3 3.1 * *2 2
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- さや とどろき
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1 Armitage * (i) (ii) *1 1
2 3 3.1 * *2 2
3 3.2 *3 (skewness) (kurtosis) (Q3) (median) (Q1) * 4* ( ) *6 ( ) *7 ( ) ( ) ( ) *3 *4 *5 SAS ver9.13 proc means *6 4 *7 3
4 6.02 ( ) * i j x ij ( i )= ( i )= j=1 11 j=1 (x ij 10) 3 (x ij 10) (a) (b) 10 (b) 2 10 (x ij 10) ( (x ij x) 3) 4 *8 4 4
5 ( (xij x) 4) (i) * ( 1) 3 10 = = 728 * 10 < (i) < = = (= 0) < < (ii) 2 4 * 11 * 12 * 13 * = 2, , 800 * = 6, 501 < (= ) * 16 < < < = < *9 ( 9) 3 = = ( 9) 3 * *11 *12 = * *14 < * = 81 < 100 * , 000 5
6 * 17 * *17 *
7
8 3 N N(0, 1) 10, N(0, 1 9 ) 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= * 21 0 * *20 *21 8
9 x z = x µ σ * 22 N(µ, σ 2 ) N(0, 1) N(0, 1) 0 0 N(0, 1) (x i x) 4 4 x * 23 * ( ) 9 4 = 6, = 10, 000 * N(0, 1) 11 N(0, 1 9 ) *22 z i = x i x bσ 1 * *24 *25 1 9
10 ( 10) (19 10) 3 = (1 10) 3 =
11 5 SAS R Excel SAS ver 9.13 proc means R ver quantile Excel 2003 quartile * 26 *26 ( ) R fivenum fivenum 11
12 5.1 5 SAS 6 R Excel R Excel SAS * SAS SAS SAS * 28 4 * 29 *27 4, 5, 6 7, 8, 9 (6+7)/2=6.5 *28 2 *29 12
13 (i) 4 3 * 30 4, 5, 6, }{{} 7, 8, 9, (ii) 4 2 * , 5, 6 7, 8, (i) 5 8 (iii) 4 * , 5, 6, 7 8, 9, 10, 11 = = 5.5, = = 9.5 (iv) 4 1 * , 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
14 5.2.2 R Excel R Excel SAS SAS R Excel 4, 5, 6, = * 34 = = 0.75, = = ) 0.75 : 0.25 (= 3 : 1) 2.25) 0.25 : 0.75 (= 1 : 3) = = 4.75, = = (i) a 1, a 2, a 3, 4n (4n + 1) (4n + 2) (4n + 3) a i (i = 1, 2, 3, ) (ii) *
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14 i ii iii iv v vi 14 13 86 13 12 28 14 16 14 15 31 (1) 13 12 28 20 (2) (3) 2 (4) (5) 14 14 50 48 3 11 11 22 14 15 10 14 20 21 20 (1) 14 (2) 14 4 (3) (4) (5) 12 12 (6) 14 15 5 6 7 8 9 10 7
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