(descrptve statstcs) 2010 9 3 1 1 2 2 3 2 3.1............................................. 3 3.2............................................. 3 4 4 4.1........................................ 5 5 6 6 -pvot table 7 7 10 8 13 9 15 10 18 11 22 12 25 13 26................................................................................ 1 1
statstcs statstcum (EBM) 2 () : ( )GDP () : () : POS STEP 1: STEP 2: STEP 3: STEP 4: 3 2
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IQ Stanley Smth Stevens 1946 On the theory of scales of measurement 4 Wkpeda, Excel help 4 Frequency Dstrbuton Hstogram QC Wndows MacOS LnuX (McroSoft) OpenOffce.org () 4
4.1 sun open-offce calc 2 1 2 3 3 1 3 1 2 3 1 2 3 5
5 5.1 [] Mcrosoft Offce Excel ( : Offce ) Mcrosoft Offce Excel Excel (Mcrosoft Offce ) [Excel ] [ ] [] [Excel ] CALC No. (cm) (kg) (cm) 1 139.4 36.4 76.1 2 139.9 32.1 73.7 3 145.5 36.4 78.5 4 153.9 47.5 83.6 5 142.0 33.5 75.6 6 156.1 59.4 88.6 7 151.5 35.1 81.1 8 146.7 48.8 78.5 9 141.6 35.3 75.9 10 134.0 27.5 72.8 11 144.7 34.4 77.5 12 145.3 36.7 78.0 13 152.8 69.9 81.0 14 155.6 51.2 84.5 15 146.3 40.9 75.0 16 142.7 35.5 79.6 17 159.5 49.3 81.4 18 144.5 38.1 80.4 19 149.5 40.6 78.3 20 138.7 46.2 77.0 146.51 1.49 145.4 #N/A 6.70 44.84-0.560 0.246 25.5 134 159.5 2930.2 20 6
(cm) 3 10 7 BMI ( ) (m) 2 BMI (body mass ndex) 18.5 18.5 25 25 30 30 100 BMI BMI 3: 5.1 #N/A (Non Avalable) 6 -pvot table A1:A10 7
A 1 2 150 3 200 4 250 5 320 6 330 7 360 8 380 9 420 10 480 (1) (4) (1) 200? (2) 200 300? (3) 300 400? (4) 400 500?? (1) A1:A10 (2) []-[] (3) [Excel ] [] [ ] (4) [] $A$1:$A$10 [] [ ] (5) [ ] [] (6) [] (7) [], [OK] (8) [] D1 (9) [] (10) D2 -[] (11) [ ] 200, [ ] 500 [] 100 (12) [OK], 6.1 100 5 1 5 : 8
4 (tally mark) 1 12 2 26 3 15 4 7 5 5 2 (Hstogram) x skewness L L L L kurtoss, excess ; leptokurtc ; platykurtc Hstogram 9
2 4 10 100 2 7 : Q 1, Q 2, Q 3 Q 1, Q 3 360 10
(1) (max) (mn) range (2) (class) 10 20 Starjes k = 1 + log 2 n = 1 + 3.3 log 1 0n (3) (class wdth) R/k (4) A B C D E F G 1 () () 2 a 0 a 1 x 1 f 1 F 1 = f 1 p 1 = f 1/n P 1 = p 1 3 a 1 a 2 x 2 f 2 F 2 = f 1 + f 2 p 2 = f 2/n P 2 = p 1 + p 2 4 a 2 a 3 x 3 f 3 F 3 = f 1 + f 2 + f 3 p 3 = f 3/n P 3 = p 1 + p 2 + p 3 5 6 a k 1 a k x k f k F k = n p k = f k /n P k = 1 7 n 1 x = (a 1 + a )/2,( = 1, 2,, k) F k = f 1 + f 2 + + f k = n, P k = p 1 + p 2 + + p k = 1 =max() =mn() D2 D6 =frequency, ( A2 A6) CTRL+SHIFT+ENTER E2 =D2 E3 =D2+D3E3 E4 E6 F2 =D2/D$7 frequency (1) 2 (2) 1 (3) (4) 11
