duurzame consumptiegoederen

*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, 05 Dec 2008 08:44:18 -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/05/t1228492023kdvwxgjo5qirqcu.htm/, Retrieved Fri, 05 Dec 2008 15:47:05 +0000

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/05/t1228492023kdvwxgjo5qirqcu.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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98,1 101,1 111,1 93,3 100 108 70,4 75,4 105,5 112,3 102,5 93,5 86,7 95,2 103,8 97 95,5 101 67,5 64 106,7 100,6 101,2 93,1 84,2 85,8 91,8 92,4 80,3 79,7 62,5 57,1 100,8 100,7 86,2 83,2 71,7 77,5 89,8 80,3 78,7 93,8 57,6 60,6 91 85,3 77,4 77,3 68,3 69,9 81,7 75,1 69,9 84 54,3 60 89,9 77 85,3 77,6 69,2 75,5 85,7 72,2 79,9 85,3 52,2 61,2 82,4 85,4 78,2 70,2 70,2 69,3 77,5 66,1 69 79,2 56,2 63,3 77,8 92 78,1 65,1 71,1

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 81.8176470588235 1.57549527713191 51.9313819891402 Geometric Mean 80.5179965950395 Harmonic Mean 79.1964698092391 Quadratic Mean 83.0820735247771 Winsorized Mean ( 1 / 28 ) 81.8282352941176 1.56695087573285 52.221315014644 Winsorized Mean ( 2 / 28 ) 81.8 1.54236531220801 53.0354251048976 Winsorized Mean ( 3 / 28 ) 81.7858823529412 1.52707419940207 53.557241936878 Winsorized Mean ( 4 / 28 ) 81.7529411764706 1.5118074850349 54.0762907881643 Winsorized Mean ( 5 / 28 ) 81.7941176470588 1.46760762368221 55.7329604501771 Winsorized Mean ( 6 / 28 ) 81.744705882353 1.44412894848020 56.6048523356457 Winsorized Mean ( 7 / 28 ) 81.6870588235294 1.41763778371386 57.6219537613688 Winsorized Mean ( 8 / 28 ) 81.8 1.39549093797960 58.6173638063392 Winsorized Mean ( 9 / 28 ) 81.8741176470588 1.37998513463878 59.3297098584251 Winsorized Mean ( 10 / 28 ) 81.9329411764706 1.36305739323101 60.1096781275332 Winsorized Mean ( 11 / 28 ) 82.0623529411765 1.33903365849148 61.2847574224727 Winsorized Mean ( 12 / 28 ) 82.1894117647059 1.31576417340888 62.465154034229 Winsorized Mean ( 13 / 28 ) 82.3117647058824 1.27005195394813 64.8097618762798 Winsorized Mean ( 14 / 28 ) 82.1305882352941 1.20112928134425 68.3778087096314 Winsorized Mean ( 15 / 28 ) 82.06 1.15400920919287 71.1086179783554 Winsorized Mean ( 16 / 28 ) 81.815294117647 1.10635103901031 73.9505737625872 Winsorized Mean ( 17 / 28 ) 81.775294117647 1.09484008256601 74.6915420980824 Winsorized Mean ( 18 / 28 ) 81.6058823529412 1.03521923271315 78.829565539528 Winsorized Mean ( 19 / 28 ) 81.5388235294118 1.02586315930443 79.4831384574704 Winsorized Mean ( 20 / 28 ) 81.5623529411765 1.00984644875232 80.7670839878162 Winsorized Mean ( 21 / 28 ) 81.5129411764706 1.00303012658282 81.266692810288 Winsorized Mean ( 22 / 28 ) 81.3835294117647 0.971378712143553 83.7814627748787 Winsorized Mean ( 23 / 28 ) 81.464705882353 0.931487328914441 87.4565905016574 Winsorized Mean ( 24 / 28 ) 81.5776470588235 0.901603576812745 90.480616045478 Winsorized Mean ( 25 / 28 ) 81.4894117647059 0.850916499686149 95.7666372608386 Winsorized Mean ( 26 / 28 ) 82.04 0.695048917126615 118.034857660321 Winsorized Mean ( 27 / 28 ) 82.1035294117647 0.679508899649288 120.827747001019 