paper central tendency export

*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: Mon, 28 Dec 2009 05:36:21 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/28/t12620038474qwbrumlmhcy1jj.htm/, Retrieved Mon, 28 Dec 2009 13:37:29 +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/2009/Dec/28/t12620038474qwbrumlmhcy1jj.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:

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Dataseries X:

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4223.4 4627.3 5175.3 4550.7 4639.3 5498.7 5031.0 4033.3 4643.5 4873.2 4608.7 4733.5 3955.6 4590.9 5127.5 5257.3 5416.9 5813.3 5261.9 4669.2 5855.8 5274.6 5516.7 5819.5 5156.0 5377.3 6386.8 5144.0 6138.5 5567.8 5822.6 5145.5 5706.6 6078.5 6074.5 5577.6 5727.5 6067.0 7069.9 5490.0 5948.3 6177.5 6890.1 5756.2 6528.8 6792.0 6657.4 5753.7 5750.9 5968.4 5871.7 7004.9 6363.4 6694.7 7101.6 5364.0 6958.6 6503.3 5316.0 5312.7 4478.0

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 5588.84262295082 100.268169699897 55.7389512512122 Geometric Mean 5534.1805271446 Harmonic Mean 5478.8297271264 Quadratic Mean 5642.55121513397 Winsorized Mean ( 1 / 20 ) 5589.59672131148 99.8001502995904 56.0078988311345 Winsorized Mean ( 2 / 20 ) 5593.69836065574 97.7412513517307 57.2296577268722 Winsorized Mean ( 3 / 20 ) 5603.94262295082 94.4851774149902 59.3102831181407 Winsorized Mean ( 4 / 20 ) 5604.21803278689 92.5019088418669 60.5848906574173 Winsorized Mean ( 5 / 20 ) 5599.47213114754 90.0622543380653 62.1733507816592 Winsorized Mean ( 6 / 20 ) 5591.6524590164 87.675157381631 63.776930957502 Winsorized Mean ( 7 / 20 ) 5589.50655737705 86.3878710327927 64.7024459632218 Winsorized Mean ( 8 / 20 ) 5574.21475409836 82.7320935948051 67.3766915823387 Winsorized Mean ( 9 / 20 ) 5571.07213114754 81.8965892365824 68.0256917055954 Winsorized Mean ( 10 / 20 ) 5556.1868852459 77.5790737964979 71.6196599590845 Winsorized Mean ( 11 / 20 ) 5563.56229508197 74.6459942656819 74.5326303147628 Winsorized Mean ( 12 / 20 ) 5554.4737704918 63.3445795552023 87.6866467422252 Winsorized Mean ( 13 / 20 ) 5579.79180327869 56.2084941121503 99.2695479822956 Winsorized Mean ( 14 / 20 ) 5588.16885245902 50.4580402720201 110.748828577826 Winsorized Mean ( 15 / 20 ) 5591.24262295082 49.6855885285293 112.532482527410 Winsorized Mean ( 16 / 20 ) 5589.66885245902 49.3083936115528 113.361406508067 Winsorized Mean ( 17 / 20 ) 5565.11639344262 44.5690501412538 124.865043697475 Winsorized Mean ( 18 / 20 ) 5564.88032786885 42.8114699035055 129.985733739387 Winsorized Mean ( 19 / 20 ) 5566.56229508197 35.5180441453666 156.724910648216 Winsorized Mean ( 20 / 20 ) 5562.85737704918 34.5576076777593 160.973451314147 Trimmed Mean ( 1 / 20 ) 5590.88474576271 96.4604451874453 57.96038712965 Trimmed Mean ( 2 / 20 ) 5592.26315789474 92.3562629968006 60.5509900079918 Trimmed Mean ( 3 / 20 ) 5591.46727272727 88.6816504790052 63.0510059581155 Trimmed Mean ( 4 / 20 ) 5586.68113207547 85.7124521650368 65.179340818747 Trimmed Mean ( 5 / 20 ) 5581.43725490196 82.7795014391604 67.4253548024096 Trimmed Mean ( 6 / 20 ) 5576.94693877551 79.929078741211 69.7736922107181 Trimmed Mean ( 7 / 20 ) 5573.76595744681 77.0608717112951 72.3293914754645 Trimmed Mean ( 8 / 20 ) 5570.71777777778 73.7464070885736 75.5388363678115 Trimmed Mean ( 9 / 20 ) 5570.0976744186 70.5257008429123 78.9796855308867 Trimmed Mean ( 10 / 20 ) 5569.93658536585 66.5040179197062 83.753384526191 Trimmed Mean ( 11 / 20 ) 5572.08717948718 62.4218475131635 89.2650153988495 Trimmed Mean ( 12 / 20 ) 5573.36486486487 57.768364241602 96.4778029988116 Trimmed Mean ( 13 / 20 ) 5576.10857142857 54.9228288810119 101.526244824515 Trimmed Mean ( 14 / 20 ) 5575.58484848485 53.0885022793578 105.024338775757 Trimmed Mean ( 15 / 20 ) 5573.81612903226 52.0795318382353 107.025081299600 Trimmed Mean ( 16 / 20 ) 5571.3724137931 50.6949096502508 109.900036359283 Trimmed Mean ( 17 / 20 ) 5568.78888888889 48.6223974199565 114.531351483776 Trimmed Mean ( 18 / 20 ) 5569.316 47.0732389226264 118.311722912337 Trimmed Mean ( 19 / 20 ) 5569.96956521739 45.1314853046261 123.416491339062 Trimmed Mean ( 20 / 20 ) 5570.49047619048 44.7702435748407 124.423948395065 Median 5567.8 Midrange 5528.6 Midmean - Weighted Average at Xnp 5557.12666666667 Midmean - Weighted Average at X(n+1)p 5573.81612903226 Midmean - Empirical Distribution Function 5573.81612903226 Midmean - Empirical Distribution Function - Averaging 5573.81612903226 Midmean - Empirical Distribution Function - Interpolation 5573.81612903226 Midmean - Closest Observation 5559.86875 Midmean - True Basic - Statistics Graphics Toolkit 5573.81612903226 Midmean - MS Excel (old versions) 5573.81612903226 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/28/t12620038474qwbrumlmhcy1jj/1cj7e1262003778.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t12620038474qwbrumlmhcy1jj/1cj7e1262003778.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t12620038474qwbrumlmhcy1jj/29q7y1262003778.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/28/t12620038474qwbrumlmhcy1jj/29q7y1262003778.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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