5 (Boxchart) 6 7 12
8 (average,mean) (SD,standard devaton),medan ( (varance) (kurtoss, excess)(bulge ) (skewness) (range) (mn) (max) (sum) (sze) (1) Excel -VBA (2)OK (3) OK n {X, = 1,, n}, sort (Order Statstcs) {X (), = 1,, n} X 1, X 2,, X n X (1) X (2) X (n) X 1 + X 2 + + X n = X (1) + X (2) + + X (n) X k x 1, x 2,, x k (k ) () x 1 x 2 x k f 1 f 2 f k n p 1 p 2 p k 1 2 f = 1, = 1, 2,, n X = X 1 + X 2 + + X n = x 1 f 1 + x 2 f 2 + + x k f k = j x f j, f = f 1 + f 2 + + f k = n X2 = X2 1 + X 2 2 + + X 2 n = x 2 1 f 1 + x 2 2 f 2 + + x 2 k f k = j x2 j f j, 1 n 1 n X = 1 n (X 1 + X 2 + + X n ) = x 1 p 1 + x 2 p 2 + + x k p k = j x j p j, X2 = 1 n (X2 1 + X 2 2 + + X 2 n) = x 2 1 p 1 + x 2 2 p 2 + + x 2 k p k = j x j p 2 j, X = 1 n n =1 X = 1 n k j=1 x jf j = k j=1 x jp j AVERAGE 13
SE SE = s = (X X) 2 = X2 nx2 j = x2 j f j nx 2 j = x2 j p j X 2 n n(n 1) n(n 1) n(n 1) n 1 Me Me = X ((n/2)+1) () = X ((n+1)/2) () = medan() 2 = quartle(, 2) Mo ( ) MODE 2 #N/A (Not Avalable) max f MODE # N/A (Not Avalable) SD SD = s = (X X) 2 STDEV VAR (n 1) s 2 s 2 = 1 n 1 VAR n (X X) 2 = ( 1 n ) (X X j ) 2 = n n 1 2 <j =1 VARP (n 1) n v 2 = 1 n n (X X) 2 = 1 n =1 k x 2 jf j X 2 = j=1 k x 2 jp j X 2 j=1 k x 2 jp j X 2 KW KURT 1 ( ) 4 X X 3 n s 3 SK SKEW 1 ( ) 3 X X n s L L L R L R = max() mn() () MAX x 1, x 2,, x n max x MIN x 1, x 2,, x n mn x SUM x 1, x 2,, x n x n, N COUNTA 95.0% 95% 1/2 95% j=1 14
TM(trmmed mean) TRIMMEAN TRIMMEAN(, ) (1) (2) 20 0.2 20 0.2 = 4 2 2 4 MD (Mean Devaton) = 1 n X X Z () Z = X X s x ( 0 1 50 10( 100) 10Z + 50 X 100 15 Q 1, Q 2, Q 3 25% 4 25% Q 1 2 50% 3 75% 3 =QUARTILE(, ) (, QUARTILE ) = (0, ), (1, 1 (25%)) (2, 2 = (50%)) (3, 3 (75%)) (4, ) Q 3 Q 1 (dectle) (percentle) ( 4 CV(Coeffcent of Varaton)= s x X ( ) 10% 10% 0.9 1.1 68.3% 0.31100 68.3 0.31 ± 0.031 X N(µ, σ 2 ) µ X 0.6826 68.3% ±2 σ 0.9544 9 1 2 15
