export belgie

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 09 Mar 2010 12:27:27 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/09/t12681629401x4v68bm5s13eua.htm/, Retrieved Tue, 09 Mar 2010 20:29:03 +0100

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/2010/Mar/09/t12681629401x4v68bm5s13eua.htm/}, year = {2010}, } @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 = {2010}, 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 «

18288.3 16049 16764.5 17880.2 16555.9 16087.1 16373.5 17842.2 22321.5 22786.7 18274.1 22392.9 23899.3 21343.5 22952.3 21374.4 21164.1 20906.5 17877.4 20664.3 22160 19813.6 17735.4 19640.2 20844.4 19823.1 18594.6 21350.6 18574.1 18924.2 17343.4 19961.2 19932.1 19464.6 16165.4 17574.9 19795.4 19439.5 17170 21072.4 17751.8 17515.5 18040.3 19090.1 17746.5 19202.1 15141.6 16258.1 18586.5 17209.4 17838.7 19123.5 16583.6 15991.2 16704.5 17422 17872 17823.2 13866.5 15912.8 17870.5 15420.3 16379.4 17903.9 15305.8 14583.3 14861 14968.9 16726.5 16283.6 11703.7 15101.8 15469.7 14956.9 15370.6 15998.1 14725.1 14768.9 13659.6 15070.3 16942.6 15761.3 12083 15023.6 15106.5

