甲、乙兩臺機床生產(chǎn)同一種零件,并且每天產(chǎn)量相等,在6天中每天生產(chǎn)零件中的次品數(shù)依次是:甲:3、0、0、2、0、1;乙:1、0、2、1、0、2.則甲、乙兩臺機床中性能較穩(wěn)定的是 .
【答案】
分析:先計算出甲乙的平均數(shù),甲的平均數(shù)=乙的平均數(shù)=1,再根據(jù)方差的計算公式分別計算出它們的方差,然后根據(jù)方差的意義得到方差小的性能較穩(wěn)定.
解答:解:甲的平均數(shù)=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155640427091394/SYS201310221556404270913013_DA/0.png)
(3+0+0+2+0+1)=1,
乙的平均數(shù)=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155640427091394/SYS201310221556404270913013_DA/1.png)
(1+0+2+1+0+2)=1,
∴S
2甲=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155640427091394/SYS201310221556404270913013_DA/2.png)
[(3-1)
2+3×(0-1)
2+(2-1)
2+(1-1)
2]=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155640427091394/SYS201310221556404270913013_DA/3.png)
S
2乙=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155640427091394/SYS201310221556404270913013_DA/4.png)
[(2×(1-1)
2+2×(0-1)
2+2×(2-1)
2]=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155640427091394/SYS201310221556404270913013_DA/5.png)
,
∴S
2甲>S
2乙,
∴乙臺機床性能較穩(wěn)定.
故答案為乙.
點評:本題考查了方差的計算公式和意義:一組數(shù)據(jù)x
1,x
2,…,x
n,其平均數(shù)為
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155640427091394/SYS201310221556404270913013_DA/6.png)
,則這組數(shù)據(jù)的方差S
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155640427091394/SYS201310221556404270913013_DA/7.png)
[(x
1-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155640427091394/SYS201310221556404270913013_DA/8.png)
)
2+(x
2-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155640427091394/SYS201310221556404270913013_DA/9.png)
)
2+…+(x
n-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131022155640427091394/SYS201310221556404270913013_DA/10.png)
)
2];方差反映一組數(shù)據(jù)在其平均數(shù)左右的波動大小,方差越大,波動就越大,越不穩(wěn)定,方差越小,波動越小,越穩(wěn)定.