Centrummaten Verkoopcijfers van computers en software

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sat, 24 Oct 2009 09:07:33 -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/Oct/24/t1256396919k8adhfm66g09biz.htm/, Retrieved Sat, 24 Oct 2009 17:08:39 +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/Oct/24/t1256396919k8adhfm66g09biz.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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

76,3 71 85,9 109 83,4 101,3 81,6 84,8 88 88,4 85,2 139,5 85,3 79,4 131 91,4 88,2 113,2 81,9 89 95,7 93,2 98 140,5 93 82,1 86,3 84,8 85,7 110,8 87,4 100,4 100,4 99,4 108 161,7 109,3 99,9 110,3 97,5 102,4 122,3 104,4 122,7 127,3 128,4 125,3 187,1 131,4 125,6 142,9 116,6 129,7 155,4 138,7 167,7 155,8 157,1 159,9 244,6 154,3 143,2 147,3 155,1 152,2 166,5 161,2 180,1 169,2 164,5 166,2 267,3

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 3 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 121.813888888889 4.51057716481644 27.0062753474358 Geometric Mean 116.663496264052 Harmonic Mean 112.171840320145 Quadratic Mean 127.605408497359 Winsorized Mean ( 1 / 24 ) 121.572222222222 4.36501340518829 27.8515117680327 Winsorized Mean ( 2 / 24 ) 120.061111111111 3.83058257885271 31.3427810625794 Winsorized Mean ( 3 / 24 ) 119.861111111111 3.74814798062272 31.9787563700186 Winsorized Mean ( 4 / 24 ) 119.272222222222 3.61818363624562 32.9646679696955 Winsorized Mean ( 5 / 24 ) 119.181944444444 3.59614443509693 33.1415899987988 Winsorized Mean ( 6 / 24 ) 119.190277777778 3.56175463592738 33.4639215670577 Winsorized Mean ( 7 / 24 ) 119.297222222222 3.53732223032053 33.7252911820285 Winsorized Mean ( 8 / 24 ) 119.108333333333 3.50244311668334 34.0072142116968 Winsorized Mean ( 9 / 24 ) 118.808333333333 3.43279472392225 34.6097983970289 Winsorized Mean ( 10 / 24 ) 118.752777777778 3.41869742249839 34.7362644603374 Winsorized Mean ( 11 / 24 ) 118.615277777778 3.37581709793724 35.1367607712682 Winsorized Mean ( 12 / 24 ) 118.181944444444 3.29216913998642 35.8978957092502 Winsorized Mean ( 13 / 24 ) 118.019444444444 3.24341070243938 36.3874499013281 Winsorized Mean ( 14 / 24 ) 118.155555555556 3.20145573358734 36.9068215799311 Winsorized Mean ( 15 / 24 ) 118.218055555556 3.17438479147352 37.2412493510845 Winsorized Mean ( 16 / 24 ) 118.084722222222 3.13943732917655 37.6133395385201 Winsorized Mean ( 17 / 24 ) 117.636111111111 3.05326943571763 38.52791690605 Winsorized Mean ( 18 / 24 ) 116.561111111111 2.84178768728542 41.0168260044981 Winsorized Mean ( 19 / 24 ) 116.1125 2.59389099443318 44.7638317297034 Winsorized Mean ( 20 / 24 ) 116.473611111111 2.52266253468644 46.1709045540601 Winsorized Mean ( 21 / 24 ) 115.831944444444 2.41292313777586 48.004821467796 Winsorized Mean ( 22 / 24 ) 116.290277777778 2.26960866078089 51.2380304971899 Winsorized Mean ( 23 / 24 ) 116.609722222222 2.16022168894586 53.9804422939227 Winsorized Mean ( 24 / 24 ) 114.343055555556 1.80046380130233 63.5075559268938 Trimmed Mean ( 1 / 24 ) 120.461428571429 4.07306218724794 29.5751508407047 Trimmed Mean ( 2 / 24 ) 119.285294117647 3.70896409832208 32.1613504351825 Trimmed Mean ( 3 / 24 ) 118.862121212121 3.62819621340193 32.7606651407289 Trimmed Mean ( 4 / 24 ) 118.4875 3.56783782785499 33.2098894952396 Trimmed Mean ( 5 / 24 ) 118.259677419355 3.54063773895405 33.4006713305525 Trimmed Mean ( 6 / 24 ) 118.038333333333 3.51175515187268 33.6123471678793 Trimmed Mean ( 7 / 24 ) 117.8 3.48296085736522 33.8217984135236 Trimmed Mean ( 8 / 24 ) 117.525 3.45045380979176 34.0607370736236 Trimmed Mean ( 9 / 24 ) 117.261111111111 3.41554838442729 34.3315619962366 Trimmed Mean ( 10 / 24 ) 117.023076923077 3.38472816211396 34.5738479777913 Trimmed Mean ( 11 / 24 ) 116.774 3.3454981142803 34.9048171635634 Trimmed Mean ( 12 / 24 ) 116.522916666667 3.30167623393829 35.2920481629648 Trimmed Mean ( 13 / 24 ) 116.306521739130 3.26053758374500 35.6709649104989 Trimmed Mean ( 14 / 24 ) 116.090909090909 3.21401992561655 36.1201584861485 Trimmed Mean ( 15 / 24 ) 115.838095238095 3.15797379941333 36.6811451252746 Trimmed Mean ( 16 / 24 ) 115.5525 3.08568237788329 37.4479566750698 Trimmed Mean ( 17 / 24 ) 115.252631578947 2.99365078917709 38.4990233315184 Trimmed Mean ( 18 / 24 ) 114.972222222222 2.88833068477638 39.8057683727871 Trimmed Mean ( 19 / 24 ) 114.785294117647 2.79907398856426 41.0083101006287 Trimmed Mean ( 20 / 24 ) 114.628125 2.737803725878 41.8686423414956 Trimmed Mean ( 21 / 24 ) 114.406666666667 2.66243745092286 42.9706495553579 Trimmed Mean ( 22 / 24 ) 114.232142857143 2.58086699252530 44.2611506861771 Trimmed Mean ( 23 / 24 ) 113.973076923077 2.49675825324518 45.648423020106 Trimmed Mean ( 24 / 24 ) 113.629166666667 2.39502412295094 47.4438505974891 Median 110.55 Midrange 169.15 Midmean - Weighted Average at Xnp 114.254054054054 Midmean - Weighted Average at X(n+1)p 114.972222222222 Midmean - Empirical Distribution Function 114.254054054054 Midmean - Empirical Distribution Function - Averaging 114.972222222222 Midmean - Empirical Distribution Function - Interpolation 114.972222222222 Midmean - Closest Observation 114.254054054054 Midmean - True Basic - Statistics Graphics Toolkit 114.972222222222 Midmean - MS Excel (old versions) 115.252631578947 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/24/t1256396919k8adhfm66g09biz/109e71256396848.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/24/t1256396919k8adhfm66g09biz/109e71256396848.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/24/t1256396919k8adhfm66g09biz/2pz6s1256396848.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/24/t1256396919k8adhfm66g09biz/2pz6s1256396848.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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