eigen reeks de centrummaten

*Unverified author*

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Sun, 26 Apr 2009 11:26:36 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Apr/26/t12407669636ilhlx4rxvjz7he.htm/, Retrieved Sun, 26 Apr 2009 19:29:25 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Apr/26/t12407669636ilhlx4rxvjz7he.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

310,95 312,97 315,07 315,43 315,73 315,77 315,77 315,77 313,99 314,57 314,63 314,65 314,65 314,93 315,27 316,26 316,98 317,01 317,07 317,07 317 317,08 317,04 317 317,05 321,59 325,59 326,23 326,28 326,35 326,35 326,35 326,39 326,74 326,9 326,9 326,91 336,93 348,5 349,43 349,26 349,26 349,28 349,61 349,66 349,68 349,91 349,91 350,89 355,52 356,36 357,04 360,28 360,63 360,79 360,97 361 361,01 361 361 361,58 363,19 363,61 364,14 365,51 365,51 365,5 365,5 364,59 364,63 364,54 363,67 365,22 369,05 370,45 370,46 370,46 370,58 370,58 370,22 370,21 370,29 370,29 370,2 370,2 372,55 374,51 375,58 375,75 375,75 375,75 375,69 375,76 377,5 377,51 377,74

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 346.400833333333 2.37751917026357 145.698439644940 Geometric Mean 345.61568646908 Harmonic Mean 344.822461172242 Quadratic Mean 347.175076996463 Winsorized Mean ( 1 / 32 ) 346.419479166667 2.37397602288487 145.923748103275 Winsorized Mean ( 2 / 32 ) 346.440520833333 2.37084058382232 146.125607599814 Winsorized Mean ( 3 / 32 ) 346.404270833333 2.36094058691227 146.722993688873 Winsorized Mean ( 4 / 32 ) 346.406354166667 2.36053151593338 146.749302785603 Winsorized Mean ( 5 / 32 ) 346.407395833333 2.36038395091119 146.758918480024 Winsorized Mean ( 6 / 32 ) 346.407395833333 2.36038395091119 146.758918480024 Winsorized Mean ( 7 / 32 ) 346.4234375 2.35693018744967 146.980780060715 Winsorized Mean ( 8 / 32 ) 346.4259375 2.35409525855739 147.158844248424 Winsorized Mean ( 9 / 32 ) 346.344375 2.33857171140783 148.100814403292 Winsorized Mean ( 10 / 32 ) 346.156875 2.31102182397488 149.785203847458 Winsorized Mean ( 11 / 32 ) 345.965520833333 2.2798166856025 151.751464500710 Winsorized Mean ( 12 / 32 ) 345.970520833333 2.27911896917500 151.80011465508 Winsorized Mean ( 13 / 32 ) 345.954270833333 2.27727512391836 151.915887193319 Winsorized Mean ( 14 / 32 ) 345.954270833333 2.27727512391836 151.915887193319 Winsorized Mean ( 15 / 32 ) 346.029270833333 2.26646408688129 152.673617392049 Winsorized Mean ( 16 / 32 ) 346.122604166667 2.24695475815442 154.040753562373 Winsorized Mean ( 17 / 32 ) 346.126145833333 2.24647131860223 154.075479605364 Winsorized Mean ( 18 / 32 ) 346.113020833333 2.2449865007594 154.171537653458 Winsorized Mean ( 19 / 32 ) 346.113020833333 2.24449266099459 154.205458920931 Winsorized Mean ( 20 / 32 ) 346.1171875 2.24340435178210 154.282123606052 Winsorized Mean ( 21 / 32 ) 346.119375 2.24310592359894 154.303624879502 Winsorized Mean ( 22 / 32 ) 345.860416666667 2.21305204192712 156.282098258066 Winsorized Mean ( 23 / 32 ) 345.012291666667 2.12310510705329 162.503632307455 Winsorized Mean ( 24 / 32 ) 345.014791666667 2.12275878187663 162.531322264349 Winsorized Mean ( 25 / 32 ) 346.186666666667 1.9635606457038 176.305563784908 Winsorized Mean ( 26 / 32 ) 347.27 1.82424067356468 190.364136175855 Winsorized Mean ( 27 / 32 ) 347.37125 1.79354722553361 193.678340360763 Winsorized Mean ( 28 / 32 ) 347.21375 1.77383021281731 195.742381368357 Winsorized Mean ( 29 / 32 ) 347.2228125 1.76995587158246 196.175971432304 Winsorized Mean ( 30 / 32 ) 347.2071875 