totale productie industrie

*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 Nov 2010 19:58:46 +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/Nov/16/t1289937452a09rz2egojk17xi.htm/, Retrieved Tue, 16 Nov 2010 20:57:32 +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/Nov/16/t1289937452a09rz2egojk17xi.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?

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User-defined keywords:

Dataseries X:

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94,6 95,9 104,7 102,8 98,1 113,9 80,9 95,7 113,2 105,9 108,8 102,3 99 100,7 115,5 100,7 109,9 114,6 85,4 100,5 114,8 116,5 112,9 102 106 105,3 118,8 106,1 109,3 117,2 92,5 104,2 112,5 122,4 113,3 100 110,7 112,8 109,8 117,3 109,1 115,9 96 99,8 116,8 115,7 99,4 94,3 91 93,2 103,1 94,1 91,8 102,7 82,6 89,1 104,5 105,1 95,1 88,7 86,3 91,8 111,5 99,7 97,5 111,7 86,2 95,4

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 103.170588235294 1.20661961658906 85.5038214337527 Geometric Mean 102.687720580833 Harmonic Mean 102.195149889976 Quadratic Mean 103.642258017948 Winsorized Mean ( 1 / 22 ) 103.142647058824 1.18843992177051 86.7882718927548 Winsorized Mean ( 2 / 22 ) 103.180882352941 1.16003325872090 88.9464862987742 Winsorized Mean ( 3 / 22 ) 103.211764705882 1.15130290244834 89.6477933707924 Winsorized Mean ( 4 / 22 ) 103.194117647059 1.14578833762218 90.0638575718221 Winsorized Mean ( 5 / 22 ) 103.348529411765 1.10496225418523 93.5312758606144 Winsorized Mean ( 6 / 22 ) 103.330882352941 1.08876305630275 94.90667574985 Winsorized Mean ( 7 / 22 ) 103.505882352941 1.04868721468543 98.7004331734787 Winsorized Mean ( 8 / 22 ) 103.576470588235 1.02818514653411 100.737178452129 Winsorized Mean ( 9 / 22 ) 103.483823529412 1.0124371674195 102.212588454424 Winsorized Mean ( 10 / 22 ) 103.557352941176 0.99008765093063 104.594126432986 Winsorized Mean ( 11 / 22 ) 103.557352941176 0.952857898435739 108.680793968525 Winsorized Mean ( 12 / 22 ) 103.610294117647 0.91059546867767 113.783010877603 Winsorized Mean ( 13 / 22 ) 103.629411764706 0.901630215154422 114.935602226859 Winsorized Mean ( 14 / 22 ) 103.629411764706 0.88240795848376 117.439343977328 Winsorized Mean ( 15 / 22 ) 103.717647058824 0.862294092881539 120.281059461081 Winsorized Mean ( 16 / 22 ) 103.717647058824 0.840765937996706 123.360905064674 Winsorized Mean ( 17 / 22 ) 103.592647058824 0.798952112699262 129.660646003971 Winsorized Mean ( 18 / 22 ) 103.592647058824 0.783169973311035 132.273517357747 Winsorized Mean ( 19 / 22 ) 103.397058823529 0.745866486427765 138.626765922594 Winsorized Mean ( 20 / 22 ) 103.602941176471 0.647813132843446 159.927201107712 Winsorized Mean ( 21 / 22 ) 103.757352941176 0.617616407743162 167.996432154899 Winsorized Mean ( 22 / 22 ) 103.886764705882 0.554947831556828 187.200956195184 Trimmed Mean ( 1 / 22 ) 103.216666666667 1.15946813490771 89.0207014398741 Trimmed Mean ( 2 / 22 ) 103.2953125 1.12456435499675 91.8536249535476 Trimmed Mean ( 3 / 22 ) 103.358064516129 1.10074622154561 93.898177884271 Trimmed Mean ( 4 / 22 ) 103.413333333333 1.07570097147751 96.1357627029857 Trimmed Mean ( 5 / 22 ) 103.477586206897 1.04698178573936 98.8341799411747 Trimmed Mean ( 6 / 22 ) 103.508928571429 1.02500008484546 100.984312198407 Trimmed Mean ( 7 / 22 ) 103.546296296296 1.00221527152351 103.317420157539 Trimmed Mean ( 8 / 22 ) 103.553846153846 0.984336074636877 105.201718012872 Trimmed Mean ( 9 / 22 ) 103.55 0.966522273991887 107.136692848601 Trimmed Mean ( 10 / 22 ) 103.560416666667 0.947204451479136 109.332696341269 Trimmed Mean ( 11 / 22 ) 103.560869565217 0.927275778649608 111.682923192530 Trimmed Mean ( 12 / 22 ) 103.561363636364 0.90966861929213 113.845153542783 Trimmed Mean ( 13 / 22 ) 103.554761904762 0.895615869708537 115.624081045440 Trimmed Mean ( 14 / 22 ) 103.545 0.877999985398049 117.932803783655 Trimmed Mean ( 15 / 22 ) 103.534210526316 0.857999561617178 120.669304691919 Trimmed Mean ( 16 / 22 ) 103.511111111111 0.834777584462042 123.998431483779 Trimmed Mean ( 17 / 22 ) 103.485294117647 0.807398193147852 128.171322398162 Trimmed Mean ( 18 / 22 ) 103.471875 0.7798655071058 132.679127435703 Trimmed Mean ( 19 / 22 ) 103.456666666667 0.743967051138743 139.060817960032 Trimmed Mean ( 20 / 22 ) 103.464285714286 0.702851604486288 147.206444509588 Trimmed Mean ( 21 / 22 ) 103.446153846154 0.675351322116144 153.173837761975 Trimmed Mean ( 22 / 22 ) 103.404166666667 0.641936584486673 161.081591492958 Median 102.95 Midrange 101.65 Midmean - Weighted Average at Xnp 103.254285714286 Midmean - Weighted Average at X(n+1)p 103.485294117647 Midmean - Empirical Distribution Function 103.254285714286 Midmean - Empirical Distribution Function - Averaging 103.485294117647 Midmean - Empirical Distribution Function - Interpolation 103.485294117647 Midmean - Closest Observation 103.254285714286 Midmean - True Basic - Statistics Graphics Toolkit 103.485294117647 Midmean - MS Excel (old versions) 103.511111111111 Number of observations 68

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289937452a09rz2egojk17xi/1dr301289937522.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289937452a09rz2egojk17xi/1dr301289937522.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289937452a09rz2egojk17xi/2dr301289937522.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289937452a09rz2egojk17xi/2dr301289937522.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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