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2 例 題 で 学 ぶ Excel 統 計 入 門 第 2 版 サンプルページ この 本 の 定 価 判 型 などは, 以 下 の URL からご 覧 いただけます. このサンプルページの 内 容 は, 第 2 版 発 行 当 時 のものです.
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5 ii Excel Excel ( ) Excel Excel 1 2 Excel Excel Excel Excel Excel Excel,
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8 v χ 2 t F A 126 A A A A A A A A A.9 n χ A.10 n t A.11 (m, n) F B 133 C Excel
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10 1 Excel Excel Excel (autofill, ) $ $ Excel Excel C average(x) =average( x ) Enter Excel Excel 3 chap1.xlsx 1 1 x y Web F1
11 , 4, 1, 3, 2, 9, 1, 1, 7, 1 =average(a3:a12) =median(a3:a12) =mode(a3:a12) =average( ) Enter n x 1,x 2,,x n (mean, average, ) x x = x 1 + x x n = 1 n x i n n i=1 average A3 A12 B18 =average(a3:a12) Enter =
12 1.1 3 Excel : (median) 1, 1, 1, 1, 1, 2, 3, 4, 7, 9 (1 + 2)/2 =1.5 median (mode) mode (A2:A13) ( ) average(a3:a12) A3 A12 median(a3:a12) A3 A12 mode(a3:a12) A3 A ( ) (outlier) ( 4, 3, 2, 1, 0, 1, 2, 3, 4) ( sum ) C , 2, 5, 3, 4, 5, 100, 2, 4, 4
13 , 1, 4, 1, 5, 9, 2, 6, 5, 3 =sum(e$3:e3) 1 Ctrl (sort) Ctrl 1, 1, 2, 3, 3, 4, 5, 5, 6, 9 1, 1+1= 2, 2+2 = 4, 4+3 = 7, 7+3 = 10,
14 1.2 5 ( cummulative sum ) 1, 2, 4, 7, 10, 14, 19, 24, 30, 39 sum G3 =sum($e$3:e3) ( ) (autofill) G4,G5,G6, =sum($e$3:e4), =sum($e$3:e5), =sum($e$3:e6) =sum($e$3:e3) $ $E$3 $ E3 E4, E5, sum $E$3 E3 ($ 2 ) [ 1] 2 [ 2] (E2:E12) (G2:G12) & sum(n:m) n m ( ) ( ) ( ) 2. 1 ( 1 )
15 x y (time series data) x y y y (moving average method) x 1,x 2,x 3,,x n x 1 + x 2 + x 3 3, x 2 + x 3 + x 4 3, x 3 + x 4 + x 5,, x n 2 + x n 1 + x n 3 3 3
16 OK 3 3 n x 1,x 2,,x n x 1 x 2 x n n n x 1 n x 2 n x n (geometric mean) 3 1 x 9 x/1 =9/x x 2 =1 9, x = 1 9=3 geomean(1,9) 3 n x 1,x 2,,x n x 1 1,,x 1 n (1/x /x n )/n (harmonic mean) 6km 4km 5km 4.8 km harmean(6,4) 4.8 (trimmed mean ) 5 3 ( C trimmean ) y f f(y) ={f(x 1 )+f(x 2 )+f(x 3 )+ + f(x n )}/n f f(x) =x, f(x) = log x, f(x) =1/x, f(x) =x 2 y ( )
17 ( (5 ) ( D C D2 =-c2 (2011)
18 1.4 9 (statistics) (state)
19 D4 =c4/$c$11 D4 D11 OK C11 =sum(c4:c10) SUM C 11 $ $C$11 C$11 11 $ /
20 C10 =$b10*c$9 * a b a b a/b a b ( ) B $ A4 A 4 $ A4, A$4, $A4, $A$4 4 $ F4 $ A4, A$4, $A4, $A$4
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22 8 ( ) t χ 2 F , 4 40 a 40 ( ) X b 40 X E( X) V ( X) c 40 X 900 (E3:AH32(30 30) ) ( ) (population) ( ).