(sample covarance): =COVAR( A, B) Cov(x, y) = 1 n 1 = COV AR(x, y ) (X X)(Y Y ) n n 1 2 X, Y 0 1 N 1 +1 2 COVAR N=2 2 COVAR VARP 2 () () (0 ) (sample correlaton coeffcent): =CORREL( A, B) = correl(x, y ) x s x, y s y ρ = Cov(x, y) s x s y ( x = Cov, y ) s x s y X X, Y Y, = 1, 2,, n s x s y N CORREL PEARSON 2 N 3 16
8 CORREL ( PEARSON) 2 2 2 1 +1 2 ( ) ( ) (0 ) 1 0.7 0.7 0.4 0.4 0.2 0.2 0 0 0.2 0.2 0.4 0.4 0.7 0.7 1 (Speaman s rank correlaton coeffcent) r s = 1 6 (x y ) 2 n(n 2 = 1 1) (x y ) 2 / ( ) n 1 3 x, y 1, 2,, n =[COUNT() + 1 - RANK(,, 0) - RANK(,, 1)]/2 RANK(,, ) 0...3 2 1 0 1 2 3... 2 2 17
2 0 : 2 9: 11 10 10 Corrado Gn 0 1 0 18
12 1 Wkpeda (Gn coeffcent) 100 Gn Index http://www.sustanablemddleclass.com/gn-coeffcent.html Japan 24.9 Unted Kngdom 36.0 Sweden 25.0 Iran 43.0 Germany 28.3 Unted States 46.6 France 32.7 Argentna 52.2 Pakstan 33.0 Mexco 54.6 Canada 33.1 South Afrca 57.8 Swtzerland 33.1 Namba 70.7 ( 0.24 0.36 0.4 0.56 0.66 Bob Sutclffe (2007), Postscrpt to the artcle World nequalty and globalzaton (Oxford Revew of Economc Polcy, Sprng 2004), http://steresources.worldbank.org/intdecineq/resources/psbsutclffe.pdf. Retreved on 2007-12-13 G = 1 2 1 0 L(x)dx = 1/2 1 0 L(x)dx 1/2 or = 1 2 L(x )(.e.l(x) ) L(x) 19
y G L (1, 1) y = x 45 1 0 L(x)dx (0.8, 0.6) y = L(x) (0.4, 0.2) 0 1 x (0, 0) F (1) = 1, 2,, n x x 1 x 2 x n p = f(x ) p 1 p 2 p n F F 1 = p 1 F 2 = p 2 + F 1 F n = p n + F n 1 = 1 L = j=1 x jf(x j ) / L = L = n j=1 x jf(x j ) L +1 + L (F +1 F ) 2 ( = 1, 2,, n) L 0 = 0 L 1 L 2 L n 1 L n = 1 0 1 (2) < x < x f(x) F (x) = x f(t)dt L(x) = x / tf(t)dt L (0 x 1) L = tf(t)dt () L(0) = 0 L(x) L(y) L(1) = 1, 0 < x < y < 1 () 0 < L(x) x, 0 < x < 1 x = (x, = 1, 2,, n) F = (/n, = 1, 2,, n) s xy G CV(x) R XF G = CV (x) R XF n X = {x 1, x 2,, x n } x = 1 n x ( ) x x j,, j = 1, 2,, n ()D D = 1 n 2 x x j = 2 n 2 x x j,j <j 20
,j n2 {(, j);, j = 1, 2,, n} <j n(n 1)/2 { < j;, j = 1, 2,, n} G G = D 2x {x 1, x 2,, x n } (order statstcs) x (1) x (2) x (n) n ( ) <j x x j = x 1 x 2 + x 1 x 3 + + x 1 x n + x 2 x 3 + + x 2 x n + + + x n 1 x n = ( ) x (2) x (1) + ( ) x (3) x (1) + + ( ) x (n) x (1) + ( ) x (3) x (2) + + ( ) x (n) x (2) + + + ( ) x (n) x (n 1) <j x x j = (n 1)x (n) + ((n 2) 1) x (n 1) + + (1 (n 2)) x (2) + (0 (n 