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【新】高中数学第2章统计2.3总体特征数的估计2.3.2方差与标准差教学案苏教版必修3

23.2



P6971 1
2

[] 1 (1) (2)
x1x2...xn x s21nin 1 (xi x )2

s

1n
n

xi x

2

i1

2
[] 1 0,1,3,4,7 ________________ 7 6 2 1,2,3,4a 3________________ 2 2 3 1,2,3x 5 1,3,3xy 6 1,2,3xy ________ 5124 3x x14. y9.



1

s215(12223214292)5.8224.56. 24.56





[] 100 cm 6

(cm)

99 100 98 100 100 103

99 100 102 99 100 100.

(1)

(2)

[]

(1)

x

1 6(9910098100100103)100

x

1 6(9910010299100100)100.

s216[(99100)2(100100)2(98100)2(100100)2(100100)2(103

100)2]73.

s216[(99100)2(100100)2(102100)2(99100)2(100100)2(100

100)2]1.

(2) s2s2

(1) s21n[(x1 x )2(x2 x )2...(xn x )2] s21n[(x21x22...x2n)n x 2] s21n(x21x22...x2n) x 2 (2) ()



2





[] (g)



x x s2s2



x

122114113111111107



6

113

x

124110112115108109



6

113

s216[(122113)2(114113)2(113113)2(111113)2(111113)2(107 113)2]
21 s216[(124113)2(110113)2(112113)2(115113)2(108113)2(109 113)2] 2913 s2s2.




3


[] x1x2...xn s2 (1) x1bx2b...xnb (2)ax1, ax2...axn (3)ax1b, ax2b...axnb. [] x1x2...xn x x1bx2b... xnb x b ax1ax2...axn a x ax1bax2b...axnb a x b x1bx2b... xnb s21 ax1ax2...axn s22 ax1bax2b...axnb s23 (1) s211n[(x1b x b)2(x2b x b)2...(xnb x b)2] 1n[(x1 x )2(x2 x )2...(xn x )2]s2 (2)s221n[(ax1a x )2(ax2a x )2...(axna x )2] a21n[(x1 x )2(x2 x )2...(xn x )2]a2s2 (3)s231n[(ax1ba x b)2(ax2ba x b)2...(axnba x b)2] 1n[(ax1a x )2(ax2a x )2...(axna x )2] a21n[(x1 x )2(x2 x )2...(xn x )2] a2s2.

(1) x1x2...xn x1bx2b...xnb (2) x1x2...xn s2 ax1ax2...axn a2s2



4


(3) x1x2...xn s2 ax1bax2b...axnb a2s2.

[] 1 x1x2...x8 2 6 x11x21... x81 ________________ 1 6 2 x1x2...xn 2 4 2x13,2x23... 2xn3 ________________ 1 16



[] () 36 .



1

40

10

36

19

27

2

44

11

31

20

43

3

40

12

38

21

41

4

41

13

39

22

37

5

33

14

43

23

34

6

40

15

45

24

42

7

45

16

39

25

37

8

42

17

38

26

44

9

43

18

36

27

42

28 29 30 31 32 33 34 35 36

34 39 43 38 42 53 37 49 39

(1) 36 9 44
(2)(1) x s2.
(3)36 x s x s ( 0.01%)?
[] (1)36 9 4 44



5


2 4n2(n1,2...9) 44,40,36,43,36,37,44,43,37. (2) x 44409 ...3740 s219[(4440)2(4040)2...(3740)2]1900. (3) s21900s130 36 x s x s [37,43] 40,40,41...39 23 36 x s x s 3263100%63.89%.

(1)
(2)

[]

100





[75,85) [85,95) [95,105) [105,115) [115,125]





6

26

38

22

8

(1)



6



(2)( )
(3)" 95 80%"
(1)

(2)
x 800.06900.261000.381100.221200.08100.
s2(20)20.06(10)20.2600.381020.222020.08104. 100 104. (3) 95 0380.220.080.68. 0.8" 95 80%"

1 ________ 2 2 10,6,8,5,6 s2



7



________.

5



x

106856



5

7

s215[(107)2(67)2

(87)2(57)2(67)2]3.2.

3.2

3 5 ()

1 2 3 4 5



87

91

90

89

93



89

90

91

88

92

()________

90 s215[(8790)2(9190)2(9090)2(89

90)2(9390)2]4.



s2

15[(8990)2



(9090)2



(91

90)2

(88

90)2

(92



90)2]

2.s2s2 2

4.

________

84,84,84,86,87

85 s215[(8485)23(8685)2(8785)2]85.

8 5

5 10 (cm)

25 41 40 37 22 14 19 39 21 42

27 16 44 27 44 16 40 40 16 40

(1)

(2)

(1)

x

1

1

10(25414037221419392142)1030030(cm)

x

1

1

10(27164427441640401640)1031031(cm)

x x



8



(2)s2110[(2530)2(4130)2(4030)2(3730)2(2230)2(1430)2 (1930)2(3930)2(2130)2(4230)2]
110(2512110049642561218181144)1101 042104.2 s2110(2272316234022442)312 128.8 s2s2
1


x 8.5 8.8 8.8 8

s2

3.5 3.5 2.1 8.7

________ 2 50 30 20 86,94,88,92,90 88,93,93,88,93.________ 8 6 3 5 () xy,10,11,9. 10 2 x2y2 ________ 15(xy10119)1015[(x10)2(y10)2011]2 x2y2208. 208



9


4 10 370 33________ s2110(x21x22...x210) x 2 33110370 x 2 x 2. 2 5 10 5 ________
2 8 5 10 2,2,2,2,5,5,8,8,8,8. x 5s2110[(25)2(25)2(25)2(25)2(55)2 (55)2(85)2(85)2(85)2(85)2]11089356.s6 5 5.
6 5 5 6 ________.



x

1 5(9899105115118)107

x

1 5(95106108112114)107.

s215[(98107)2(99107)2(105107)2(115107)2(118107)2]66.8.

s215[(95107)2(106107)2(108107)2(112107)2(114107)2]44.





7 80 1.2

4.4________

1.28081.2.



10


81.2,4.4 8 ""( ) s1s2s3________

"" 2 200 2 250 2 150 s1s3>s2. s1s3 s2.
s1s3>s2 9 6 (m/s)
27 38 30 37 35 31 33 29 38 34 28 36 (1) (2)(m/s) (1).



11


33.5 33.
(2) x 33 x 33s 3.96s 3.56 33 33.5
10 2,3,3,7ab,12,13.7,18.3,20 10.5 ab 10 10.5ab21 10(a10)2(b10)2 (a10)2(b 10)2(a10)2(a11)22a242a221 a10.5 b10.5.
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