Central tendency werkl.

*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: Fri, 19 Dec 2008 06:17:53 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/19/t1229692712vu2gxtodw7cr8z2.htm/, Retrieved Fri, 19 Dec 2008 14:18:37 +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/2008/Dec/19/t1229692712vu2gxtodw7cr8z2.htm/}, year = {2008}, } @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 = {2008}, 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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467037 460070 447988 442867 436087 431328 484015 509673 512927 502831 470984 471067 476049 474605 470439 461251 454724 455626 516847 525192 522975 518585 509239 512238 519164 517009 509933 509127 500857 506971 569323 579714 577992 565464 547344 554788 562325 560854 555332 543599 536662 542722 593530 610763 612613 611324 594167 595454 590865 589379 584428 573100 567456 569028 620735 628884 628232 612117 595404 597141 593408 590072 579799 574205 572775 572942 619567 625809 619916 587625 565742 557274 560576 548854 531673 525919 511038 498662 555362 564591 541657 527070 509846 514258

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 541870.047619048 5658.42196666791 95.7634568102279 Geometric Mean 539356.622085083 Harmonic Mean 536784.861334912 Quadratic Mean 544316.654950367 Winsorized Mean ( 1 / 28 ) 541918.940476191 5643.9202657087 96.018177962006 Winsorized Mean ( 2 / 28 ) 542022.678571429 5597.93896276612 96.825399879601 Winsorized Mean ( 3 / 28 ) 542024.357142857 5527.78763307378 98.05448275542 Winsorized Mean ( 4 / 28 ) 542306.119047619 5457.20636513298 99.3743103637247 Winsorized Mean ( 5 / 28 ) 542339.035714286 5443.30786999418 99.6340917448172 Winsorized Mean ( 6 / 28 ) 542159.75 5300.9645077327 102.275680059569 Winsorized Mean ( 7 / 28 ) 542216.833333333 5276.07693519664 102.768939875803 Winsorized Mean ( 8 / 28 ) 542692.357142857 5164.40762236794 105.083176392267 Winsorized Mean ( 9 / 28 ) 542996.75 5091.31038625516 106.651668982098 Winsorized Mean ( 10 / 28 ) 541439.964285714 4837.07816893688 111.935334798345 Winsorized Mean ( 11 / 28 ) 541229.916666667 4804.82351572578 112.643037750558 Winsorized Mean ( 12 / 28 ) 541728.202380952 4716.04064583247 114.869281896388 Winsorized Mean ( 13 / 28 ) 541760.238095238 4651.74204645201 116.463946772038 Winsorized Mean ( 14 / 28 ) 542981.738095238 4417.31430806634 122.921236803031 Winsorized Mean ( 15 / 28 ) 545575.488095238 4018.7429016914 135.757748490359 Winsorized Mean ( 16 / 28 ) 545509.202380952 3891.68502397249 140.173009639952 Winsorized Mean ( 17 / 28 ) 545748.214285714 3814.48749983838 143.072487276164 Winsorized Mean ( 18 / 28 ) 546486.857142857 3676.02892680726 148.662284226772 Winsorized Mean ( 19 / 28 ) 546577.785714286 3558.05323249124 153.617090582871 Winsorized Mean ( 20 / 28 ) 545843.261904762 3450.45617345999 158.194521090645 Winsorized Mean ( 21 / 28 ) 544794.511904762 3284.18149078256 165.884410905363 Winsorized Mean ( 22 / 28 ) 544817.559523809 3275.49017363978 166.331611649562 Winsorized Mean ( 23 / 28 ) 544369.880952381 3212.42592867428 169.457566661166 Winsorized Mean ( 24 / 28 ) 543603.595238095 3037.69486388819 178.95266628008 Winsorized Mean ( 25 / 28 ) 543631.869047619 2952.01034283314 184.156491987720 Winsorized Mean ( 26 / 28 ) 