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【329822】6.4 数据的离散程度 综合测试2

时间:2025-02-05 18:10:25 作者: 字数:10913字


 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a>

《数据的离散程度》综合测试2

【教材训练】 5分钟 

1.极差、方差、标准差的概念

(1)一组数据的最大数据最小数据的差叫这组数据的极差.

(2)方差是各个数据与其平均数差的平方的平均数.

(3)标准差是方差的算术平方根.

2.判断训练(打“√”或“×”)

(1)极差是刻画数据离散程度的最简单的统计量. ( )

(2)一组数据:-1,5,9,7的极差是8. ( )

(3)在样本容量相同的情况下,方差越小,说明数据的波动越大,越不稳定.( )

(4)一组数据5,5,5,4,6,则这组数据的方差是0,标准差是0. ( )

(5)已知,一组数据x1,x2,…,xn的平均数是10,方差是2,则数据x1+3,x2+3,…,xn+3的平均数是10,方差是2. ( )

【课堂达标】 20分钟

训练点一:极差、方差、标准差的计算

1.(3)若一组数据1,2,3,x的极差为6,x的值是 (  )

A.7 B.8 C.9 D.7-3

2.(3)在方差的计算公式s2= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ×[(x1-20)2+(x2-20)2+…+(x10-20)2],数字1020分别表示的意义可以是 (  )

A.数据的个数和方差 B.平均数和数据的个数

C.数据的个数和平均数 D.数据的方差和平均数

3.(3)在植树节当天,某校一个班同学分成10个小组参加植树造林活动,

10个小组植树的株数见下表:

植树株树()

5

6

7

小组个数

3

4

3

则这10个小组植树株数的方差是________.

4.(3)已知数据0,1,2,3,4的方差为2,则数据10,11,12,13,14的方差为____________,标准差为__________.

5.(4)甲、乙两位同学五次数学测验成绩如下表:

测验()

1

2

3

4

5

平均分

方差

()

75

90

96

83

81



()

86

70

90

95

84



请你在表中的空白处填上适当的数,用学到的统计知识对两位同学的成绩进行分析,并写出一条合理化建议.

训练点二:极差、方差、标准差的简单应用

1.(3)已知甲、乙两组数据的平均数相等,若甲组数据的方差 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> =0.055,乙组数据的方差 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> =0.105,则 (  )

A.甲组数据比乙组数据波动大

B.乙组数据比甲组数据波动大

C.甲组数据与乙组数据的波动一样大

D.甲、乙两组数据的波动不能比较

2.(3)某同学对甲、乙、丙、丁四个市场二月份每天的白菜价格进行调查,计算后发现这个月四个市场的价格平均值相同,方差分别为 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> =8.5, <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> =2.5, <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> =10.1, <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> =7.4,二月份白菜价格最稳定的市场是 (  )

A. B. C. D.

3.(3)已知一组数据:3,4,5,6,5,7,那么这组数据的方差是 (  )

A. <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> B. <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> C. <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> D. <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a>

4.(5)在某旅游景区上山的一条路上,有一些断断续续的台阶,如图是其中的甲、乙两段台阶路的示意图.请你用所学过的有关统计知识(平均数、中位数、方差和极差)回答下列问题:

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a>

图中的数字表示每一级台阶的高度(单位:cm),并且数据15,16,16,14,14,15的方差: <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ,数据11,15,18,17,10,19的方差: <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> .

(1)两段台阶路有哪些相同点和不同点?

(2)哪段台阶路走起来更舒服?为什么?

(3)为方便游客行走,需要重新整修上山的小路.对于这两段台阶路,在台阶数不变的情况下,请你提出合理的整修建议.

【课后作业】 30分钟

一、选择题(每小题4,8)

1.甲、乙两人在相同的条件下,各射靶10,经过计算:甲、乙射击成绩的平均数都是8,甲的方差是1.2,乙的方差是1.8.下列说法中不

一定正确的是 (  )

A.甲、乙的众数相同 B.甲的成绩稳定

C.乙的成绩波动较大 D.甲、乙射中的总环数相同

2.甲、乙两学生在军训打靶训练中,打靶的总次数相同,且所中环数的平均数也相同,但甲的成绩比乙的成绩稳定,那么两者的方差的大小关系是 (  )

A. <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> < <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> B. <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> > <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> C. <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> D.不能确定

二、填空题(每小题4,12)

3.如图是一组数据的折线统计图,这组数据的极差是________.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a>

4.已知一组数据x1,x2,…,xn的方差是s2,则新的一组数据ax1+1,ax2+1,…,axn+1(a为常数,a≠0)的方差是________(用含a,s2的代数式表示).

(友情提示:s2= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> [(x1- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+(x2- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+…+(xn- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2])

5.如图是甲、乙两名射击运动员的10次射击训练成绩(环数)的折线统计图,观察图形,甲、乙这10次射击成绩的方差 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> , <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> 之间的大小关系是________.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a>

三、解答题(30)

6.(8)甲、乙两名同学进行射击训练,在相同条件下各射靶5,成绩统计如下:

命中环数

7

8

9

10

甲命中相应环数的次数

2

2

0

1

乙命中相应环数的次数

1

3

1

0

若从甲、乙两人射击成绩方差的角度评价两人的射击水平,则谁的射击成绩更稳定些?

7.(10)已知A组数据如下:0,1,-2,-1,0,-1,3.

(1)A组数据的平均数.

(2)A组数据中选取5个数据,记这5个数据为B组数据.要求B组数据满足两个条件:①它的平均数与A组数据的平均数相等;②它的方差比A组数据的方差大.你选取的B组数据是________,请说明理由.