Winsorized Mean ( 28 / 28 ) 81.115294117647 0.543547600554189 149.233101268304 Trimmed Mean ( 1 / 28 ) 81.8072289156626 1.52924357249063 53.4952249512651 Trimmed Mean ( 2 / 28 ) 81.7851851851852 1.48561321993035 55.0514656762542 Trimmed Mean ( 3 / 28 ) 81.7772151898734 1.45023691599647 56.3888660451618 Trimmed Mean ( 4 / 28 ) 81.774025974026 1.41576709049779 57.7595188663934 Trimmed Mean ( 5 / 28 ) 81.78 1.38084841396235 59.2244587987264 Trimmed Mean ( 6 / 28 ) 81.7767123287671 1.35310472312196 60.4363512530555 Trimmed Mean ( 7 / 28 ) 81.7830985915493 1.32650277092420 61.6531683040279 Trimmed Mean ( 8 / 28 ) 81.8 1.30123555947594 62.8633297056099 Trimmed Mean ( 9 / 28 ) 81.8 1.27598101243619 64.1075370266064 Trimmed Mean ( 10 / 28 ) 81.7892307692308 1.24891130104176 65.4884223571422 Trimmed Mean ( 11 / 28 ) 81.7698412698413 1.21969592149628 67.0411697118153 Trimmed Mean ( 12 / 28 ) 81.7327868852459 1.18902936332063 68.7390819827938 Trimmed Mean ( 13 / 28 ) 81.677966101695 1.15612633364061 70.647959245503 Trimmed Mean ( 14 / 28 ) 81.6052631578947 1.12458965240424 72.5644798379858 Trimmed Mean ( 15 / 28 ) 81.5472727272727 1.09907170669966 74.1964989455932 Trimmed Mean ( 16 / 28 ) 81.4924528301887 1.07607187948376 75.7314212776238 Trimmed Mean ( 17 / 28 ) 81.4588235294118 1.05605323867056 77.1351486331868 Trimmed Mean ( 18 / 28 ) 81.4265306122449 1.03246112867731 78.8664370508173 Trimmed Mean ( 19 / 28 ) 81.4085106382979 1.01359778959301 80.316385329713 Trimmed Mean ( 20 / 28 ) 81.3955555555556 0.990495007128772 82.1766439706783 Trimmed Mean ( 21 / 28 ) 81.3790697674419 0.963184767498097 84.4895730430066 Trimmed Mean ( 22 / 28 ) 81.3658536585366 0.928253078375388 87.6548169395157 Trimmed Mean ( 23 / 28 ) 81.3641025641026 0.888944598413428 91.528878975495 Trimmed Mean ( 24 / 28 ) 81.354054054054 0.845688540792026 96.1986004656777 Trimmed Mean ( 25 / 28 ) 81.3314285714286 0.794040528023638 102.427301505456 Trimmed Mean ( 26 / 28 ) 81.3151515151515 0.736894605300159 110.348414726187 Trimmed Mean ( 27 / 28 ) 81.2387096774194 0.703992873548895 115.397062569522 Trimmed Mean ( 28 / 28 ) 81.1448275862069 0.659593586746608 123.022462947900 Median 80.3 Midrange 82.25 Midmean - Weighted Average at Xnp 80.846511627907 Midmean - Weighted Average at X(n+1)p 81.125 Midmean - Empirical Distribution Function 81.125 Midmean - Empirical Distribution Function - Averaging 81.125 Midmean - Empirical Distribution Function - Interpolation 81.125 Midmean - Closest Observation 81.125 Midmean - True Basic - Statistics Graphics Toolkit 81.125 Midmean - MS Excel (old versions) 81.125 Number of observations 85

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228492023kdvwxgjo5qirqcu/1hcz11228491856.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228492023kdvwxgjo5qirqcu/1hcz11228491856.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228492023kdvwxgjo5qirqcu/2x73h1228491856.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228492023kdvwxgjo5qirqcu/2x73h1228491856.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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