totaal maandelijkse verkoop autos

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sat, 16 Oct 2010 11:00:15 +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/16/t1287226761z77r91tus102ha6.htm/, Retrieved Sat, 16 Oct 2010 12:59:21 +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/16/t1287226761z77r91tus102ha6.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 «

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

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 39368.9166666667 1425.97023679976 27.6085121909841 Geometric Mean 36387.4749682362 Harmonic Mean 31595.7989601643 Quadratic Mean 41457.0025707933 Winsorized Mean ( 1 / 28 ) 39374 1420.22982320368 27.7236820102694 Winsorized Mean ( 2 / 28 ) 39357.7380952381 1410.44324575259 27.9045174017174 Winsorized Mean ( 3 / 28 ) 39355.6309523810 1407.12706073561 27.9687826711305 Winsorized Mean ( 4 / 28 ) 39479.3928571429 1375.46115753020 28.7026592070639 Winsorized Mean ( 5 / 28 ) 39477.8452380952 1354.5563347024 29.1444838628795 Winsorized Mean ( 6 / 28 ) 38698.0595238095 1159.86858012640 33.3641760686304 Winsorized Mean ( 7 / 28 ) 39546.2261904762 798.854696409598 49.5036536283935 Winsorized Mean ( 8 / 28 ) 39502.7023809524 780.43535608754 50.6162388374949 Winsorized Mean ( 9 / 28 ) 39645.9523809524 730.859221489664 54.2456757953256 Winsorized Mean ( 10 / 28 ) 39682.6190476190 719.258501512442 55.1715676132785 Winsorized Mean ( 11 / 28 ) 39763.4166666667 700.041528808342 56.8015110965697 Winsorized Mean ( 12 / 28 ) 39739.1309523810 651.447015888014 61.001324717423 Winsorized Mean ( 13 / 28 ) 39663.2976190476 621.138366911144 63.8558165651384 Winsorized Mean ( 14 / 28 ) 39701.1309523810 600.7124040368 66.0900801874382 Winsorized Mean ( 15 / 28 ) 39584.3452380952 566.99817220062 69.8138850861925 Winsorized Mean ( 16 / 28 ) 39595.5833333333 556.212484268253 71.1878723567754 Winsorized Mean ( 17 / 28 ) 39346.6547619048 505.592288697839 77.822893349981 Winsorized Mean ( 18 / 28 ) 39350.2976190476 491.185299266633 80.112938391682 Winsorized Mean ( 19 / 28 ) 39422 475.234655026254 82.9527046966348 Winsorized Mean ( 20 / 28 ) 39453.4285714286 446.681344525659 88.325668969509 Winsorized Mean ( 21 / 28 ) 39452.6785714286 430.538019881638 91.6357597925377 Winsorized Mean ( 22 / 28 ) 39128.1785714286 379.475944675941 103.111090756603 Winsorized Mean ( 23 / 28 ) 38878.1904761905 342.269085140076 113.589547417872 Winsorized Mean ( 24 / 28 ) 38774.1904761905 315.664615678672 122.833502870846 Winsorized Mean ( 25 / 28 ) 38827.7619047619 298.144920721246 130.231170166619 Winsorized Mean ( 26 / 28 ) 38893.0714285714 284.589111960567 136.663947403443 Winsorized Mean ( 27 / 28 ) 39039.3214285714 259.605887118746 150.379183853849 Winsorized Mean ( 28 / 28 ) 39030.9880952381 253.84822710075 153.757182159665 Trimmed Mean ( 1 / 28 ) 39378.0121951219 1351.72139891593 29.1317517253946 Trimmed Mean ( 2 / 28 ) 39382.225 1270.96195278817 30.9861557331478 Trimmed Mean ( 3 / 28 ) 39395.4102564103 1181.11390084327 33.3544548313956 Trimmed Mean ( 4 / 28 ) 39410.0657894737 1073.59085338345 36.7086452583606 Trimmed Mean ( 5 / 28 ) 39390.3918918919 953.816564936579 41.2976596758005 Trimmed Mean ( 6 / 28 ) 39369.9861111111 808.168380752613 48.7150785018928 Trimmed Mean ( 7 / 28 ) 39504.3714285714 693.729083931855 56.9449549450516 Trimmed Mean ( 8 / 28 ) 39496.9852941177 666.012097092467 59.3037055431052 Trimmed Mean ( 9 / 28 ) 39496.0757575758 637.359760272225 61.9682606581665 Trimmed Mean ( 10 / 28 ) 39474.21875 614.458412029217 64.2422952916186 Trimmed Mean ( 11 / 28 ) 39445.9838709677 589.313350441814 66.9355001738799 Trimmed Mean ( 12 / 28 ) 39405.5833333333 562.827096254061 70.0136571170795 Trimmed Mean ( 13 / 28 ) 39365.3275862069 540.940393210391 72.7720245710996 Trimmed Mean ( 14 / 28 ) 39330.9464285714 520.442652142 75.5721043744127 Trimmed Mean ( 15 / 28 ) 39289.8148148148 499.202811782402 78.7051152106509 Trimmed Mean ( 16 / 28 ) 39258.0961538462 479.914465150767 81.8022772902106 Trimmed Mean ( 17 / 28 ) 39222.66 457.815801663793 85.6734517626022 Trimmed Mean ( 18 / 28 ) 39209.8958333333 441.023232207951 88.9066447520957 Trimmed Mean ( 19 / 28 ) 39195.6521739130 422.565410101093 92.7564141242324 Trimmed Mean ( 20 / 28 ) 39172.9090909091 402.130019598047 97.4135408494614 Trimmed Mean ( 21 / 28 ) 39144.8571428571 382.039056098895 102.462972091325 Trimmed Mean ( 22 / 28 ) 39114.075 359.257870009081 108.874650398087 Trimmed Mean ( 23 / 28 ) 39112.6578947368 342.423471688880 114.223063336832 Trimmed Mean ( 24 / 28 ) 39136.4444444444 328.892271271754 118.99472217183 Trimmed Mean ( 25 / 28 ) 39173.7352941177 316.678515517577 123.701903901161 Trimmed Mean ( 26 / 28 ) 39210.0625 304.182411375347 128.903122053354 Trimmed Mean ( 27 / 28 ) 39244.2 290.143335168204 135.257975087551 Trimmed Mean ( 28 / 28 ) 39266.9642857143 277.94567377782 141.275680790423 Median 39362 Midrange 38996 Midmean - Weighted Average at Xnp 39038.488372093 Midmean - Weighted Average at X(n+1)p 39144.8571428571 Midmean - Empirical Distribution Function 39038.488372093 Midmean - Empirical Distribution Function - Averaging 39144.8571428571 Midmean - Empirical Distribution Function - Interpolation 39144.8571428571 Midmean - Closest Observation 39038.488372093 Midmean - True Basic - Statistics Graphics Toolkit 39144.8571428571 Midmean - MS Excel (old versions) 39172.9090909091 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/16/t1287226761z77r91tus102ha6/1baqt1287226811.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/16/t1287226761z77r91tus102ha6/1baqt1287226811.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/16/t1287226761z77r91tus102ha6/24j7w1287226811.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/16/t1287226761z77r91tus102ha6/24j7w1287226811.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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