Armitage 1 2 11 10 3.32 *1 9 5 5.757 3.3667 7.5 1 9 6 5.757 7 7.5 7.5 9 7 7 9 7.5 10 9 8 7 9 9 10 9 9 9 10 9 11 9 10 10 10 9 11 9 11 11 10 9 11 9 12 13 11 10 11 9 13 13 11 10 12.5 9 14 14.243 13 12.5 12.5 20 15 14.243 16.6333 19 12.5 (i) (ii) *1 1
3 3.1 *2 1 2 3 4 5 6 *2 2
3.2 *3 (skewness) (kurtosis) (Q3) (median) (Q1) * 4*5 1 11 10.00 3.32 3.32 11.00 20.0 9.00 9.00 9.00 9.0 11 10.00 3.32 0.00 1.20 15.0 13.00 10.00 7.00 5.0 11 10.00 3.32 0.00 1.71 14.2 13.00 10.00 7.00 5.8 11 10.00 3.32 0.00 1.95 16.6 11.00 10.00 9.00 3.4 11 10.00 3.32 2.32 6.02 19.0 10.00 9.00 7.50 7.5 11 10.00 3.32 2.32 6.02 12.5 12.50 11.00 10.00 1.0 1 ( ) *6 ( ) 0 2 3 0 *7 ( ) ( ) ( ) 1.5 9 1 2.32 *3 *4 *5 SAS ver9.13 proc means *6 4 *7 3
6.02 ( ) 1.5 9 1 6.02 2.32 3.3 3.3.1 *8 4.2 10 3.32 i j x ij ( i )= 1 3.32 3 1 11 ( i )= 1 3.32 4 1 11 11 j=1 11 j=1 (x ij 10) 3 (x ij 10) 4 3 10 2 (a) (b) 10 (b) 2 10 (x ij 10) 1 5 4.243 6.6333 2.5 9 1 4 4.243 3 2.5 2.5 1 3 3 1 2.5 0 1 2 3 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 2 3 1 0 1 1 3 3 1 0 2.5 1 4 4.243 3 2.5 2.5 10 5 4.243 6.6333 9 2.5 3.32 3 3.32 4 11 3 2 3 ( (x ij x) 3) 4 *8 4 4
( (xij x) 4) 3.3.2 (i) 0 3 2 3 0 *9 3 10 3 + ( 1) 3 10 = 990 9 3 = 728 * 10 < (i) < = = (= 0) < < 3.3.3 (ii) 2 4 * 11 * 12 * 13 * 14 6.6333 7 7 4 = 2, 401 2 2 7 4 4, 800 * 15 9 9 4 = 6, 501 < (= ) * 16 < < < = < *9 ( 9) 3 = 728 2.5 3 = 15.625 2.5 3 ( 9) 3 *10 9 2.5 4 2.5 4 1 4 3 *11 *12 = *13 4 2 *14 < *15 3 4 = 81 < 100 *16 6.6333 7 6.7 4 2 4, 000 5
3.4 3.4.1 + * 17 * 18 3.4.2 7 *17 *18 0 1.95 6
4 4.1 8 9 7
3 N N(0, 1) 10,000 0.00 1.00 0.11 N(0, 1 9 ) 10.000 0.00 0.33-0.05 N(0, 1) N(0, 1 9 ) 4.2 f(x) µ σ ( ) = 1 σ 4 (x µ) 4 f(x)dx 3 ( ) = 1 σ 3 (x µ) 3 f(x)dx * 19 n n x 1,, x n x = 1 1 n x i, σ = n 1 (x i x) 2 * 20 i=1 ( ) = 1 σ 4 1 n ( ) = 1 σ 3 1 n n (x i x) 4 3 i=1 n (x i x) 3 i=1 i=1 4.3 0 * 21 0 *19 3 0 3 3 *20 *21 8
x z = x µ σ * 22 N(µ, σ 2 ) N(0, 1) N(0, 1) 0 0 N(0, 1) 4.4 4.4.1 (x i x) 4 4 x * 23 * 24 11.00 9 20 19 6.02 4 19 20 ( 10 9 10 ) 9 4 = 6, 561 10 4 = 10, 000 * 25 10 N(0, 1) 11 N(0, 1 9 ) *22 z i = x i x bσ 1 *23 2 4 16 5 4 625 *24 *25 1 9
4.4.2 4 10 4 ( 10) 4 19 10 (19 10) 3 = 287 1 (1 10) 3 = 287 10
5 SAS R Excel 4 4 4 5 4 5 6 4 5 6 7 4 5 6 7 8 4 5 6 7 8 9 4 5 6 7 8 9 10 4 5 6 7 8 9 10 11 SAS ver 9.13 proc means R ver 2.12.1 quantile Excel 2003 quartile * 26 *26 (2011 3 ) R fivenum fivenum 11
5.1 5 SAS 6 R 4 4 4 4 4.5 5 4 5 6 4.5 5.5 6.5 5 6 7 5 6.5 8 5 7 9 5.5 7.5 9.5 4 4 4 4.25 4.5 4.75 4.5 5 5.5 4.75 5.5 6.25 5 6 7 5.25 6.5 7.75 5.5 7 8.5 5.75 7.5 9.25 7 Excel 4 4 4 4.25 4.5 4.75 4.5 5 5.5 4.75 5.5 6.25 5 6 7 5.25 6.5 7.75 5.5 7 8.5 5.75 7.5 9.25 R Excel SAS 5.2 2 2 * 27 5.2.1 SAS SAS SAS * 28 4 * 29 *27 4, 5, 6 7, 8, 9 (6+7)/2=6.5 *28 2 *29 12
(i) 4 3 * 30 4, 5, 6, }{{} 7, 8, 9, 10 7 5 9 (ii) 4 2 * 31 4 2 4, 5, 6 7, 8, 9 6.5 (i) 5 8 (iii) 4 * 32 4 4, 5, 6, 7 8, 9, 10, 11 = 5 + 6 2 = 5.5, = 9 + 10 2 = 9.5 (iv) 4 1 * 33 4 1 4, 5, }{{} 6, 7, 8 4, 5, 6 } {{ } 6, 7, 8 } {{ } 5 7 *30 (4n + 3) 1 (2n + 1) *31 (4n + 2) (i) (2n + 1) *32 (4n) 2 2n *33 (4n + 1) (2n) 13
5.2.2 R Excel R Excel SAS SAS R Excel 4, 5, 6, 7 4 1 = 3 4 6 2 2 * 34 = 3 0.25 = 0.75, = 3 0.75 = 2.25 0.75) 0.75 : 0.25 (= 3 : 1) 2.25) 0.25 : 0.75 (= 1 : 3) = 4 1 + 5 3 1 + 3 = 4.75, = 6 3 + 7 1 3 + 1 = 6.25 5.3 (i) a 1, a 2, a 3, 4n (4n + 1) (4n + 2) (4n + 3) a i (i = 1, 2, 3, ) (ii) *34 6 4 3 1 14