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*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 16 Mar 2010 10:57:14 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/16/t1268758703lsorppxepr488if.htm/, Retrieved Tue, 16 Mar 2010 17:58:26 +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/Mar/16/t1268758703lsorppxepr488if.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 «

7054 8170 8620 8771 11379 12066 12657 27438 27733 29722 30169 30936 31879 32228 32745 33008 33228 33425 33666 34077 34571 34801 34870 34931 35117 35429 35699 36222 36279 36432 37013 37848 37898 37967 38064 38401 38529 38683 38708 39018 39253 39341 39383 39401 39486 39525 39556 40439 40600 40809 40870 40891 40898 41117 41519 41547 41629 41697 41756 41888 42438 43412 44720 44953 45315 45409 45633 47060 47221 48138 48428 49267 50380 50530 50669 51321 52073 56676 62557 68184 68897 68906 69116 70249 70938

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 39641.7176470588 1435.25851131042 27.6199146945766 Geometric Mean 36620.1768456173 Harmonic Mean 31780.8486880732 Quadratic Mean 41767.2480004299 Winsorized Mean ( 1 / 28 ) 39646.7411764706 1429.67843773940 27.7312297156555 Winsorized Mean ( 2 / 28 ) 39630.6705882353 1420.22324175155 27.904536007564 Winsorized Mean ( 3 / 28 ) 39628.5882352941 1417.01229831776 27.9662980217886 Winsorized Mean ( 4 / 28 ) 39750.8941176471 1386.03433997980 28.6795882115204 Winsorized Mean ( 5 / 28 ) 39749.3647058824 1365.78672661225 29.1036396322859 Winsorized Mean ( 6 / 28 ) 39393.8823529412 1262.68068961431 31.1986099708029 Winsorized Mean ( 7 / 28 ) 40126.8235294118 891.105511924803 45.0303841603865 Winsorized Mean ( 8 / 28 ) 39721.3647058824 798.034283301229 49.7740078804221 Winsorized Mean ( 9 / 28 ) 39852.3411764706 747.545801329161 53.3109022960357 Winsorized Mean ( 10 / 28 ) 39828.2235294118 725.302184174816 54.9125928453183 Winsorized Mean ( 11 / 28 ) 39909.4941176471 706.717777858747 56.4716147916458 Winsorized Mean ( 12 / 28 ) 40021.4470588235 683.399275599267 58.5623199903586 Winsorized Mean ( 13 / 28 ) 39904.6 645.76983181802 61.7938436170942 Winsorized Mean ( 14 / 28 ) 39851.5647058824 610.345362913481 65.2934668261443 Winsorized Mean ( 15 / 28 ) 39846.8 595.432493710098 66.9207683841998 Winsorized Mean ( 16 / 28 ) 39715.6 561.70233432037 70.7057770163156 Winsorized Mean ( 17 / 28 ) 39722.8 551.201313150692 72.0658660498151 Winsorized Mean ( 18 / 28 ) 39471.6470588235 497.904127403742 79.2755972211829 Winsorized Mean ( 19 / 28 ) 39513.4470588235 477.939544864270 82.6745714670775 Winsorized Mean ( 20 / 28 ) 39607.5647058824 459.21565009317 86.2504679399459 Winsorized Mean ( 21 / 28 ) 39574.9529411765 438.679505307688 90.2138177470104 Winsorized Mean ( 22 / 28 ) 39532.5058823529 427.607507612781 92.4504485504765 Winsorized Mean ( 23 / 28 ) 39195.0823529412 376.123840239585 104.207918136682 Winsorized Mean ( 24 / 28 ) 38972.5882352941 333.528235860173 116.849441951394 Winsorized Mean ( 25 / 28 ) 38902.5882352941 301.349657920636 129.094515997558 Winsorized Mean ( 26 / 28 ) 38944.8 285.339952441616 136.485618879356 Winsorized Mean ( 27 / 28 ) 39092.1882352941 260.988019029195 149.785374749027 Winsorized Mean ( 28 / 28 ) 39088.5647058824 255.877096201518 152.763046345883 Trimmed Mean ( 1 / 28 ) 39657.2771084337 1364.22575236383 29.0694388664916 Trimmed Mean ( 2 / 28 ) 39668.3333333333 1287.36833103548 30.8135071968303 Trimmed Mean ( 3 / 28 ) 39688.5949367089 1202.36021522387 33.008905679168 Trimmed Mean ( 4 / 28 ) 39710.6753246753 1101.37451413373 36.0555604066335 Trimmed Mean ( 5 / 28 ) 39699.28 990.412780186502 40.0835699964658 Trimmed Mean ( 6 / 28 ) 39687.6164383562 857.980778246807 46.2569995093056 Trimmed Mean ( 7 / 28 ) 39746.2253521127 725.39419719683 54.7925879552188 Trimmed Mean ( 8 / 28 ) 39679.2463768116 681.127046173399 58.2552793927819 Trimmed Mean ( 9 / 28 ) 39672.5671641791 652.11232748925 60.8370145630058 Trimmed Mean ( 10 / 28 ) 39646.4461538462 628.970758014925 63.0338464048361 Trimmed Mean ( 11 / 28 ) 39621.9206349206 605.98587723721 65.3842310906048 Trimmed Mean ( 12 / 28 ) 39585.4918032787 582.026935710301 68.0131612035599 Trimmed Mean ( 13 / 28 ) 39533.1525423729 557.550465181035 70.9050660186188 Trimmed Mean ( 14 / 28 ) 39490.5438596491 535.563268980952 73.7364680269992 Trimmed Mean ( 15 / 28 ) 39450.6909090909 515.773808430707 76.4883564543991 Trimmed Mean ( 16 / 28 ) 39408.3396226415 494.165713601051 79.7472154340043 Trimmed Mean ( 17 / 28 ) 39376.3333333333 474.332560317946 83.0141901010112 Trimmed Mean ( 18 / 28 ) 39340.9795918367 451.38188566779 87.156753163974 Trimmed Mean ( 19 / 28 ) 39327.8510638298 434.096428813383 90.5970389374863 Trimmed Mean ( 20 / 28 ) 39309.4 416.114496432670 94.4677494703926 Trimmed Mean ( 21 / 28 ) 39279.9302325581 396.749327952461 99.0044026924343 Trimmed Mean ( 22 / 28 ) 39250.8048780488 376.118815911052 104.357461572279 Trimmed Mean ( 23 / 28 ) 39222.8974358974 351.274213788077 111.658914592463 Trimmed Mean ( 24 / 28 ) 39225.6756756757 332.092313801399 118.116782730279 Trimmed Mean ( 25 / 28 ) 39251.2857142857 317.125783097058 123.771978837409 Trimmed Mean ( 26 / 28 ) 39287.2121212121 304.747945271045 128.917069764883 Trimmed Mean ( 27 / 28 ) 39323.3225806452 291.568802212898 134.868073271886 Trimmed Mean ( 28 / 28 ) 39348.4137931034 280.285518208386 140.386895636359 Median 39383 Midrange 38996 Midmean - Weighted Average at Xnp 39144.8571428571 Midmean - Weighted Average at X(n+1)p 39279.9302325581 Midmean - Empirical Distribution Function 39279.9302325581 Midmean - Empirical Distribution Function - Averaging 39279.9302325581 Midmean - Empirical Distribution Function - Interpolation 39279.9302325581 Midmean - Closest Observation 39172.9090909091 Midmean - True Basic - Statistics Graphics Toolkit 39279.9302325581 Midmean - MS Excel (old versions) 39279.9302325581 Number of observations 85

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/16/t1268758703lsorppxepr488if/1eywv1268758632.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/16/t1268758703lsorppxepr488if/1eywv1268758632.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/16/t1268758703lsorppxepr488if/24nv41268758632.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/16/t1268758703lsorppxepr488if/24nv41268758632.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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