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Workshop 8

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

Title produced by software: Central Tendency

Date of computation: Tue, 04 Dec 2007 17:20:40 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/05/t1196813308bw9c3jxjve3dl25.htm/, Retrieved Wed, 05 Dec 2007 01:08:32 +0100

User-defined keywords:

Q4

Dataseries X:

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-0.0165645093211093 -0.00761598592253563 0.0523833206242285 0.00920737060564757 -0.0280702792780465 0.00281750898310281 -0.022332672139411 -0.00787112294803327 0.0221173379073692 0.0067280366738747 -0.0600557158843458 0.0298374026517252 0.000186581259647118 -0.00109191298840832 0.0539321780862091 -0.0519810358661653 0.0492086359384103 -0.056871289610396 0.0208163463146961 -0.00141406559195286 0.0621450147583607 0.0311274742024184 0.0780561050492554 0.0490248023672456 -0.00193488014247141 0.122250249716408 -0.0222516431313169 -0.00120574581849320 0.0487207501912845 0.0597652785553623 -0.00525080774645977 -0.00331131630947451 -0.0175706498857684 -0.048353844587374 0.0444051450583285 -0.0266478587556102 -0.0457651808789366 -0.0102960122787207 -0.00191866736296624 0.00397209654179794 0.0134055150094126 -0.0287488997462509 0.0212584862568654 0.0155484994010022 0.131325821456894 0.0106379461815768 -0.000189969366080745 -0.115253383167950 0.140566998360777 0.0105175216495473 -0.118755378638246 -0.00166721169156504 -0.100503512640737 -0.0286018925746096 0.0546731356976751 0.0882854487984557 0.0501534873653888 0.0171490345644563 -0.0949198659626559 -0.0443474847780983 -0.027525485099238 -0.0178788782127245 -0.0507294153310545 -0.0220504349813639 0.0580044197496768 0.0227984732059170 0.0223448342740036 -0.0112084529924838