1.76834288261839 196.346076834312 Winsorized Mean ( 31 / 32 ) 347.078020833333 1.75507028411640 197.757334264293 Winsorized Mean ( 32 / 32 ) 346.9346875 1.73745306609036 199.680034109167 Trimmed Mean ( 1 / 32 ) 346.444574468085 2.37505441985067 145.868057410604 Trimmed Mean ( 2 / 32 ) 346.470760869565 2.37509103219658 145.876834265647 Trimmed Mean ( 3 / 32 ) 346.486888888889 2.37572764932797 145.844532721123 Trimmed Mean ( 4 / 32 ) 346.516931818182 2.3790878989387 145.651168236685 Trimmed Mean ( 5 / 32 ) 346.547790697674 2.38158642135547 145.511322868745 Trimmed Mean ( 6 / 32 ) 346.579880952381 2.38299514244993 145.438769378298 Trimmed Mean ( 7 / 32 ) 346.613536585366 2.38310424210206 145.446233723972 Trimmed Mean ( 8 / 32 ) 346.646125 2.38241779975449 145.501819637060 Trimmed Mean ( 9 / 32 ) 346.68 2.38059748570488 145.627306624392 Trimmed Mean ( 10 / 32 ) 346.727105263158 2.37959911717263 145.708200495186 Trimmed Mean ( 11 / 32 ) 346.801081081081 2.38118117538076 145.642458737154 Trimmed Mean ( 12 / 32 ) 346.902361111111 2.38580672482293 145.402541413684 Trimmed Mean ( 13 / 32 ) 347.008857142857 2.38903778843484 145.250468126834 Trimmed Mean ( 14 / 32 ) 347.123382352941 2.39074333926415 145.194750374075 Trimmed Mean ( 15 / 32 ) 347.244848484848 2.39034149419163 145.269974741530 Trimmed Mean ( 16 / 32 ) 347.36640625 2.38902638989743 145.400824251637 Trimmed Mean ( 17 / 32 ) 347.486774193548 2.38776094173393 145.528293105093 Trimmed Mean ( 18 / 32 ) 347.614833333333 2.38357663992565 145.837489556944 Trimmed Mean ( 19 / 32 ) 347.752931034483 2.37595597353577 146.363373272854 Trimmed Mean ( 20 / 32 ) 347.900892857143 2.36397802356434 147.167566444881 Trimmed Mean ( 21 / 32 ) 348.059444444444 2.34671553957152 148.317697043075 Trimmed Mean ( 22 / 32 ) 348.23 2.32274662530581 149.921647159493 Trimmed Mean ( 23 / 32 ) 348.4368 2.29474879582022 151.840933802716 Trimmed Mean ( 24 / 32 ) 348.734583333333 2.26968924510731 153.648603695457 Trimmed Mean ( 25 / 32 ) 349.058043478261 2.23428702586925 156.227932864830 Trimmed Mean ( 26 / 32 ) 349.308636363636 2.21778384400803 157.503463336787 Trimmed Mean ( 27 / 32 ) 349.487857142857 2.21910225373018 157.490650354389 Trimmed Mean ( 28 / 32 ) 349.676 2.22024458112164 157.494360294012 Trimmed Mean ( 29 / 32 ) 349.898157894737 2.21804441615652 157.750744460315 Trimmed Mean ( 30 / 32 ) 350.144166666667 2.20831456865343 158.557196350960 Trimmed Mean ( 31 / 32 ) 350.420588235294 2.18742614608922 160.197677467553 Trimmed Mean ( 32 / 32 ) 350.7440625 2.15283453712282 162.921978652737 Median 350.4 Midrange 344.345 Midmean - Weighted Average at Xnp 347.821764705882 Midmean - Weighted Average at X(n+1)p 349.07693877551 Midmean - Empirical Distribution Function 347.821764705882 Midmean - Empirical Distribution Function - Averaging 349.07693877551 Midmean - Empirical Distribution Function - Interpolation 349.07693877551 Midmean - Closest Observation 347.821764705882 Midmean - True Basic - Statistics Graphics Toolkit 349.07693877551 Midmean - MS Excel (old versions) 347.821764705882 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/26/t12407669636ilhlx4rxvjz7he/136ky1240766794.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/26/t12407669636ilhlx4rxvjz7he/136ky1240766794.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/26/t12407669636ilhlx4rxvjz7he/266ol1240766794.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/26/t12407669636ilhlx4rxvjz7he/266ol1240766794.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