【注:A组数据的方差的计算式是:

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> [(x1- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+(x2- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+(x3- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+(x4- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+(x5- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+(x6- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+(x7- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2]

8.(12)(能力拔高题)甲、乙两人在相同条件下各射靶10,每次射靶的成绩情况如图所示.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a>

(1)请填写下表:


平均数

方差

中位数

命中9环以上的次

(包括9)

7

1.2


1


5.4




(2)请从下列四个不同的角度对这次测试结果进行分析.

从平均数和方差相结合看(分析谁的成绩更稳定);

从平均数和中位数相结合看(分析谁的成绩好些);

从平均数和命中9环以上的次数相结合看(分析谁的成绩好些);

从折线图上两人射击命中环数的走势看(分析谁更有潜力).



参考答案

【教材训练】

2.(1)√ (2)√ (3)× (4)× (5)×

【课堂达标】

训练点1

1【解析】选D.由题意可得x的值为-37.故选D.

2【解析】选C.由方差的计算公式知10个数据,平均数为20.

3【解析】先求得平均数为 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> =6,然后套用方差公式得s2=0.6.

答案:0.6

4【解析】因为第二组数据在第一组数据的基础上都加上了10,数据波动情况没有发生变化,故方差不变,依然是2,标准差是 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> .

答案:2  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a>

5【解析】


平均分

方差

85

53.2

85

70.4

从上述数据可以看出,两人的成绩的平均分相等,乙同学的数学成绩不够稳定,波动较大,希望乙同学在学习上查缺补漏,稳定自己的成绩.

训练点2

1【解析】选B.方差大的数据波动大,方差小的数据波动小.故选B.

2【解析】选B.根据数据方差的意义,方差越小说明二月份白菜的价格越稳定.因为 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> =2.5最小,所以乙市场的价格最稳定.

3【解析】选A.因为 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> =5,所以

s2= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ×[(3-5)2+(4-5)2+(5-5)2+(6-5)2+(5-5)2+(7-5)2]= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> .故选A.

4【解析】(1) <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ×(15+16+16+14+14+15)=15,

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ×(11+15+18+17+10+19)=15,

甲路段的中位数为15;乙路段的中位数为16.

甲路段的极差为16-14=2;乙路段的极差为19-10=9.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> , <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ,所以:

相同点:两段台阶路高度的平均数相同.

不同点:两段台阶路高度的中位数、方差、极差不同.

(2)甲段台阶路走起来更舒服一些,因为它的台阶高度的方差小.

(3)每个台阶高度均修为15cm,使得方差为0.

【课后作业】

1【解析】选A.因为两人各射击10,平均数都是8,所以两人的总环数都是80,因而D正确;又因为甲的方差小于乙的方差,说明甲的成绩比较稳定,乙的成绩波动较大,所以B,C正确;而通过方差和平均数不能确定数据的众数,所以A不正确.

2【解析】选A.由于甲、乙两位学生在军训打靶训练中,打靶的总次数相同,所中环数的平均数也相同,由于甲的成绩稳定,说明他的成绩波动性较小,所以他的方差也小.

3【解析】极差是最大值与最小值的差:59-28=31.

答案:31

4【解析】设数据x1,x2,…,xn的平均数为 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ,方差为s2,

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ,

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> [(x1- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+(x2- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+…+(xn- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2]=s2,

所以 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a>

=a <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> +1.

新的一组数据ax1+1,ax2+1,…,axn+1(a为常数,a≠0)的方差是

s′2= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> [(ax1+1-a <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> -1)2+(ax2+1-a <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> -1)2+…+(axn+1-a <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> -1)2]

= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> [(ax1-a <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+(ax2-a <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+…+(axn-a <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2]

= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> {[a(x1- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )]2+[a(x2- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )]2+…+[a(xn- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )]2}

= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> {[a2(x1- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2]+[a2(x2- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2]+…+[a2(xn- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2]}

=a2· <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> [(x1- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+(x2- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2+…+(xn- <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> )2]

=a2s2.

即新的一组数据ax1+1,ax2+1,…,axn+1(a为常数,a≠0)的方差是a2s2.

答案:a2s2

5【解析】根据图象可以看出甲的成绩波动比乙的成绩波动要小. <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> < <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> .

答案: <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> < <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a>

6【解析】甲、乙两人射击成绩的平均成绩分别为:

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ×(7×2+8×2+10×1)=8,

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ×(7×1+8×3+9×1)=8,

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ×[2×(7-8)2+2×(8-8)2+(10-8)2]=1.2,

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ×[(7-8)2+3×(8-8)2+(9-8)2]=0.4,

因为 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> < <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ,

所以乙同学的射击成绩更稳定些.

7【解析】(1) <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ×(0+1-2-1+0-1+3)=0.

(2)答案不唯一,如选取1,-2,-1,-1,3.

因为 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ×(1-2-1-1+3)=0,所以 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> .

因为 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ×[02+12+(-2)2+(-1)2+02+(-1)2+32]= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ,

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ×[12+(-2)2+(-1)2+(-1)2+32]= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> .

所以 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> > <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> ,所以数据1,-2,-1,-1,3符合题意.

8【解析】(1)


平均数

方差

中位数

命中9环以上次数

(包括9)

7

1.2

7

1

7

5.4

7.5

3


(2)①因为平均数相同, <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a> < <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/171/" title="数据" class="c1" target="_blank">数据</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/1408/" title="程度" class="c1" target="_blank">程度</a> <a href="/tags/1409/" title="离散" class="c1" target="_blank">离散</a>

所以甲的成绩比乙稳定.

因为平均数相同,甲的中位数<乙的中位数,

所以乙的成绩比甲好些.

因为平均数相同,命中9环以上的次数甲比乙少,

所以乙的成绩比甲好些.

甲的成绩在平均数上下波动;而乙处于上升势头,从第4次以后就没有比甲少的情况发生,乙较有潜力.