WS import - wisselkoers gem

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Fri, 16 Oct 2009 07:54:20 -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/16/t1255701457sb8yi51wfm7buls.htm/, Retrieved Fri, 16 Oct 2009 15:57:39 +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/16/t1255701457sb8yi51wfm7buls.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:

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1075,881535 1035,099359 1036,230236 1153,254177 1236,437747 995,831597 1237,442482 1152,627083 1267,312226 1155,17797 1143,669228 1232,086463 1054,384073 1108,867707 1078,951536 1125,456545 1195,973759 1129,562339 1182,768053 1200,08507 1425,816915 1079,609486 1324,611605 1229,219421 1125,114269 1173,707041 1151,123663 1438,54317 1343,53071 1318,335123 1256,844827 1248,360136 1396,359862 1347,254788 1547,470924 1376,865893 1402,180368 1166,897111 1392,218987 1546,313658 1419,32056 1265,721942 1280,155961 1127,96512 1448,857203 1511,057037 1547,665885 1651,33222 1649,804106 1370,049362 1652,514577 1473,55645 1418,044656 1553,317833 1155,833716 1222,64185 1336,767399 1098,18653 1036,890176 1201,799131

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 1275.14931426667 22.1228966952456 57.6393467741819 Geometric Mean 1264.18275393179 Harmonic Mean 1253.59726363632 Quadratic Mean 1286.42205539546 Winsorized Mean ( 1 / 20 ) 1275.78407101667 21.9864256524227 58.0259879975573 Winsorized Mean ( 2 / 20 ) 1275.77082978333 21.9647204842400 58.0827254641696 Winsorized Mean ( 3 / 20 ) 1270.97951313333 20.7005760149977 61.3982679618433 Winsorized Mean ( 4 / 20 ) 1271.7689764 20.3966762153804 62.3517755035502 Winsorized Mean ( 5 / 20 ) 1273.54418481667 20.0815995153067 63.4184634468952 Winsorized Mean ( 6 / 20 ) 1273.73545831667 20.0039154689093 63.6743071773295 Winsorized Mean ( 7 / 20 ) 1269.6989467 19.0742253222070 66.5662130572486 Winsorized Mean ( 8 / 20 ) 1267.17580763333 17.6297097650919 71.8772926223909 Winsorized Mean ( 9 / 20 ) 1265.07309713333 16.6575975050142 75.9457116641536 Winsorized Mean ( 10 / 20 ) 1266.06185196667 15.9203613722017 79.5246930875146 Winsorized Mean ( 11 / 20 ) 1263.79145581667 15.489765852033 81.5888030774071 Winsorized Mean ( 12 / 20 ) 1262.99389981667 15.1854421713190 83.1713614636857 Winsorized Mean ( 13 / 20 ) 1263.06351806667 15.0852230116153 83.7285280498758 Winsorized Mean ( 14 / 20 ) 1262.6534583 13.9642519476322 90.4204151454095 Winsorized Mean ( 15 / 20 ) 1263.06194055 13.4527898732747 93.8884761040679 Winsorized Mean ( 16 / 20 ) 1262.35861921667 13.2115880849154 95.5493473686173 Winsorized Mean ( 17 / 20 ) 1258.18625255 12.4729653538404 100.873065614875 Winsorized Mean ( 18 / 20 ) 1256.71843115 12.0629013267047 104.180445243956 Winsorized Mean ( 19 / 20 ) 1249.70780228333 10.9099139326317 114.547906610467 Winsorized Mean ( 20 / 20 ) 1252.15424128333 10.1909110416575 122.869705776539 Trimmed Mean ( 1 / 20 ) 1273.45883934483 21.3855171773008 59.5477223574708 Trimmed Mean ( 2 / 20 ) 1270.96751969643 20.6392646301238 61.5800777049685 Trimmed Mean ( 3 / 20 ) 1268.29901409259 19.7203792657575 64.3141289019157 Trimmed Mean ( 4 / 20 ) 1267.26805292308 19.2052867950249 65.9853750922044 Trimmed Mean ( 5 / 20 ) 1265.91777588 18.6715766620594 67.799190116191 Trimmed Mean ( 6 / 20 ) 1264.01117364583 18.0937473828273 69.8590041577293 Trimmed Mean ( 7 / 20 ) 1261.89719871739 17.3682797571189 72.6552782638228 Trimmed Mean ( 8 / 20 ) 1260.37737768182 16.7214970715169 75.37467322999 Trimmed Mean ( 9 / 20 ) 1259.16337233333 16.2944402878733 77.2756443355976 Trimmed Mean ( 10 / 20 ) 1258.1784182 15.9846638191058 78.7115970932181 Trimmed Mean ( 11 / 20 ) 1256.9336655 15.7392153171521 79.8599955698067 Trimmed Mean ( 12 / 20 ) 1255.89460636111 15.493258732596 81.0607134391202 Trimmed Mean ( 13 / 20 ) 1254.85059261765 15.2033362728610 82.5378436743285 Trimmed Mean ( 14 / 20 ) 1253.6660360625 14.7890522649134 84.769869874406 Trimmed Mean ( 15 / 20 ) 1252.3821186 14.4937989301842 86.408133894547 Trimmed Mean ( 16 / 20 ) 1250.85642975 14.1661082381423 88.2992286040895 Trimmed Mean ( 17 / 20 ) 1249.19746011538 13.7005954309184 91.1783335559488 Trimmed Mean ( 18 / 20 ) 1247.875578875 13.2193606400983 94.3975743493838 Trimmed Mean ( 19 / 20 ) 1246.53575277273 12.5618860016853 99.2315765805785 Trimmed Mean ( 20 / 20 ) 1246.03490285 11.9789126316555 104.019032542004 Median 1236.9401145 Midrange 1324.173087 Midmean - Weighted Average at Xnp 1248.87525116129 Midmean - Weighted Average at X(n+1)p 1252.3821186 Midmean - Empirical Distribution Function 1248.87525116129 Midmean - Empirical Distribution Function - Averaging 1252.3821186 Midmean - Empirical Distribution Function - Interpolation 1252.3821186 Midmean - Closest Observation 1248.87525116129 Midmean - True Basic - Statistics Graphics Toolkit 1252.3821186 Midmean - MS Excel (old versions) 1253.6660360625 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/16/t1255701457sb8yi51wfm7buls/1fev81255701258.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/16/t1255701457sb8yi51wfm7buls/1fev81255701258.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/16/t1255701457sb8yi51wfm7buls/2u8gr1255701258.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/16/t1255701457sb8yi51wfm7buls/2u8gr1255701258.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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