US dollar in Euro Centrummaten SVEN VAN LAERE 2MAR04B

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

Title produced by software: Central Tendency

Date of computation: Sat, 19 Apr 2008 06:26:51 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/19/t12086093778zxt3f4jomi5jv8.htm/, Retrieved Sat, 19 Apr 2008 14:49:39 +0200

User-defined keywords:

Dataseries X:

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1.1591 1.1203 1.0886 1.0701 1.0630 1.0377 1.0370 1.0606 1.0497 1.0706 1.0328 1.0110 1.0131 0.9834 0.9643 0.9449 0.9059 0.9505 0.9386 0.9045 0.8695 0.8525 0.8552 0.8983 0.9376 0.9205 0.9083 0.8925 0.8753 0.8530 0.8615 0.9014 0.9114 0.9050 0.8883 0.8912 0.8832 0.8706 0.8766 0.8860 0.9170 0.9561 0.9935 0.9781 0.9806 0.9812 1.0013 1.0194 1.0622 1.0785 1.0805 1.0862 1.1556 1.1674 1.1365 1.1155 1.1266 1.1714 1.1710 1.2298 1.2638 1.2640 1.2261 1.1989 1.2000 1.2146 1.2266 1.2191 1.2224 1.2507 1.2997 1.3406

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.03442361111111 0.0157056759490028 65.8630430469814 Geometric Mean 1.02615511339297 Harmonic Mean 1.01812349322224 Quadratic Mean 1.04285456966550 Winsorized Mean ( 1 / 24 ) 1.0338625 0.0155581558850723 66.4514809876643 Winsorized Mean ( 2 / 24 ) 1.03293194444444 0.0153234205590863 67.4087055472707 Winsorized Mean ( 3 / 24 ) 1.03318611111111 0.0152794360851321 67.6193876105458 Winsorized Mean ( 4 / 24 ) 1.03290277777778 0.0150587912770914 68.5913469927105 Winsorized Mean ( 5 / 24 ) 1.03152777777778 0.0147618737150776 69.8778351371606 Winsorized Mean ( 6 / 24 ) 1.03165277777778 0.0146521595149512 70.409605950923 Winsorized Mean ( 7 / 24 ) 1.03173055555556 0.01462411529618 70.5499467598601 Winsorized Mean ( 8 / 24 ) 1.03205277777778 0.0144394387129541 71.4745772529156 Winsorized Mean ( 9 / 24 ) 1.03199027777778 0.0143126156581727 72.1035415485709 Winsorized Mean ( 10 / 24 ) 1.03168472222222 0.0141524465581976 72.8979768960609 Winsorized Mean ( 11 / 24 ) 1.02989722222222 0.0136909085886252 75.2248994692649 Winsorized Mean ( 12 / 24 ) 1.02993055555556 0.0136280151132436 75.5745093469025 Winsorized Mean ( 13 / 24 ) 1.0260125 0.0126423083894643 81.1570536323134 Winsorized Mean ( 14 / 24 ) 1.0265375 0.0125444724432360 81.8318589837159 Winsorized Mean ( 15 / 24 ) 1.02643333333333 0.0123329345830731 83.2270151454553 Winsorized Mean ( 16 / 24 ) 1.0247 0.0120237112506028 85.2232708057281 Winsorized Mean ( 17 / 24 ) 1.02408611111111 0.0118643416554347 86.3163031588865 Winsorized Mean ( 18 / 24 ) 1.01991111111111 0.0110514645705079 92.2874162609056 Winsorized Mean ( 19 / 24 ) 1.01811666666667 0.0105516638283337 96.4887323203743 Winsorized Mean ( 20 / 24 ) 1.01792222222222 0.0100792420253336 100.991941622568 Winsorized Mean ( 21 / 24 ) 1.01754305555556 0.00973624804146028 104.510798330374 Winsorized Mean ( 22 / 24 ) 1.01454861111111 0.00787891815562481 128.767502221967 Winsorized Mean ( 23 / 24 ) 1.01410138888889 0.007733905872913 131.124092477082 Winsorized Mean ( 24 / 24 ) 1.01430138888889 0.0071990646380604 140.893496569877 Trimmed Mean ( 1 / 24 ) 1.03264857142857 0.0153219919001489 67.3964963666726 Trimmed Mean ( 2 / 24 ) 1.03136323529412 0.0150373034693575 68.5869801986635 Trimmed Mean ( 3 / 24 ) 1.03050757575758 0.0148418493105993 69.4325588538108 Trimmed Mean ( 4 / 24 ) 1.029503125 0.0146211229715150 70.4120420165869 Trimmed Mean ( 5 / 24 ) 1.02851612903226 0.0144286604058774 71.2828564884164 Trimmed Mean ( 6 / 24 ) 1.02779333333333 0.0142800512482793 71.9740647609494 Trimmed Mean ( 7 / 24 ) 1.02699482758621 0.0141192423012143 72.7372479115176 Trimmed Mean ( 8 / 24 ) 1.026125 0.0139194947031926 73.7185524245103 Trimmed Mean ( 9 / 24 ) 1.02513703703704 0.0137074485600286 74.7868600453021 Trimmed Mean ( 10 / 24 ) 1.02408269230769 0.0134634650932215 76.0638279385661 Trimmed Mean ( 11 / 24 ) 1.022988 0.0131850377910350 77.5870358669408 Trimmed Mean ( 12 / 24 ) 1.02204583333333 0.0129301324083978 79.0437252343632 Trimmed Mean ( 13 / 24 ) 1.02101739130435 0.0126083456389866 80.9794893429342 Trimmed Mean ( 14 / 24 ) 1.02038863636364 0.0124098611372218 82.2240172618137 Trimmed Mean ( 15 / 24 ) 1.01963571428571 0.0121572860061914 83.8703402853599 Trimmed Mean ( 16 / 24 ) 1.01882 0.0118590489089826 85.9107680404538 Trimmed Mean ( 17 / 24 ) 1.01812368421053 0.0115246624251808 88.3430374486264 Trimmed Mean ( 18 / 24 ) 1.01742222222222 0.0110994881271302 91.6638867098174 Trimmed Mean ( 19 / 24 ) 1.01712941176471 0.0107283833395542 94.8073329944019 Trimmed Mean ( 20 / 24 ) 1.0170125 0.0103359513408766 98.3956354339562 Trimmed Mean ( 21 / 24 ) 1.01690333333333 0.00990216913811548 102.695007442265 Trimmed Mean ( 22 / 24 ) 1.016825 0.0093641068989986 108.587504496424 Trimmed Mean ( 23 / 24 ) 1.01711153846154 0.0091869980481164 110.712066458975 Trimmed Mean ( 24 / 24 ) 1.01750416666667 0.0089198960950573 114.071302605250 Median 1.01625 Midrange 1.09655 Midmean - Weighted Average at Xnp 1.01440810810811 Midmean - Weighted Average at X(n+1)p 1.01742222222222 Midmean - Empirical Distribution Function 1.01440810810811 Midmean - Empirical Distribution Function - Averaging 1.01742222222222 Midmean - Empirical Distribution Function - Interpolation 1.01742222222222 Midmean - Closest Observation 1.01440810810811 Midmean - True Basic - Statistics Graphics Toolkit 1.01742222222222 Midmean - MS Excel (old versions) 1.01812368421053 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t12086093778zxt3f4jomi5jv8/1pt961208608009.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t12086093778zxt3f4jomi5jv8/1pt961208608009.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t12086093778zxt3f4jomi5jv8/2xdzx1208608009.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t12086093778zxt3f4jomi5jv8/2xdzx1208608009.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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