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 17704.7247058824 272.696823184808 64.9245726411846 Geometric Mean 17528.6463738250 Harmonic Mean 17352.2001635969 Quadratic Mean 17880.2633014894 Winsorized Mean ( 1 / 28 ) 17698.0458823529 268.752638611517 65.8525474346526 Winsorized Mean ( 2 / 28 ) 17731.2458823529 259.753473619837 68.2618239335023 Winsorized Mean ( 3 / 28 ) 17724.6494117647 255.291211240733 69.4291406493066 Winsorized Mean ( 4 / 28 ) 17755.0211764706 248.960313859487 71.3166725299499 Winsorized Mean ( 5 / 28 ) 17753.8623529412 245.663939973484 72.2688985402476 Winsorized Mean ( 6 / 28 ) 17701.5 234.089364397039 75.6185572360157 Winsorized Mean ( 7 / 28 ) 17707.1247058824 232.605524981324 76.1251251762145 Winsorized Mean ( 8 / 28 ) 17715.4823529412 231.182293727845 76.6299272633588 Winsorized Mean ( 9 / 28 ) 17697.7576470588 227.50378110181 77.7910484008127 Winsorized Mean ( 10 / 28 ) 17693.4047058824 224.644651182837 78.7617448833972 Winsorized Mean ( 11 / 28 ) 17677.9788235294 219.992540534946 80.3571738411796 Winsorized Mean ( 12 / 28 ) 17673.6588235294 217.840808105125 81.1310744633325 Winsorized Mean ( 13 / 28 ) 17646.8329411765 213.029752708167 82.8374098774418 Winsorized Mean ( 14 / 28 ) 17536.8094117647 193.751644529922 90.5117964511338 Winsorized Mean ( 15 / 28 ) 17560.6505882353 188.792037384784 93.0158434195201 Winsorized Mean ( 16 / 28 ) 17552.3305882353 184.022551192523 95.3814109982214 Winsorized Mean ( 17 / 28 ) 17560.3705882353 182.347354418350 96.3017568543796 Winsorized Mean ( 18 / 28 ) 17566.9776470588 180.325313930662 97.4182562843818 Winsorized Mean ( 19 / 28 ) 17597.4670588235 166.436242437174 105.730980230860 Winsorized Mean ( 20 / 28 ) 17591.7964705882 155.831102092630 112.890149876058 Winsorized Mean ( 21 / 28 ) 17604.9647058824 152.480725187802 115.456984377529 Winsorized Mean ( 22 / 28 ) 17545.3058823529 143.629084967522 122.157053958259 Winsorized Mean ( 23 / 28 ) 17537.8105882353 138.962379337770 126.205456986361 Winsorized Mean ( 24 / 28 ) 17539.1376470588 136.314959289084 128.666272128384 Winsorized Mean ( 25 / 28 ) 17513.3729411765 126.860817283635 138.051869096982 Winsorized Mean ( 26 / 28 ) 17440.9094117647 110.278613322658 158.153143989354 Winsorized Mean ( 27 / 28 ) 17446.4364705882 108.926245726064 160.167426631629 Winsorized Mean ( 28 / 28 ) 17471.9658823529 104.683688912065 166.902466505833 Trimmed Mean ( 1 / 28 ) 17702.3927710843 259.004822441867 68.3477342398039 Trimmed Mean ( 2 / 28 ) 17706.9543209877 247.652403900224 71.4992224671542 Trimmed Mean ( 3 / 28 ) 17693.8860759494 240.101378483762 73.6933964631362 Trimmed Mean ( 4 / 28 ) 17682.5662337662 233.290393490993 75.7963753636041 Trimmed Mean ( 5 / 28 ) 17662.0373333333 227.534719051748 77.6234827236034 Trimmed Mean ( 6 / 28 ) 17640.6534246575 221.745968323188 79.5534347616496 Trimmed Mean ( 7 / 28 ) 17628.5126760563 218.023830744147 80.8558982561111 Trimmed Mean ( 8 / 28 ) 17614.6782608696 213.922713781724 82.341318270872 Trimmed Mean ( 9 / 28 ) 17598.6925373134 209.312067762590 84.0787285961674 Trimmed Mean ( 10 / 28 ) 17584.2984615385 204.571098564170 85.9569048851863 Trimmed Mean ( 11 / 28 ) 17569.5777777778 199.433112372343 88.0975960750956 Trimmed Mean ( 12 / 28 ) 17555.8459016393 194.151234114165 90.4235606934959 Trimmed Mean ( 13 / 28 ) 17541.7016949153 188.129520222800 93.242685539945 Trimmed Mean ( 14 / 28 ) 17529.6421052632 181.735539925743 96.4568741613543 Trimmed Mean ( 15 / 28 ) 17528.8509090909 177.723639108963 98.6298221045538 Trimmed Mean ( 16 / 28 ) 17525.4509433962 173.635391488119 100.932481524628 Trimmed Mean ( 17 / 28 ) 17522.6509803922 169.391479665638 103.444701085203 Trimmed Mean ( 18 / 28 ) 17518.8020408163 164.310691902726 106.619976082796 Trimmed Mean ( 19 / 28 ) 17513.9617021277 158.211099114469 110.699955945922 Trimmed Mean ( 20 / 28 ) 17505.66 153.281730295636 114.205782817278 Trimmed Mean ( 21 / 28 ) 17497.1465116279 149.088976508583 117.360430807039 Trimmed Mean ( 22 / 28 ) 17486.5024390244 144.191711116587 121.272591216326 Trimmed Mean ( 23 / 28 ) 17480.6769230769 139.735891543461 125.097973970704 Trimmed Mean ( 24 / 28 ) 17474.9702702703 134.755750341955 129.678846549598 Trimmed Mean ( 25 / 28 ) 17468.4771428571 128.506724022861 135.934343324709 Trimmed Mean ( 26 / 28 ) 17463.8515151515 122.450472371951 142.619715358092 Trimmed Mean ( 27 / 28 ) 17466.2709677419 118.689884540909 147.158884139969 Trimmed Mean ( 28 / 28 ) 17468.4241379310 113.429631042348 154.002300610581 Median 17735.4 Midrange 17801.5 Midmean - Weighted Average at Xnp 17450.9 Midmean - Weighted Average at X(n+1)p 17497.1465116279 Midmean - Empirical Distribution Function 17497.1465116279 Midmean - Empirical Distribution Function - Averaging 17497.1465116279 Midmean - Empirical Distribution Function - Interpolation 17497.1465116279 Midmean - Closest Observation 17461.1386363636 Midmean - True Basic - Statistics Graphics Toolkit 17497.1465116279 Midmean - MS Excel (old versions) 17497.1465116279 Number of observations 85

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/09/t12681629401x4v68bm5s13eua/1ee0a1268162845.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/09/t12681629401x4v68bm5s13eua/1ee0a1268162845.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/09/t12681629401x4v68bm5s13eua/26ax11268162845.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/09/t12681629401x4v68bm5s13eua/26ax11268162845.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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