23 (B38:AO41 ) ( ) ( ) N n X 1,X 2,,X n N C n X 1,X 2,,X n 1/ N C n X 1,X 2,,X n ( )
24 X 1,X 2,,X n ( ) x 1,x 2,,x n (900 ) ( ) ( ) 30 ( ) 30 ( 4 40 ) 4 ( ) X 1,X 2,X 3,X 4 ( ) randbetween (i, j) index (=average(b38:b41) =average(ao38:ao41)) 4.34 ( =average(b42:ao42)) 4.37 ( =average(e3:ah32)) 1.69 ( =varp(b42:ao42)) 8.31 ( =varp (e3:ah32)) =countif($b$42:ao42,a62)-countif($b$42:ao42,a63) 8.2 randbetween(0,9) index(,i, j) i j (i, j) ( )
25 , 20, =countif($d$69:$bk$69,a75) countif ($d$69:$bk$69,a76)
26 n =10, 20, 30 X = X 1 + X X X = X 1 + X X X X = X 1 + X X X X X m m m E( X) =m m, σ 2 n n σ 2 /n 0 X m (law of large numbers) n X N(m,σ 2 /n) ( 6.8 ) E( X) =m X X m (unbiased estimator) m σ 2 n X N(m, σ 2 /n) n =10 20 n =20 E( X) n =10,n=20,n= , 4.33, 4.3 V ( X) 0.98, 0.31, 0.27 n V ( X) σ 2 /n V ( X)
27 s 2 u S 2 S 2 = (X 1 X) 2 +(X 2 X) 2 +(X 3 X) 2 +(X 4 X) 2 = 1 4 (X i 4 n X) 2 i= S 2
28 (2, 4) x =(2+4)/2 =3 s 2 = ((2 3) 2 +(4 3) 2 )/2 =1 m x m x (2 < 3) ((2 2) 2 +(4 2) 2 )/2 =2 1 (3 < 4) ((2 4) 2 +(4 4) 2 )/2 =2 1 (2.4 ) E(S 2 ) σ 2 4/3 4/3=1.33 ( n/(n 1) ) S U 2 = (X 1 X) 2 +(X 2 X) 2 +(X 3 X) 2 +(X 4 X) 2 3 U 2 E(U 2 )=σ 2 n n n 1 S 2 = U 2 m σ 2 n E( X) =m ( X m ) E(U 2 )=σ 2 (U 2 σ 2 ) (7,2,4,8) s 2 u 2 u 2 /s 2 2. X m 2 So = 1 n m (X i m) 2 i=1
29 [α, β] n X N(m,σ 2 /n) Z =( X m)/(σ/ n)
30 N(0,1) ( σ 2 ) Z 1.96 Z ( X m)/(σ/ n) 1.96 m X 1.96σ/ n m X +1.96σ/ n [ X 1.96 σ ] σ, X n n m 0.95 ( ) 95 % (confidence interval) (interval estimation) (58.8, 64.1, 63.7, 41.3) x = 57, σ =10 95 % [ x σ, x σ ] [ = ] 10, =[47.2, 66.8] % 90 %, 99 % 99 % [ ] X 2.58σ/ n, X +2.58σ/ n 90 % σ/ n σ 2 m σ 2 σ 2 S 2 U 2 95 % [ X 1.96 S ] S, X n n
31 106 8 σ U T = ( X m)/(u/ n)=( X m)/(s/ n 1) t n =4 n 1=3 t 95 % [ X 3.18 U ] U, X (D AQ) 4 ( ) 4.37 t D43 =average(d38:d41) D57 D58 =d *$d$46/2 =d *$d$46/2 95 % N(0,1) 5% t 5% 1% , % % 9 t 1% 3.25 ( n = 1)
32 2012 Printed in Japan ISBN
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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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2 Excel =sum( ) =average( ) B15:D20 : $E$26 E26 $ =A26*$E$26 $ $E26 E$26 E$26 $G34 $ E26 F4
1234567 0.1234567 = 2 3 =2+3 =2-3 =2*3 =2/3 =2^3 1:^, 2:*/, 3:+- () =2+3*4 =(2+3)*4 =3*2^2 =(3*2)^2 =(3+6)^0.5 A12 =A12+B12 ( ) ( )0.4 ( 100)0.9 % 1 2 Excel =sum( ) =average( ) B15:D20 : $E$26 E26 $ =A26*$E$26
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Excel ではじめる数値解析 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
Excel ではじめる数値解析 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009631 このサンプルページの内容は, 初版 1 刷発行時のものです. Excel URL http://www.morikita.co.jp/books/mid/009631 i Microsoft Windows
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医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987
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微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
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