index eletriciteit en brandstof consumptie door huishoudens 1995=100

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 18 Oct 2010 13:48:50 +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/18/t1287409787qywrwnozw3xbgll.htm/, Retrieved Mon, 18 Oct 2010 15:49:49 +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/18/t1287409787qywrwnozw3xbgll.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 «

132,1 125 127,1 101,5 85,7 79,3 70,9 77,1 83,9 96,2 111,7 127,2 143,6 134,9 135,6 105,3 86,4 74,6 67,6 73,4 78,5 98,2 118,6 136,9 137,9 115,6 119,3 98,5 84,3 73,5 60,7 69,5 77,9 113,9 126,3 135,1 130,5 113,1 110 90,8 85,4 72,5 64,7 67,2 77,9 105,2 107,2 120,7 121,3 107,9 105,6 81,3 71,7 64,8 57,3 61,9 70,1 88,8 106,8 110,7 114,1 108 111,5 86,8 78,4 68 57,3 65,3 73,3 88,6 101,3 122,9 126,6 114,1 124,7

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 97.5746666666667 2.79323964666903 34.9324365286830 Geometric Mean 94.5373778483119 Harmonic Mean 91.4932199499188 Quadratic Mean 100.489688359884 Winsorized Mean ( 1 / 25 ) 97.4986666666667 2.77730538493721 35.1054900895859 Winsorized Mean ( 2 / 25 ) 97.5626666666667 2.75504501906177 35.4123674900571 Winsorized Mean ( 3 / 25 ) 97.5586666666667 2.73657778877086 35.6498788621995 Winsorized Mean ( 4 / 25 ) 97.6813333333333 2.70613163841755 36.0962977360754 Winsorized Mean ( 5 / 25 ) 97.6746666666667 2.70254807581699 36.1416944033972 Winsorized Mean ( 6 / 25 ) 97.4906666666667 2.65540019096448 36.7141145046227 Winsorized Mean ( 7 / 25 ) 97.5186666666667 2.60095248896435 37.4934440672912 Winsorized Mean ( 8 / 25 ) 97.2093333333333 2.53591369771968 38.3330605535769 Winsorized Mean ( 9 / 25 ) 97.2453333333333 2.52645554752773 38.4908150980503 Winsorized Mean ( 10 / 25 ) 97.3786666666667 2.4850285356154 39.1861362036841 Winsorized Mean ( 11 / 25 ) 97.4226666666667 2.46478738248167 39.5257892664870 Winsorized Mean ( 12 / 25 ) 97.3426666666667 2.41314506258805 40.3385060333955 Winsorized Mean ( 13 / 25 ) 97.4293333333333 2.38472373479430 40.8556060024023 Winsorized Mean ( 14 / 25 ) 97.2426666666667 2.31186767704299 42.0623842931381 Winsorized Mean ( 15 / 25 ) 97.0826666666667 2.24145896288161 43.3122659278392 Winsorized Mean ( 16 / 25 ) 96.976 2.21981075404724 43.6866069880911 Winsorized Mean ( 17 / 25 ) 96.6813333333333 2.17129155181956 44.5271079566968 Winsorized Mean ( 18 / 25 ) 96.7773333333333 2.10992726345177 45.8676159172469 Winsorized Mean ( 19 / 25 ) 96.6506666666667 1.91726942970102 50.4105814078194 Winsorized Mean ( 20 / 25 ) 96.464 1.83528836627582 52.5606775330599 Winsorized Mean ( 21 / 25 ) 96.464 1.83528836627582 52.5606775330599 Winsorized Mean ( 22 / 25 ) 96.552 1.80769960830716 53.4115289710202 Winsorized Mean ( 23 / 25 ) 96.3373333333333 1.77194124049297 54.3682437835983 Winsorized Mean ( 24 / 25 ) 96.1453333333333 1.68051825268207 57.2117161952198 Winsorized Mean ( 25 / 25 ) 96.7453333333333 1.58301262944583 61.1146945600817 Trimmed Mean ( 1 / 25 ) 97.4958904109589 2.74351694539432 35.5368282213931 Trimmed Mean ( 2 / 25 ) 97.4929577464789 2.70304643987323 36.0678071631841 Trimmed Mean ( 3 / 25 ) 97.4550724637681 2.66830608405261 36.5231983865036 Trimmed Mean ( 4 / 25 ) 97.4164179104478 2.63431895375927 36.9797354156492 Trimmed Mean ( 5 / 25 ) 97.34 2.60344981928565 37.3888520066459 Trimmed Mean ( 6 / 25 ) 97.2603174603175 2.56638789924145 37.8977462795334 Trimmed Mean ( 7 / 25 ) 97.2131147540984 2.53343055113630 38.3721253817263 Trimmed Mean ( 8 / 25 ) 97.157627118644 2.50551023767221 38.7775813715733 Trimmed Mean ( 9 / 25 ) 97.1491228070175 2.48464472633092 39.0998044016046 Trimmed Mean ( 10 / 25 ) 97.1345454545455 2.45902066156813 39.5013132555796 Trimmed Mean ( 11 / 25 ) 97.1 2.43396085777572 39.8938215007841 Trimmed Mean ( 12 / 25 ) 97.056862745098 2.40467396983289 40.3617554656871 Trimmed Mean ( 13 / 25 ) 97.0204081632653 2.37620356111933 40.8300070544307 Trimmed Mean ( 14 / 25 ) 96.9702127659574 2.34341227302134 41.3799201627183 Trimmed Mean ( 15 / 25 ) 96.9377777777778 2.31394605650456 41.8928425341996 Trimmed Mean ( 16 / 25 ) 96.9209302325581 2.28739760378033 42.3717022665316 Trimmed Mean ( 17 / 25 ) 96.9146341463415 2.25381130038682 43.0003319841852 Trimmed Mean ( 18 / 25 ) 96.9410256410256 2.21656053224362 43.7348875570302 Trimmed Mean ( 19 / 25 ) 96.9594594594595 2.17704189286637 44.5372501912672 Trimmed Mean ( 20 / 25 ) 96.9942857142857 2.16370341890796 44.8279024133721 Trimmed Mean ( 21 / 25 ) 97.0545454545455 2.15713268454511 44.992385563437 Trimmed Mean ( 22 / 25 ) 97.1225806451613 2.13929296770333 45.3993829323099 Trimmed Mean ( 23 / 25 ) 97.1896551724138 2.11261368264717 46.0044616631623 Trimmed Mean ( 24 / 25 ) 97.2925925925926 2.07458454239172 46.8973862498885 Trimmed Mean ( 25 / 25 ) 97.436 2.03695753514893 47.8340850600384 Median 98.5 Midrange 100.45 Midmean - Weighted Average at Xnp 96.371052631579 Midmean - Weighted Average at X(n+1)p 96.9410256410256 Midmean - Empirical Distribution Function 96.9410256410256 Midmean - Empirical Distribution Function - Averaging 96.9410256410256 Midmean - Empirical Distribution Function - Interpolation 96.9594594594594 Midmean - Closest Observation 96.371052631579 Midmean - True Basic - Statistics Graphics Toolkit 96.9410256410256 Midmean - MS Excel (old versions) 96.9410256410256 Number of observations 75

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/18/t1287409787qywrwnozw3xbgll/1zlge1287409728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/18/t1287409787qywrwnozw3xbgll/1zlge1287409728.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/18/t1287409787qywrwnozw3xbgll/2avgh1287409728.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/18/t1287409787qywrwnozw3xbgll/2avgh1287409728.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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