Central tendency werkloosheid

*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: Tue, 16 Dec 2008 10:58:10 -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/16/t1229450384ka5u30v2ys3os3w.htm/, Retrieved Tue, 16 Dec 2008 18:59:44 +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/16/t1229450384ka5u30v2ys3os3w.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 516922 507561 492622 490243 469357 477580 528379 533590 517945 506174

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 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 537845.287234043 5240.53955361467 102.631662585785 Geometric Mean 535438.60392308 Harmonic Mean 533003.027855208 Quadratic Mean 540214.434921429 Winsorized Mean ( 1 / 31 ) 537888.978723404 5228.4148034022 102.878023062247 Winsorized Mean ( 2 / 31 ) 537981.680851064 5189.6157283085 103.665032059399 Winsorized Mean ( 3 / 31 ) 537983.180851064 5129.30624923893 104.884199677274 Winsorized Mean ( 4 / 31 ) 538234.968085106 5070.83757441711 106.143208135981 Winsorized Mean ( 5 / 31 ) 538264.382978723 5059.16434532929 106.393931139173 Winsorized Mean ( 6 / 31 ) 538104.170212766 4935.72850955893 109.022238393102 Winsorized Mean ( 7 / 31 ) 538155.180851064 4914.8681710562 109.495343948445 Winsorized Mean ( 8 / 31 ) 538580.117021277 4823.22015320391 111.664012820048 Winsorized Mean ( 9 / 31 ) 538748.531914894 4779.45900676256 112.721655558214 Winsorized Mean ( 10 / 31 ) 537414.489361702 4541.10406167967 118.344455899327 Winsorized Mean ( 11 / 31 ) 537280.85106383 4503.32782837827 119.307514695708 Winsorized Mean ( 12 / 31 ) 537285.063829787 4500.7646162423 119.376397043925 Winsorized Mean ( 13 / 31 ) 537603.287234043 4400.69090293305 122.163382771494 Winsorized Mean ( 14 / 31 ) 537723.478723404 4354.66879564603 123.482061198556 Winsorized Mean ( 15 / 31 ) 537948.319148936 4315.00235570289 124.669299064915 Winsorized Mean ( 16 / 31 ) 538610.787234043 4094.3750492191 131.548961870694 Winsorized Mean ( 17 / 31 ) 539593.712765957 3917.46961267565 137.740369707019 Winsorized Mean ( 18 / 31 ) 539916.563829787 3838.04025461038 140.675065401209 Winsorized Mean ( 19 / 31 ) 540782.882978723 3631.75280945267 148.904099852606 Winsorized Mean ( 20 / 31 ) 540569.691489362 3480.70231430152 155.304775495528 Winsorized Mean ( 21 / 31 ) 539976.553191489 3289.42567804455 164.155267831583 Winsorized Mean ( 22 / 31 ) 540739.063829787 3193.77018454993 169.310574206512 Winsorized Mean ( 23 / 31 ) 540512.734042553 3116.24399476458 173.450068399855 Winsorized Mean ( 24 / 31 ) 539696.478723404 2975.92994686841 181.353892181276 Winsorized Mean ( 25 / 31 ) 539819.085106383 2891.46615735996 186.693897050229 Winsorized Mean ( 26 / 31 ) 539806.361702128 2882.52677014648 187.268464353133 Winsorized Mean ( 27 / 31 ) 539883.053191489 2862.418014034 188.610835504991 Winsorized Mean ( 28 / 31 ) 538906.329787234 2731.41401004222 197.299394308556 Winsorized Mean ( 29 / 31 ) 538842.159574468 2717.45946548145 198.288940982972 Winsorized Mean ( 30 / 31 ) 538693.117021277 2617.64866038832 205.792750254484 Winsorized Mean ( 31 / 31 ) 538523.606382979 2506.45058255964 214.855066415483 Trimmed Mean ( 1 / 31 ) 538013.532608696 5131.42131110959 