ³ö´ð°¸£®

½â´ð£º½â£º£¨1£©¼×µÄƽ¾ù³É¼¨ÊÇ£º£¨685+696+710+698+712+697+704+700+713+701£©¡Â10=701.6£¬
ÒÒµÄƽ¾ù³É¼¨ÊÇ£º£¨713+718+680+674+718+693+685+690+698+724£©¡Â10=699.3£¬

£¨2£©¼×µÄ·½²îÊÇ£º

1

10

[£¨685-701.6£©²+£¨696-701.6£©²+£¨710-701.6£©²+£¨698-701.6£©²+[£¨712-701.6£©²+£¨697-701.6£©²+£¨704-701.6£©²+£¨700-701.6£©²+£¨713-701.6£©²+£¨701-701.6£©²]=13.168£»
Òҵķ½²îÊÇ£º

1

10

[£¨713-699.3£©²+£¨718-699.3£©²+£¨680-699.3£©²+£¨674-699.3£©²+[£¨718-699.3£©²+£¨693-699.3£©²+£¨685-699.3£©²+£¨690-699.3£©²+£¨698-699.3£©²+£¨724-699.3£©²]=56.842£»

£¨3£©¸ù¾Ý£¨1£©ºÍ£¨2£©µÃ³öµÄ½á¹û¿ÉÒÔ¿´³ö£¬¼×µÄƽ¾ù³É¼¨¸ß£¬ÒÒµÄƽ¾ù³É¼¨µÍ£¬¼×µÄ·½²î´ó£¬²»Îȶ¨£¬Òҵķ½²îС£¬±È½ÏÎȶ¨£®

£¨4£©ÎªÁ˶á¹ÚӦѡ¼×²ÎÈü£¬ÒòΪ10´Î±ÈÈüÖУ¬¼×ÓÐ9´Î³¬¹ý6.96Ã×£¬¶øÒÒÖ»ÓÐ5´Î£»
ΪÁË´òÆƼǼ£¬Ó¦Ñ¡ÒÒ²ÎÈü£¬ÒòΪÒÒ³¬¹ý7.10mÓÐ4´Î£¬±È¼×´ÎÊý¶à£®

µãÆÀ£º´ËÌ⿼²éÁË·½²îºÍƽ¾ùÊý£¬Ò»°ãµØÉèn¸öÊý¾Ý£¬x₁£¬x₂£¬¡­x_nµÄƽ¾ùÊýΪ

.

x

£¬Ôò·½²îS²=

1

n

[£¨x₁-

.

x

£©²+£¨x₂-

.

x

£©²+¡­+£¨x_n-

.

x

£©²]£¬Ëü·´Ó³ÁËÒ»×éÊý¾ÝµÄ²¨¶¯´óС£¬·½²îÔ½´ó£¬²¨¶¯ÐÔÔ½´ó£¬·´Ö®Ò²³ÉÁ¢£®