1)) x (1) = x () (n + 1)x () = 2 x () n(n + 1)x = 2 ( x () x ) x = x () = nx, = n(n + 1)/2 x = (x (1), x (2),, x (n) ) F = (F ) = F = 1 n s 2 F = s F F = ( 1 n 2) (F F j ) 2 <j 2 s XF = = = n = n + 1 2n 1 n 1 (x () x)(f F ) ( 1 n 1 (x () x) n n + 1 ) ( ) 2n 1 n 1 (x () x) n X F ρ ρ = s XF s X s F = 1 n 1 D = 4 n 2 ( x () x ), (x () x) nd 4 = 21 ( 1 n, 2 n,, n ) n = 1 n 1 (F F ) 2 = n + 1 12n ( ) ( / ) n + 1 s X n 12n ( ) (x () x) = S xy n
G = D 2X D 2x = 2 (n 1)x n D = ( 1 n ) 4 x () x (j) = ( x () x ) n(n 1) 2 <j ( ) (x () x) = 2 n x s XF = 2 x ρs Xs F = 2 n + 1 n + 1 x ρs X 12n = ρcv (X) 3n G = n + 1 3n,j x x j /n 2 2x 0.577 G = 1 n 2 x x x j 0.577ρCV <j 11 R-2 1 / LINEST X Y (1 Y a X + b Y = a X b Y = a e X Y = a logx R2 OK 9 R2 0.5 0.8 0.8 R2 2 (1) (2) (3) R-2 R Y 2 (X 1, X 2,, X n ) b 22
13 Y a 1 X 1 + a 2 X 2 + + a n X n + b A (Y ) B (X 1 ) C (X 2 ) b Y a 1 X 1 + a 2 X 2 + b a 1, a 2, b 10 A B C 1 Y X1 X2 2 10 18 10 3 12 17 11 4 3 3 2 5 14 26 15 6 4 7 5 7 10 18 9 8 6 10 6 9 11 15 13 10 8 15 7 11 11 14 14 R 0.98 R2 0.96 R2 0.95 0.78 10.00 F 2.00 110.61 55.31 90.29 0.00 7.00 4.29 0.61 9.00 114.90 23
t P - 95% 95% 95.0% 95.0% 0.82 0.65 1.26 0.25 0.72 2.36 0.72 2.36 X 1 0.25 0.07 3.53 0.01 0.08 0.42 0.08 0.42 X 2 0.49 0.11 4.47 0.00 0.23 0.74 0.23 0.74 Y = 0.25 X 1 + 0.49 X 2 + 0.82 2 Y 2 X P P 0.05 X 0 t p 0 0 0 Y X (1) P (T t) < (2) t < t t tnv t = tnv 5%(0.05) 1%(0.01) n k 1 n k tnv 2 5% 0.1 2 t P NG 3 24
14 0.7 R2 0.5 R2 R2 R2 R2 AIC 12 http://www.stat.go.jp/data/ndex.htm 25
http://www.pref.chba.jp/outlne/statstcs/ndex-j.html 13 / = 2+3 A2:B10 A2;B10 A2 B10 = (,,, ) 26
1 (true) false 1 2 =rand(): 1 27
=f =and( 2) =or( 2) =sum( 2) =sumf( ) =count( ) =countf( ), 1 2 {=f(and( 2),, )} {=f(or( 2) )} 2 Ctrl, Shft, Home actve( shft+ ctrl+ arrow key ), nonactve () [] [ ] [ ] /VBA VBA Vsual Basc 3 28
, abs() round() nt() sum( 1 2) average( 1 2 ) count( 1 2) counta( 1 2 ) max( 1 2) mn( 1 2) mode( 1 2) medan( 1 2 ) rank() quartle var( ) varp( ) stdev( ) stdevp( ) normdst( ) normnv( ) frequency(, ) = (), 1 2 1 2 1 2 50% 2 ( 1 2 3 ) 25% 50%75% /(n-1) /n populaton varance var standard devaton varp standard devaton of populaton,true true false x nverse (0) 4 29