*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 18 Oct 2010 18:40:38 +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/Oct/18/t12874273281objottucaibsqe.htm/, Retrieved Mon, 18 Oct 2010 20:42:10 +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/2010/Oct/18/t12874273281objottucaibsqe.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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

13,2 13,8 16,2 14,7 13,9 16,0 14,4 12,3 15,9 15,9 15,5 15,1 14,5 15,1 17,4 16,2 15,6 17,2 14,9 13,8 17,5 16,2 17,5 16,6 16,2 16,6 19,6 15,9 18,0 18,3 16,3 14,9 18,2 18,4 18,5 16,0 17,4 17,2 19,6 17,2 18,3 19,3 18,1 16,2 18,4 20,5 19,0 16,5 18,7 19,0 19,2 20,5 19,3 20,6 20,1 16,1 20,4 19,7 15,6 14,4 13,9 14,3 15,3 14,4 13,8 15,7 14,7 12,5 16,2 16,1 16 15,8 15,2

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 16.5958904109589 0.240381469699206 69.0398075680528 Geometric Mean 16.4707613353066 Harmonic Mean 16.3459959709283 Quadratic Mean 16.7207647134555 Winsorized Mean ( 1 / 24 ) 16.5972602739726 0.239402260164278 69.3279180513315 Winsorized Mean ( 2 / 24 ) 16.6164383561644 0.235185196130211 70.6525692499993 Winsorized Mean ( 3 / 24 ) 16.6369863013699 0.229638943403951 72.4484534493971 Winsorized Mean ( 4 / 24 ) 16.6205479452055 0.226009985031083 73.538998477964 Winsorized Mean ( 5 / 24 ) 16.5931506849315 0.220395803901030 75.2879609830626 Winsorized Mean ( 6 / 24 ) 16.5931506849315 0.217370902983678 76.3356569677473 Winsorized Mean ( 7 / 24 ) 16.5931506849315 0.217370902983678 76.3356569677473 Winsorized Mean ( 8 / 24 ) 16.6041095890411 0.203969720088434 81.4047770514276 Winsorized Mean ( 9 / 24 ) 16.6164383561644 0.202063307614175 82.2338234108898 Winsorized Mean ( 10 / 24 ) 16.6027397260274 0.199561663895846 83.1960377655128 Winsorized Mean ( 11 / 24 ) 16.5726027397260 0.194220726340498 85.3287033365933 Winsorized Mean ( 12 / 24 ) 16.5890410958904 0.191699537024922 86.5366779353973 Winsorized Mean ( 13 / 24 ) 16.5712328767123 0.177260132822313 93.4853912883132 Winsorized Mean ( 14 / 24 ) 16.5328767123288 0.170994659259088 96.686509297805 Winsorized Mean ( 15 / 24 ) 16.5534246575342 0.161743287776397 102.343812130359 Winsorized Mean ( 16 / 24 ) 16.5534246575342 0.161743287776397 102.343812130359 Winsorized Mean ( 17 / 24 ) 16.5767123287671 0.151596282378038 109.347749619806 Winsorized Mean ( 18 / 24 ) 16.5767123287671 0.151596282378038 109.347749619806 Winsorized Mean ( 19 / 24 ) 16.5767123287671 0.144014529591390 115.104443807163 Winsorized Mean ( 20 / 24 ) 16.5767123287671 0.136136634347112 121.765257443496 Winsorized Mean ( 21 / 24 ) 16.6054794520548 0.124353585992358 133.534383584847 Winsorized Mean ( 22 / 24 ) 16.4849315068493 0.0979172613967504 168.355724738400 Winsorized Mean ( 23 / 24 ) 16.4849315068493 0.0979172613967504 168.355724738400 Winsorized Mean ( 24 / 24 ) 16.4849315068493 0.0891288643650371 184.956148878252 Trimmed Mean ( 1 / 24 ) 16.6 0.232742377070672 71.3234959998686 Trimmed Mean ( 2 / 24 ) 16.6028985507246 0.224842191646653 73.8424511393156 Trimmed Mean ( 3 / 24 ) 16.5955223880597 0.218143899533675 76.0760324883523 Trimmed Mean ( 4 / 24 ) 16.58 0.212654920903833 77.9666886123827 Trimmed Mean ( 5 / 24 ) 16.5682539682540 0.207388183517529 79.8900578000074 Trimmed Mean ( 6 / 24 ) 16.5622950819672 0.202796890697678 81.6693738498074 Trimmed Mean ( 7 / 24 ) 16.5559322033898 0.198036403776116 83.6004486433043 Trimmed Mean ( 8 / 24 ) 16.5491228070175 0.192173343700244 86.1156000534145 Trimmed Mean ( 9 / 24 ) 16.54 0.188250853486469 87.8614874444057 Trimmed Mean ( 10 / 24 ) 16.5283018867925 0.183743869470920 89.9529433791984 Trimmed Mean ( 11 / 24 ) 16.5176470588235 0.178637674316257 92.4645213953076 Trimmed Mean ( 12 / 24 ) 16.5102040816327 0.173407351852578 95.2105196535659 Trimmed Mean ( 13 / 24 ) 16.5 0.167254590541947 98.652000800312 Trimmed Mean ( 14 / 24 ) 16.4911111111111 0.162674062866572 101.375172049630 Trimmed Mean ( 15 / 24 ) 16.4860465116279 0.158116733422297 104.265033528090 Trimmed Mean ( 16 / 24 ) 16.4780487804878 0.154150393586752 106.895924149648 Trimmed Mean ( 17 / 24 ) 16.4692307692308 0.148730745412494 110.731851195626 Trimmed Mean ( 18 / 24 ) 16.4567567567568 0.143818607627831 114.427173424895 Trimmed Mean ( 19 / 24 ) 16.4428571428571 0.136909816007062 120.099914107028 Trimmed Mean ( 20 / 24 ) 16.4272727272727 0.129339283041700 127.009152524654 Trimmed Mean ( 21 / 24 ) 16.4096774193548 0.120870929001259 135.761986401080 Trimmed Mean ( 22 / 24 ) 16.3862068965517 0.112157979048801 146.099341620822 Trimmed Mean ( 23 / 24 ) 16.3740740740741 0.109074400572214 150.118396142213 Trimmed Mean ( 24 / 24 ) 16.36 0.103923048454133 157.424173399038 Median 16.2 Midrange 16.45 Midmean - Weighted Average at Xnp 16.3702702702703 Midmean - Weighted Average at X(n+1)p 16.4692307692308 Midmean - Empirical Distribution Function 16.4692307692308 Midmean - Empirical Distribution Function - Averaging 16.4692307692308 Midmean - Empirical Distribution Function - Interpolation 16.4692307692308 Midmean - Closest Observation 16.4692307692308 Midmean - True Basic - Statistics Graphics Toolkit 16.4692307692308 Midmean - MS Excel (old versions) 16.4692307692308 Number of observations 73

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/18/t12874273281objottucaibsqe/1rhrl1287427236.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/18/t12874273281objottucaibsqe/1rhrl1287427236.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/18/t12874273281objottucaibsqe/2k9861287427236.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/18/t12874273281objottucaibsqe/2k9861287427236.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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by