geomean <- function(x) { return(exp(mean(log(x)))) } harmean <- function(x) { return(1/mean(1/x)) } quamean <- function(x) { return(sqrt(mean(x*x))) } winmean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) win <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn } return(win) } trimean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) tri <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { tri[j,1] <- mean(x,trim=j/n) tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2) } return(tri) } midrange <- function(x) { return((max(x)+min(x))/2) } q1 <- function(data,n,p,i,f) { np <- n*p; i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q2 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q3 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- data[i+1] } } q4 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- (data[i]+data[i+1])/2 } else { qvalue <- data[i+1] } } q5 <- function(data,n,p,i,f) { np <- (n-1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i+1] } else { qvalue <- data[i+1] + f*(data[i+2]-data[i+1]) } } q6 <- function(data,n,p,i,f) { np <- n*p+0.5 i <<- floor(np) f <<- np - i qvalue <- data[i] } q7 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- f*data[i] + (1-f)*data[i+1] } } q8 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { if (f == 0.5) { qvalue <- (data[i]+data[i+1])/2 } else { if (f < 0.5) { qvalue <- data[i] } else { qvalue <- data[i+1] } } } } midmean <- function(x,def) { x <-sort(x[!is.na(x)]) n<-length(x) if (def==1) { qvalue1 <- q1(x,n,0.25,i,f) qvalue3 <- q1(x,n,0.75,i,f) } if (def==2) { qvalue1 <- q2(x,n,0.25,i,f) qvalue3 <- q2(x,n,0.75,i,f) } if (def==3) { qvalue1 <- q3(x,n,0.25,i,f) qvalue3 <- q3(x,n,0.75,i,f) } if (def==4) { qvalue1 <- q4(x,n,0.25,i,f) qvalue3 <- q4(x,n,0.75,i,f) } if (def==5) { qvalue1 <- q5(x,n,0.25,i,f) qvalue3 <- q5(x,n,0.75,i,f) } if (def==6) { qvalue1 <- q6(x,n,0.25,i,f) qvalue3 <- q6(x,n,0.75,i,f) } if (def==7) { qvalue1 <- q7(x,n,0.25,i,f) qvalue3 <- q7(x,n,0.75,i,f) } if (def==8) { qvalue1 <- q8(x,n,0.25,i,f) qvalue3 <- q8(x,n,0.75,i,f) } midm <- 0 myn <- 0 roundno4 <- round(n/4) round3no4 <- round(3*n/4) for (i in 1:n) { if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){ midm = midm + x[i] myn = myn + 1 } } midm = midm / myn return(midm) } (arm <- mean(x)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) midm bitmap(file='test1.png') lb <- win[,1] - 2*win[,2] ub <- win[,1] + 2*win[,2] if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() bitmap(file='test2.png') lb <- tri[,1] - 2*tri[,2] ub <- tri[,1] + 2*tri[,2] if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Measure',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.element(a,'S.E.',header=TRUE) a<-table.element(a,'Value/S.E.',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE) a<-table.element(a,arm) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean')) a<-table.element(a,armose) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE) a<-table.element(a,geo) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE) a<-table.element(a,har) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE) a<-table.element(a,qua) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) for (j in 1:length(win[,1])) { a<-table.row.start(a) mylabel <- paste('Winsorized Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(win[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE) a<-table.element(a,win[j,1]) a<-table.element(a,win[j,2]) a<-table.element(a,win[j,1]/win[j,2]) a<-table.row.end(a) } for (j in 1:length(tri[,1])) { a<-table.row.start(a) mylabel <- paste('Trimmed Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(tri[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE) a<-table.element(a,tri[j,1]) a<-table.element(a,tri[j,2]) a<-table.element(a,tri[j,1]/tri[j,2]) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE) a<-table.element(a,median(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE) a<-table.element(a,midr) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[1]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[2]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[3]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[4]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[5]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[6]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[7]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[8]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Number of observations',header=TRUE) a<-table.element(a,length(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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