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

Title produced by software: Central Tendency

Date of computation: Mon, 21 Apr 2008 10:14:09 -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/21/t1208794478pxkolxsix6w2rla.htm/, Retrieved Mon, 21 Apr 2008 18:14:40 +0200

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Dataseries X:

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102,8 103,1 103,1 103,3 103,5 103,3 103,5 103,8 103,9 103,9 104,2 104,6 104,9 105,2 105,2 105,6 105,6 106,2 106,3 106,4 106,9 107,2 107,3 107,3 107,4 107,55 107,87 108,37 108,38 107,92 108,03 108,14 108,3 108,64 108,66 109,04 109,03 109,03 109,54 109,75 109,83 109,65 109,82 109,95 110,12 110,15 110,2 109,99 110,14 110,14 110,81 110,97 110,99 109,73 109,81 110,02 110,18 110,21 110,25 110,36 110,51 110,64 110,95 111,18 111,19 111,69 111,7 111,83 111,77 111,73 112,01 111,86 112,04

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 108.29 0.322262324959465 336.030592510685 Geometric Mean 108.255122977392 Harmonic Mean 108.219898205174 Quadratic Mean 108.324519460916 Winsorized Mean ( 1 / 24 ) 108.293698630137 0.321248486475438 337.102595620842 Winsorized Mean ( 2 / 24 ) 108.289589041096 0.320600501909801 337.771115129329 Winsorized Mean ( 3 / 24 ) 108.296575342466 0.318591017843586 339.923504672171 Winsorized Mean ( 4 / 24 ) 108.293287671233 0.318088256732827 340.450442224882 Winsorized Mean ( 5 / 24 ) 108.304246575342 0.314727535385757 344.120658024394 Winsorized Mean ( 6 / 24 ) 108.301780821918 0.31435604628847 344.519477517968 Winsorized Mean ( 7 / 24 ) 108.329589041096 0.308223011138013 351.464962467028 Winsorized Mean ( 8 / 24 ) 108.285753424658 0.298122161800288 363.226110969899 Winsorized Mean ( 9 / 24 ) 108.284520547945 0.297955555375790 363.42507664062 Winsorized Mean ( 10 / 24 ) 108.299589041096 0.286209245226506 378.393049306941 Winsorized Mean ( 11 / 24 ) 108.356849315068 0.274074468315377 395.355503126918 Winsorized Mean ( 12 / 24 ) 108.402876712329 0.264402666678264 409.991616477294 Winsorized Mean ( 13 / 24 ) 108.431369863014 0.251408536998985 431.29549679314 Winsorized Mean ( 14 / 24 ) 108.398767123288 0.247213076865112 438.483143763604 Winsorized Mean ( 15 / 24 ) 108.454246575342 0.229369289236946 472.836825436145 Winsorized Mean ( 16 / 24 ) 108.421369863014 0.225358273445909 481.106676072566 Winsorized Mean ( 17 / 24 ) 108.535479452055 0.198693319085748 546.246244974222 Winsorized Mean ( 18 / 24 ) 108.550273972603 0.193510583662625 560.952646196625 Winsorized Mean ( 19 / 24 ) 108.573698630137 0.189019389980993 574.405084267041 Winsorized Mean ( 20 / 24 ) 108.705205479452 0.167099109025231 650.543298007881 Winsorized Mean ( 21 / 24 ) 108.782876712329 0.153363665782329 709.3132272068 Winsorized Mean ( 22 / 24 ) 108.81 0.148704194947989 731.721119488645 Winsorized Mean ( 23 / 24 ) 108.81 0.148704194947989 731.721119488645 Winsorized Mean ( 24 / 24 ) 108.836301369863 0.143279100238110 759.6104469458 Trimmed Mean ( 1 / 24 ) 108.314507042254 0.317689773683565 340.944267063945 Trimmed Mean ( 2 / 24 ) 108.336521739130 0.313358782551522 345.726776371165 Trimmed Mean ( 3 / 24 ) 108.362089552239 0.308497587551029 351.257494142688 Trimmed Mean ( 4 / 24 ) 108.386615384615 0.303487285638754 357.137252575483 Trimmed Mean ( 5 / 24 ) 108.413650793651 0.297535473502205 364.372185667627 Trimmed Mean ( 6 / 24 ) 108.439836065574 0.291315040984849 372.242489433333 Trimmed Mean ( 7 / 24 ) 108.468305084746 0.283753248530428 382.262778123277 Trimmed Mean ( 8 / 24 ) 108.493684210526 0.276092229647746 392.961744519027 Trimmed Mean ( 9 / 24 ) 108.528181818182 0.268979126386396 403.481799038481 Trimmed Mean ( 10 / 24 ) 108.565471698113 0.260033012032540 417.506496000313 Trimmed Mean ( 11 / 24 ) 108.603529411765 0.251539077933821 431.756092547726 Trimmed Mean ( 12 / 24 ) 108.636938775510 0.243678792857676 445.820243532481 Trimmed Mean ( 13 / 24 ) 108.667234042553 0.235889620882949 460.669840562739 Trimmed Mean ( 14 / 24 ) 108.696666666667 0.228797912683846 475.077177897441 Trimmed Mean ( 15 / 24 ) 108.732790697674 0.220226734461516 493.731112907525 Trimmed Mean ( 16 / 24 ) 108.765853658537 0.213240095875505 510.062862296014 Trimmed Mean ( 17 / 24 ) 108.806153846154 0.204447385701532 532.196356890557 Trimmed Mean ( 18 / 24 ) 108.837567567568 0.199534896661703 545.456305580941 Trimmed Mean ( 19 / 24 ) 108.870857142857 0.193748676950136 561.917938520307 Trimmed Mean ( 20 / 24 ) 108.905454545455 0.186575037157595 583.708604348098 Trimmed Mean ( 21 / 24 ) 108.929032258065 0.182856871484735 595.706529230202 Trimmed Mean ( 22 / 24 ) 108.946551724138 0.181016747899784 601.85896050046 Trimmed Mean ( 23 / 24 ) 108.963333333333 0.178884641877706 609.12626254313 Trimmed Mean ( 24 / 24 ) 108.9828 0.174657302547971 623.980780706649 Median 109.03 Midrange 107.42 Midmean - Weighted Average at Xnp 108.799444444444 Midmean - Weighted Average at X(n+1)p 108.837567567568 Midmean - Empirical Distribution Function 108.837567567568 Midmean - Empirical Distribution Function - Averaging 108.837567567568 Midmean - Empirical Distribution Function - Interpolation 108.837567567568 Midmean - Closest Observation 108.768157894737 Midmean - True Basic - Statistics Graphics Toolkit 108.837567567568 Midmean - MS Excel (old versions) 108.837567567568 Number of observations 73

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208794478pxkolxsix6w2rla/1bwh41208794447.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208794478pxkolxsix6w2rla/1bwh41208794447.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208794478pxkolxsix6w2rla/2yrut1208794447.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208794478pxkolxsix6w2rla/2yrut1208794447.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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