543796.226190476 2918.87801307892 186.303169832323 Winsorized Mean ( 27 / 28 ) 544170.369047619 2858.18171800804 190.390402968104 Winsorized Mean ( 28 / 28 ) 543882.702380952 2613.01179548958 208.143990516908 Trimmed Mean ( 1 / 28 ) 542156.975609756 5534.24033314721 97.9641184649173 Trimmed Mean ( 2 / 28 ) 542406.9125 5406.94009136809 100.316797178117 Trimmed Mean ( 3 / 28 ) 542613.807692308 5287.24937978295 102.626861098536 Trimmed Mean ( 4 / 28 ) 542830.973684211 5178.17988835180 104.830458846224 Trimmed Mean ( 5 / 28 ) 542979.918918919 5074.97719576045 106.991597789349 Trimmed Mean ( 6 / 28 ) 543129.458333333 4957.4231358502 109.558825916155 Trimmed Mean ( 7 / 28 ) 543323.4 4856.17722701788 111.882943022994 Trimmed Mean ( 8 / 28 ) 543518.676470588 4741.6170028098 114.627283508666 Trimmed Mean ( 9 / 28 ) 543650.136363636 4630.49806661609 117.4064060804 Trimmed Mean ( 10 / 28 ) 543745.421875 4512.97456969004 120.484929280766 Trimmed Mean ( 11 / 28 ) 544057.774193548 4422.43626750547 123.022185348627 Trimmed Mean ( 12 / 28 ) 544417.683333333 4317.58791296176 126.093016357338 Trimmed Mean ( 13 / 28 ) 544742.275862069 4206.97197836343 129.485596448870 Trimmed Mean ( 14 / 28 ) 545086.357142857 4082.8838116103 133.505233627472 Trimmed Mean ( 15 / 28 ) 545320.203703704 3976.87083684594 137.122935613418 Trimmed Mean ( 16 / 28 ) 545292.711538462 3921.09689605829 139.066369945262 Trimmed Mean ( 17 / 28 ) 545269.98 3871.56618263494 140.839638089022 Trimmed Mean ( 18 / 28 ) 545220.75 3819.66648147434 142.740407479124 Trimmed Mean ( 19 / 28 ) 545092.304347826 3775.13814826972 144.390028374898 Trimmed Mean ( 20 / 28 ) 544943.045454545 3735.25567090303 145.891765776451 Trimmed Mean ( 21 / 28 ) 544853.023809524 3699.14282227850 147.291697019127 Trimmed Mean ( 22 / 28 ) 544858.875 3678.10585000352 148.13572453318 Trimmed Mean ( 23 / 28 ) 544863.026315789 3643.38679868692 149.548498806703 Trimmed Mean ( 24 / 28 ) 544913.055555556 3601.79564717917 151.289275942770 Trimmed Mean ( 25 / 28 ) 545047.852941177 3574.98475923415 152.461587852458 Trimmed Mean ( 26 / 28 ) 545196.53125 3546.29836146324 153.736791346864 Trimmed Mean ( 27 / 28 ) 545347.333333333 3501.03536256943 155.767445014637 Trimmed Mean ( 28 / 28 ) 545478.107142857 3439.67358306576 158.584265038509 Median 548099 Midrange 530106 Midmean - Weighted Average at Xnp 544024.790697674 Midmean - Weighted Average at X(n+1)p 544853.023809524 Midmean - Empirical Distribution Function 544024.790697674 Midmean - Empirical Distribution Function - Averaging 544853.023809524 Midmean - Empirical Distribution Function - Interpolation 544853.023809524 Midmean - Closest Observation 544024.790697674 Midmean - True Basic - Statistics Graphics Toolkit 544853.023809524 Midmean - MS Excel (old versions) 544943.045454545 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/19/t1229692712vu2gxtodw7cr8z2/19c3x1229692671.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/19/t1229692712vu2gxtodw7cr8z2/19c3x1229692671.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/19/t1229692712vu2gxtodw7cr8z2/2eh3o1229692671.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/19/t1229692712vu2gxtodw7cr8z2/2eh3o1229692671.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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