九年級一班四位同學參加電視臺組織的“快樂中學生”比賽,得分依次為7、8、9、8,那么下面說法正確的是( )
A.方差是2
B.眾數(shù)是8
C.中位數(shù)是8.5
D.極差是1
【答案】
分析:分別計算出這組數(shù)據(jù)的平均數(shù),方差,眾數(shù),中位數(shù),極差再判定.
解答:解:A.由平均數(shù)的定義知:(7+8+9+8)÷4=8;
故方差為:
s
2=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101190936625268688/SYS201311011909366252686002_DA/0.png)
[(x
1-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101190936625268688/SYS201311011909366252686002_DA/1.png)
)
2+(x
2-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101190936625268688/SYS201311011909366252686002_DA/2.png)
)
2+…+(x
n-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101190936625268688/SYS201311011909366252686002_DA/3.png)
)
2],
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101190936625268688/SYS201311011909366252686002_DA/4.png)
[(7-8)
2+(8-8)
2+(9-8)
2+(8-8)
2]
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101190936625268688/SYS201311011909366252686002_DA/5.png)
,故此選項錯誤;
B.眾數(shù)是出現(xiàn)次數(shù)最多的數(shù),即為8;故此選項正確;
C.中位數(shù)是將數(shù)據(jù)由小到大排列,為中間兩個數(shù)的平均數(shù),為
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101190936625268688/SYS201311011909366252686002_DA/6.png)
=8.
D.極差是最大值與最小值之間的差值,為9-7=2,故此選項錯誤;
故選:B.
點評:本題考查了平均數(shù)、方差、中位數(shù)、眾數(shù)和極差的定義.一組數(shù)據(jù)的中位數(shù)與這組數(shù)據(jù)的排序及數(shù)據(jù)個數(shù)有關(guān),因此求一組數(shù)據(jù)的中位數(shù)時,先將該組數(shù)據(jù)按從小到大(或按從大到�。┑捻樞蚺帕�,然后根據(jù)數(shù)據(jù)的個數(shù)確定中位數(shù):當數(shù)據(jù)個數(shù)為奇數(shù)時,則中間的一個數(shù)即為這組數(shù)據(jù)的中位數(shù);當數(shù)據(jù)個數(shù)為偶數(shù)時,則最中間的兩個數(shù)的算術(shù)平均數(shù)即為這組數(shù)據(jù)的中位數(shù).