Central Tendency Nieuwbouw

*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: Sat, 18 Dec 2010 22:46:22 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/18/t12927123010l09ryottionl3p.htm/, Retrieved Sat, 18 Dec 2010 23:45:02 +0100

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/2010/Dec/18/t12927123010l09ryottionl3p.htm/}, year = {2010}, } @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 = {2010}, 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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4143 4429 5219 4929 5761 5592 4163 4962 5208 4755 4491 5732 5731 5040 6102 4904 5369 5578 4619 4731 5011 5299 4146 4625 4736 4219 5116 4205 4121 5103 4300 4578 3809 5657 4248 3830 4736 4839 4411 4570 4104 4801 3953 3828 4440 4026 4109 4785 3224 3552 3940 3913 3681 4309 3830 4143 4087 3818 3380 3430 3458 3970 5260 5024 5634 6549 4676

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 4581.20895522388 87.0545183322465 52.6245971259015 Geometric Mean 4527.52601444762 Harmonic Mean 4474.7490542078 Quadratic Mean 4635.47794473444 Winsorized Mean ( 1 / 22 ) 4576.86567164179 84.470717284047 54.1828673746348 Winsorized Mean ( 2 / 22 ) 4568.17910447761 81.6290988607066 55.9626305843807 Winsorized Mean ( 3 / 22 ) 4568.13432835821 81.081654448835 56.3399249732976 Winsorized Mean ( 4 / 22 ) 4573.68656716418 79.9429019693746 57.211915685977 Winsorized Mean ( 5 / 22 ) 4577.79104477612 76.9668749265725 59.4774186836012 Winsorized Mean ( 6 / 22 ) 4587.19402985075 74.6099558860959 61.4823313507092 Winsorized Mean ( 7 / 22 ) 4583.74626865672 73.5392200786149 62.3306347790553 Winsorized Mean ( 8 / 22 ) 4583.26865671642 73.005261738865 62.7799770530304 Winsorized Mean ( 9 / 22 ) 4555.46268656716 67.4874205688224 67.5009156991204 Winsorized Mean ( 10 / 22 ) 4545.01492537313 65.623273788026 69.2591920978262 Winsorized Mean ( 11 / 22 ) 4552.23880597015 62.3297140715609 73.034809701577 Winsorized Mean ( 12 / 22 ) 4549.73134328358 60.3346523719026 75.4082631526416 Winsorized Mean ( 13 / 22 ) 4550.11940298507 59.5921898573057 76.3542909545763 Winsorized Mean ( 14 / 22 ) 4534.44776119403 55.9258501609846 81.0796393464107 Winsorized Mean ( 15 / 22 ) 4544.07462686567 53.5889269828704 84.7950291730637 Winsorized Mean ( 16 / 22 ) 4543.59701492537 49.1536927268392 92.4365345280447 Winsorized Mean ( 17 / 22 ) 4543.85074626866 47.9315113948151 94.7988205262432 Winsorized Mean ( 18 / 22 ) 4541.70149253731 47.2168272125001 96.1881973157008 Winsorized Mean ( 19 / 22 ) 4531.20895522388 44.6818166452707 101.410580308253 Winsorized Mean ( 20 / 22 ) 4527.92537313433 42.346048689753 106.926750269146 Winsorized Mean ( 21 / 22 ) 4520.08955223881 41.230945087521 109.628570061734 Winsorized Mean ( 22 / 22 ) 4499.73134328358 38.147335014945 117.956636853419 Trimmed Mean ( 1 / 22 ) 4571.81538461538 81.736157650428 55.9338182272805 Trimmed Mean ( 2 / 22 ) 4566.44444444444 78.4325768609285 58.2212726803732 Trimmed Mean ( 3 / 22 ) 4565.49180327869 76.3044936438631 59.832541771226 Trimmed Mean ( 4 / 22 ) 4564.49152542373 73.9677784307843 61.7091877336153 Trimmed Mean ( 5 / 22 ) 4561.78947368421 71.5393302663907 63.7661752870413 Trimmed Mean ( 6 / 22 ) 4557.89090909091 69.5346420590557 65.5484917175514 Trimmed Mean ( 7 / 22 ) 4551.71698113208 67.720715731282 67.213066666239 Trimmed Mean ( 8 / 22 ) 4545.70588235294 65.7294114137511 69.1578668450079 Trimmed Mean ( 9 / 22 ) 4539.28571428571 63.3334027031485 71.6728538266277 Trimmed Mean ( 10 / 22 ) 4536.72340425532 61.7443529956594 73.4759242610291 Trimmed Mean ( 11 / 22 ) 4535.48888888889 60.1418409474444 75.4132034776301 Trimmed Mean ( 12 / 22 ) 4533.11627906977 58.8233198318321 77.0632513096733 Trimmed Mean ( 13 / 22 ) 4530.85365853659 57.5233628144465 78.765451754825 Trimmed Mean ( 14 / 22 ) 4528.30769230769 55.9180665539663 80.9811206175635 Trimmed Mean ( 15 / 22 ) 4527.51351351351 54.6408506063679 82.8594991342589 Trimmed Mean ( 16 / 22 ) 4525.4 53.4050040144321 84.7373777703876 Trimmed Mean ( 17 / 22 ) 4523.09090909091 52.7358404742298 85.7688218944986 Trimmed Mean ( 18 / 22 ) 4520.45161290323 51.9516491238486 87.0126683009971 Trimmed Mean ( 19 / 22 ) 4517.72413793103 50.8535494242403 88.8379314537595 Trimmed Mean ( 20 / 22 ) 4515.96296296296 49.8579886834575 90.5765170679925 Trimmed Mean ( 21 / 22 ) 4514.36 48.9094360357317 92.3003895751721 Trimmed Mean ( 22 / 22 ) 4513.5652173913 47.5805464817898 94.86156740799 Median 4570 Midrange 4886.5 Midmean - Weighted Average at Xnp 4510.26470588235 Midmean - Weighted Average at X(n+1)p 4525.4 Midmean - Empirical Distribution Function 4525.4 Midmean - Empirical Distribution Function - Averaging 4525.4 Midmean - Empirical Distribution Function - Interpolation 4523.09090909091 Midmean - Closest Observation 4510.26470588235 Midmean - True Basic - Statistics Graphics Toolkit 4525.4 Midmean - MS Excel (old versions) 4525.4 Number of observations 67

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t12927123010l09ryottionl3p/12vhc1292712379.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t12927123010l09ryottionl3p/12vhc1292712379.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t12927123010l09ryottionl3p/22vhc1292712379.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t12927123010l09ryottionl3p/22vhc1292712379.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')

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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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