*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sat, 06 Jun 2009 09:54:02 -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/Jun/06/t1244303663uqpgv7xl1ueuj3x.htm/, Retrieved Sat, 06 Jun 2009 17:54:25 +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/Jun/06/t1244303663uqpgv7xl1ueuj3x.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:

» Textbox « » Textfile « » CSV «

3851,3 3851,8 3854,1 3858,4 3861,6 3856,3 3855,8 3860,4 3855,1 3839,5 3833 3833,6 3826,8 3818,2 3811,4 3806,8 3810,3 3818,2 3858,9 3867,8 3872,3 3873,3 3876,7 3882,6 3883,5 3882,2 3888,1 3893,7 3901,9 3914,3 3930,3 3948,3 3971,5 3990,1 3993 3998 4015,8 4041,2 4060,7 4076,7 4103 4125,3 4139,7 4146,7 4158 4155,1 4144,8 4148,2 4142,5 4142,1 4145,4 4146,3 4143,5 4149,2 4158,9 4166,1 4179,1 4194,4 4211,7 4226,3 4235,8 4243,6 4258,7 4278,2 4298 4315,1 4334,3 4356 4374 4395,5 4417,8 4432,8 4446,3

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 4044.32739726027 22.0845037391469 183.129648056856 Geometric Mean 4040.03594011021 Harmonic Mean 4035.79716097815 Quadratic Mean 4048.6664864149 Winsorized Mean ( 1 / 24 ) 4044.19041095890 22.0313590294923 183.565181137720 Winsorized Mean ( 2 / 24 ) 4043.80958904110 21.9279014526502 184.413889207459 Winsorized Mean ( 3 / 24 ) 4043.17260273973 21.6751663395184 186.534790063787 Winsorized Mean ( 4 / 24 ) 4041.99452054794 21.4153124752127 188.743196029774 Winsorized Mean ( 5 / 24 ) 4041.35068493151 21.0702775216055 191.803391331106 Winsorized Mean ( 6 / 24 ) 4040.07671232877 20.6370945370357 195.767708728493 Winsorized Mean ( 7 / 24 ) 4038.29315068493 20.2721224152167 199.204260312364 Winsorized Mean ( 8 / 24 ) 4037.06575342466 19.8330677257816 203.552259753379 Winsorized Mean ( 9 / 24 ) 4036.07945205479 19.1981635147693 210.232580264764 Winsorized Mean ( 10 / 24 ) 4033.47671232877 18.7318500201428 215.327194483806 Winsorized Mean ( 11 / 24 ) 4031.54794520548 18.3121483150306 220.157016852926 Winsorized Mean ( 12 / 24 ) 4030.4301369863 18.0857901541021 222.850652509210 Winsorized Mean ( 13 / 24 ) 4028.86301369863 17.8052767077903 226.273541255099 Winsorized Mean ( 14 / 24 ) 4026.15890410959 17.3688681059868 231.803182541401 Winsorized Mean ( 15 / 24 ) 4023.03561643836 16.7943953072494 239.546321426756 Winsorized Mean ( 16 / 24 ) 4019.79178082192 16.3142590554709 246.397446991251 Winsorized Mean ( 17 / 24 ) 4017.11369863014 15.8635190888018 253.229669668054 Winsorized Mean ( 18 / 24 ) 4015.63424657534 15.5938441854756 257.514067654696 Winsorized Mean ( 19 / 24 ) 4017.01369863014 15.3442707560349 261.792415064773 Winsorized Mean ( 20 / 24 ) 4017.45205479452 15.0775132076412 266.453227363681 Winsorized Mean ( 21 / 24 ) 4016.04246575342 14.8255666801954 270.886270480185 Winsorized Mean ( 22 / 24 ) 4016.76575342466 14.6514567017213 274.154702511783 Winsorized Mean ( 23 / 24 ) 4018.02602739726 14.36376561565 279.733472051328 Winsorized Mean ( 24 / 24 ) 4018.02602739726 14.3301435374138 280.389796299445 Trimmed Mean ( 1 / 24 ) 4042.01126760563 21.7221437100796 186.077917610408 Trimmed Mean ( 2 / 24 ) 4039.70579710145 21.3480544387725 189.230630298774 Trimmed Mean ( 3 / 24 ) 4037.47014925373 20.9612711746668 192.615710927556 Trimmed Mean ( 4 / 24 ) 4035.33538461538 20.6059338950311 195.833656711306 Trimmed Mean ( 5 / 24 ) 4033.40634920635 20.2662692318204 199.020663500978 Trimmed Mean ( 6 / 24 ) 4031.50491803279 19.9542197936934 202.037712309201 Trimmed Mean ( 7 / 24 ) 4029.73728813559 19.6850719247375 204.710315692145 Trimmed Mean ( 8 / 24 ) 4028.17192982456 19.4375055310110 207.23708211416 Trimmed Mean ( 9 / 24 ) 4026.69636363636 19.2228348644654 209.474637431337 Trimmed Mean ( 10 / 24 ) 4025.26037735849 19.0802613718361 210.964635070465 Trimmed Mean ( 11 / 24 ) 4024.08431372549 18.9807566890938 212.008634831597 Trimmed Mean ( 12 / 24 ) 4023.07346938776 18.915700874873 212.684345983282 Trimmed Mean ( 13 / 24 ) 4022.12127659574 18.8479985260559 213.397792398777 Trimmed Mean ( 14 / 24 ) 4021.28 18.7845379141054 214.073937745383 Trimmed Mean ( 15 / 24 ) 4020.68837209302 18.7536238533642 214.395276535941 Trimmed Mean ( 16 / 24 ) 4020.40975609756 18.7839269657495 214.034571334756 Trimmed Mean ( 17 / 24 ) 4020.48205128205 18.8642193106331 213.127401938964 Trimmed Mean ( 18 / 24 ) 4020.87297297297 18.9939573323959 211.692218878212 Trimmed Mean ( 19 / 24 ) 4021.48 19.1437278492562 210.067758571707 Trimmed Mean ( 20 / 24 ) 4022 19.3122708871376 208.261370374560 Trimmed Mean ( 21 / 24 ) 4022.53548387097 19.5022797390222 206.259757202757 Trimmed Mean ( 22 / 24 ) 4023.31379310345 19.7079193930112 204.147059507976 Trimmed Mean ( 23 / 24 ) 4024.11851851852 19.9097980410461 202.117495628152 Trimmed Mean ( 24 / 24 ) 4024.892 20.1283712869836 199.961136577542 Median 4015.8 Midrange 4126.55 Midmean - Weighted Average at Xnp 4017.03888888889 Midmean - Weighted Average at X(n+1)p 4020.87297297297 Midmean - Empirical Distribution Function 4020.87297297297 Midmean - Empirical Distribution Function - Averaging 4020.87297297297 Midmean - Empirical Distribution Function - Interpolation 4020.87297297297 Midmean - Closest Observation 4016.65 Midmean - True Basic - Statistics Graphics Toolkit 4020.87297297297 Midmean - MS Excel (old versions) 4020.87297297297 Number of observations 73

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244303663uqpgv7xl1ueuj3x/1y8wq1244303640.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244303663uqpgv7xl1ueuj3x/1y8wq1244303640.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244303663uqpgv7xl1ueuj3x/2tmi31244303640.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t1244303663uqpgv7xl1ueuj3x/2tmi31244303640.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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