104.846883541581 Trimmed Mean ( 2 / 31 ) 538143.622222222 5020.77179295159 107.183445974919 Trimmed Mean ( 3 / 31 ) 538143.622222222 4917.7371427179 109.429114774688 Trimmed Mean ( 4 / 31 ) 538320.081395349 4825.29775823205 111.562044119861 Trimmed Mean ( 5 / 31 ) 538343.892857143 4738.66869178025 113.606569244007 Trimmed Mean ( 6 / 31 ) 538343.892857143 4641.89867381004 115.974934113604 Trimmed Mean ( 7 / 31 ) 538412.6375 4561.0070602052 118.046876576371 Trimmed Mean ( 8 / 31 ) 538456.961538462 4471.52531624578 120.419079275289 Trimmed Mean ( 9 / 31 ) 538437.921052632 4386.51752935691 122.748380109989 Trimmed Mean ( 10 / 31 ) 538394.081081081 4295.48902117635 125.339415006499 Trimmed Mean ( 11 / 31 ) 538521.972222222 4233.11455827121 127.216489138001 Trimmed Mean ( 12 / 31 ) 538521.972222222 4165.2961113385 129.287800393420 Trimmed Mean ( 13 / 31 ) 538833.426470588 4084.49721198067 131.921604669010 Trimmed Mean ( 14 / 31 ) 538968.196969697 4005.2410106612 134.565734130621 Trimmed Mean ( 15 / 31 ) 539098.78125 3917.65065789637 137.607670598040 Trimmed Mean ( 16 / 31 ) 539215.064516129 3818.60624233343 141.207296667130 Trimmed Mean ( 17 / 31 ) 539274.233333333 3736.86850488561 144.311803486872 Trimmed Mean ( 18 / 31 ) 539243.775862069 3666.72264506929 147.06423912024 Trimmed Mean ( 19 / 31 ) 539181.035714286 3592.98285108051 150.065017858947 Trimmed Mean ( 20 / 31 ) 539034.277777778 3535.36423521299 152.469234261319 Trimmed Mean ( 21 / 31 ) 538895.5 3487.34354330984 154.528939666361 Trimmed Mean ( 22 / 31 ) 538798.72 3456.92192682969 155.860829779898 Trimmed Mean ( 23 / 31 ) 538626 3429.79184915734 157.043349476830 Trimmed Mean ( 24 / 31 ) 538626 3403.98881838776 158.233774767542 Trimmed Mean ( 25 / 31 ) 538348.159090909 3390.72669513212 158.770731909412 Trimmed Mean ( 26 / 31 ) 538216.476190476 3381.48277790676 159.165819121412 Trimmed Mean ( 27 / 31 ) 538072.775 3363.04378473741 159.995768548108 Trimmed Mean ( 28 / 31 ) 537906.921052632 3334.36161447378 161.322310908837 Trimmed Mean ( 29 / 31 ) 537813.722222222 3316.28546830927 162.173530403706 Trimmed Mean ( 30 / 31 ) 537715.676470588 3284.64958335283 163.705644338995 Trimmed Mean ( 31 / 31 ) 537715.676470588 3254.75661423585 165.209181577109 Median 535126 Midrange 530106 Midmean - Weighted Average at Xnp 537788.425531915 Midmean - Weighted Average at X(n+1)p 538626 Midmean - Empirical Distribution Function 538626 Midmean - Empirical Distribution Function - Averaging 538626 Midmean - Empirical Distribution Function - Interpolation 538458.369565217 Midmean - Closest Observation 538626 Midmean - True Basic - Statistics Graphics Toolkit 538626 Midmean - MS Excel (old versions) 538626 Number of observations 94

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229450384ka5u30v2ys3os3w/1jhfb1229450284.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229450384ka5u30v2ys3os3w/1jhfb1229450284.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229450384ka5u30v2ys3os3w/2lutu1229450284.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229450384ka5u30v2ys3os3w/2lutu1229450284.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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