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.00445023229155833 0.00615614373127049 0.722892850755436 Geometric Mean NaN Harmonic Mean -0.0179249833802911 Quadratic Mean 0.050586338524674 Winsorized Mean ( 1 / 22 ) 0.00436583256459382 0.00609736372424042 0.716019703275564 Winsorized Mean ( 2 / 22 ) 0.00453272370537990 0.00589477910471031 0.768938687076155 Winsorized Mean ( 3 / 22 ) 0.00328061395950323 0.00542838127388351 0.604344793407677 Winsorized Mean ( 4 / 22 ) 0.00472972021415675 0.00480171275394059 0.985006904104217 Winsorized Mean ( 5 / 22 ) 0.00379393609526374 0.00450762847549102 0.841670096790856 Winsorized Mean ( 6 / 22 ) 0.00401545234890189 0.00438289862720604 0.916163637455977 Winsorized Mean ( 7 / 22 ) 0.00396303076222508 0.00432433897560483 0.916447758740001 Winsorized Mean ( 8 / 22 ) 0.00385059390242259 0.00420007205771253 0.916792342967497 Winsorized Mean ( 9 / 22 ) 0.00409514323878645 0.00411962889640144 0.994056343852627 Winsorized Mean ( 10 / 22 ) 0.00407585480332434 0.00404126957570779 1.00855801053819 Winsorized Mean ( 11 / 22 ) 0.00623844700189912 0.00356286601037831 1.75096312455396 Winsorized Mean ( 12 / 22 ) 0.00609765095683961 0.00352852029367204 1.72810426165750 Winsorized Mean ( 13 / 22 ) 0.00616413825728343 0.00350724873902684 1.75754236894923 Winsorized Mean ( 14 / 22 ) 0.00621370278728142 0.00347954596803806 1.78577976677371 Winsorized Mean ( 15 / 22 ) 0.00545532511316491 0.00328018420555276 1.66311547501815 Winsorized Mean ( 16 / 22 ) 0.00334650529205646 0.00260237439751409 1.28594305848275 Winsorized Mean ( 17 / 22 ) 0.00304424465640668 0.00254837926530713 1.19458068814564 Winsorized Mean ( 18 / 22 ) 0.00123425960750384 0.00226071161973292 0.545960659789792 Winsorized Mean ( 19 / 22 ) 0.00227308959129492 0.00206794405113113 1.09920265495170 Winsorized Mean ( 20 / 22 ) 0.00229683428550719 0.00204509280513173 1.12309538214783 Winsorized Mean ( 21 / 22 ) 0.00234232056781986 0.00196194729101131 1.19387538011405 Winsorized Mean ( 22 / 22 ) 0.00393211704579098 0.00170065420698822 2.31212025915284 Trimmed Mean ( 1 / 22 ) 0.00425460872883993 0.00569123660779675 0.747571928921616 Trimmed Mean ( 2 / 22 ) 0.00413643340335143 0.0051880246909721 0.79730410893175 Trimmed Mean ( 3 / 22 ) 0.00391911291514227 0.00470213729778833 0.833474793895456 Trimmed Mean ( 4 / 22 ) 0.00416032363171701 0.00434169336740909 0.958226037551724 Trimmed Mean ( 5 / 22 ) 0.00399343152996743 0.00415752165966651 0.960531743877376 Trimmed Mean ( 6 / 22 ) 0.00404188042125261 0.00403144750659164 1.00258788304794 Trimmed Mean ( 7 / 22 ) 0.00404742705372128 0.00391266674760965 1.03444206082564 Trimmed Mean ( 8 / 22 ) 0.00406319339389090 0.00378047566957028 1.07478363810043 Trimmed Mean ( 9 / 22 ) 0.00409933530744052 0.00364738635602139 1.12391035862516 Trimmed Mean ( 10 / 22 ) 0.00409999517009903 0.0034992156225246 1.17168977633364 Trimmed Mean ( 11 / 22 ) 0.00410356374605703 0.00332935821548091 1.23253897011628 Trimmed Mean ( 12 / 22 ) 0.00380362147044285 0.00323018743719001 1.17752345472301 Trimmed Mean ( 13 / 22 ) 0.00349410955561154 0.00310721890022843 1.12451348546917 Trimmed Mean ( 14 / 22 ) 0.00314495195616214 0.00294733153241169 1.06705062582109 Trimmed Mean ( 15 / 22 ) 0.00275270560932734 0.00273636213128583 1.00597270290166 Trimmed Mean ( 16 / 22 ) 0.00241237574588113 0.00250779519448487 0.961950860734728 Trimmed Mean ( 17 / 22 ) 0.00229560955260922 0.00240447600424897 0.954723419386437 Trimmed Mean ( 18 / 22 ) 0.00220203016463453 0.00227305620580217 0.968753064272526 Trimmed Mean ( 19 / 22 ) 0.00232389756812506 0.00217419800436116 1.06885277397166 Trimmed Mean ( 20 / 22 ) 0.0023303918208026 0.00209042219993991 1.11479481076578 Trimmed Mean ( 21 / 22 ) 0.00233478011387969 0.00196744376255111 1.18670742123387 Trimmed Mean ( 22 / 22 ) 0.0023337627510465 0.00180616541878422 1.29210908744860 Median -0.000640941177244533 Midrange 0.0109058098612655 Midmean - Weighted Average at Xnp 0.00159194436140864 Midmean - Weighted Average at X(n+1)p 0.00229560955260922 Midmean - Empirical Distribution Function 0.00159194436140864 Midmean - Empirical Distribution Function - Averaging 0.00229560955260922 Midmean - Empirical Distribution Function - Interpolation 0.00229560955260922 Midmean - Closest Observation 0.00159194436140864 Midmean - True Basic - Statistics Graphics Toolkit 0.00229560955260922 Midmean - MS Excel (old versions) 0.00241237574588113 Number of observations 68

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/05/t1196813308bw9c3jxjve3dl25/1c9mu1196814034.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/05/t1196813308bw9c3jxjve3dl25/1c9mu1196814034.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/05/t1196813308bw9c3jxjve3dl25/2cevd1196814034.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/05/t1196813308bw9c3jxjve3dl25/2cevd1196814034.ps (open in new window)

Parameters:

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')

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Software written by Ed van Stee & Patrick Wessa

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