Centrummaten-Consumentenprijzen Kabeljauw-Toon Baeten

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 17 May 2011 14:56:23 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/17/t13056439818a6rep1g8fysngh.htm/, Retrieved Tue, 17 May 2011 16:53:03 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

12,32 12,34 12,36 12,54 12,77 12,79 12,96 12,96 13 13,19 13,25 13,61 13,8 13,83 14,04 14,16 14,2 14,27 14,31 14,69 14,9 14,92 15,01 15,09 15,14 15,24 15,33 15,36 15,44 15,5 15,58 15,65 15,72 15,82 15,87 16,07 16,18 16,19 16,39 16,54 16,61 16,62 16,66 16,71 16,72 16,79 16,82 16,83 16,91 16,97 17,02 17,03 17,04 17,07 17,11 17,12 17,14 17,18 17,24 17,26 17,26 17,29 17,36 17,44 17,48 17,48 17,52 17,54 17,58 17,64 17,69 17,69 17,76 17,79 17,82 17,89 17,95 18 18,03 18,06 18,08 18,13 18,16 18,18 18,18 18,27 18,31 18,35 18,45 18,5

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 'Herman Ole Andreas Wold' @ www.yougetit.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 16.1562222222222 0.187362838905401 86.2295976972226 Geometric Mean 16.0533005034694 Harmonic Mean 15.9441604319974 Quadratic Mean 16.2526258391272 Winsorized Mean ( 1 / 30 ) 16.1558888888889 0.187234549137233 86.2869003788799 Winsorized Mean ( 2 / 30 ) 16.1541111111111 0.186833251941597 86.4627197955147 Winsorized Mean ( 3 / 30 ) 16.1587777777778 0.1853153891414 87.1960923086005 Winsorized Mean ( 4 / 30 ) 16.1672222222222 0.182896109747429 88.3956593967385 Winsorized Mean ( 5 / 30 ) 16.1633333333333 0.182030303001962 88.7947394844422 Winsorized Mean ( 6 / 30 ) 16.1746666666667 0.179711184578678 90.0036728631398 Winsorized Mean ( 7 / 30 ) 16.1731111111111 0.179516944032082 90.0923932184403 Winsorized Mean ( 8 / 30 ) 16.174 0.17847416819839 90.6237589633762 Winsorized Mean ( 9 / 30 ) 16.188 0.17412418258616 92.96813205133 Winsorized Mean ( 10 / 30 ) 16.1924444444444 0.172569934519032 93.8312023445699 Winsorized Mean ( 11 / 30 ) 16.2327777777778 0.1639452747963 99.013392108719 Winsorized Mean ( 12 / 30 ) 16.2541111111111 0.158977058815334 102.241865790156 Winsorized Mean ( 13 / 30 ) 16.2512222222222 0.157342936590194 103.285362370916 Winsorized Mean ( 14 / 30 ) 16.2745555555556 0.150666448005469 108.017118416204 Winsorized Mean ( 15 / 30 ) 16.2828888888889 0.145972330287624 111.547776601258 Winsorized Mean ( 16 / 30 ) 16.2846666666667 0.144185360655012 112.942580250088 Winsorized Mean ( 17 / 30 ) 16.2922222222222 0.141385932705435 115.232271771801 Winsorized Mean ( 18 / 30 ) 16.2862222222222 0.138487782356845 117.60042615353 Winsorized Mean ( 19 / 30 ) 16.3664444444444 0.126041460304272 129.849689181122 Winsorized Mean ( 20 / 30 ) 16.402 0.117898494186041 139.119673353233 Winsorized Mean ( 21 / 30 ) 16.3926666666667 0.115596569116521 141.809283717953 Winsorized Mean ( 22 / 30 ) 16.4048888888889 0.111348924029413 147.32867005123 Winsorized Mean ( 23 / 30 ) 16.4202222222222 0.107908498920476 152.168016296133 Winsorized Mean ( 24 / 30 ) 16.4228888888889 0.10485353252041 156.626948984215 Winsorized Mean ( 25 / 30 ) 16.4506666666667 0.101074230147946 162.758268280522 Winsorized Mean ( 26 / 30 ) 16.4651111111111 0.0962833993732436 171.006749016868 Winsorized Mean ( 27 / 30 ) 16.4501111111111 0.0923970553714212 178.037179269235 Winsorized Mean ( 28 / 30 ) 16.4532222222222 0.0867272660188568 189.712220590983 Winsorized Mean ( 29 / 30 ) 16.4628888888889 0.0831558025740474 197.976429536944 Winsorized Mean ( 30 / 30 ) 16.4895555555556 0.0797110748795593 206.866556252951 Trimmed Mean ( 1 / 30 ) 16.1731818181818 0.184621145124631 87.6020014243973 Trimmed Mean ( 2 / 30 ) 16.1912790697674 0.181590917147496 89.1634852893893 Trimmed Mean ( 3 / 30 ) 16.2111904761905 0.178312466655666 90.9145096820147 Trimmed Mean ( 4 / 30 ) 16.2303658536585 0.175151798500544 92.6645686347786 Trimmed Mean ( 5 / 30 ) 16.248125 0.172291342685117 94.306102365778 Trimmed Mean ( 6 / 30 ) 16.2676923076923 0.169170757984963 96.1613726950275 Trimmed Mean ( 7 / 30 ) 16.2860526315789 0.166101224574567 98.0489618501741 Trimmed Mean ( 8 / 30 ) 16.3056756756757 0.162506523786807 100.338591311369 Trimmed Mean ( 9 / 30 ) 16.32625 0.158467257112258 103.026014947899 Trimmed Mean ( 10 / 30 ) 16.346 0.154593489506931 105.73537121217 Trimmed Mean ( 11 / 30 ) 16.3663235294118 0.150271762072495 108.911503423486 Trimmed Mean ( 12 / 30 ) 16.3828787878788 0.146838122682081 111.571017720986 Trimmed Mean ( 13 / 30 ) 16.3828787878788 0.143646560383101 114.049920472764 Trimmed Mean ( 14 / 30 ) 16.4143548387097 0.140047703017407 117.205455605863 Trimmed Mean ( 15 / 30 ) 16.4293333333333 0.136903996769452 120.006235909975 Trimmed Mean ( 16 / 30 ) 16.4444827586207 0.133875223486758 122.834400050486 Trimmed Mean ( 17 / 30 ) 16.4605357142857 0.130420752582101 126.211016179527 Trimmed Mean ( 18 / 30 ) 16.477037037037 0.12662324910462 130.126474826303 Trimmed Mean ( 19 / 30 ) 16.4953846153846 0.122355730152868 134.814974294835 Trimmed Mean ( 20 / 30 ) 16.5076 0.11953807693256 138.094910204328 Trimmed Mean ( 21 / 30 ) 16.5175 0.117482268165597 140.595685271566 Trimmed Mean ( 22 / 30 ) 16.5291304347826 0.115156615088929 143.536091452654 Trimmed Mean ( 23 / 30 ) 16.5406818181818 0.112896891033354 146.511402278518 Trimmed Mean ( 24 / 30 ) 16.5519047619048 0.110552533796523 149.719813680339 Trimmed Mean ( 25 / 30 ) 16.564 0.107968893905986 153.414556737268 Trimmed Mean ( 26 / 30 ) 16.564 0.105296936258876 157.307520888138 Trimmed Mean ( 27 / 30 ) 16.5852777777778 0.102689612549533 161.508816383719 Trimmed Mean ( 28 / 30 ) 16.5985294117647 0.099819027289793 166.286226809004 Trimmed Mean ( 29 / 30 ) 16.613125 0.097096391145022 171.099304557951 Trimmed Mean ( 30 / 30 ) 16.6286666666667 0.0940013858216913 176.89810124937 Median 16.755 Midrange 15.41 Midmean - Weighted Average at Xnp 16.5066666666667 Midmean - Weighted Average at X(n+1)p 16.5291304347826 Midmean - Empirical Distribution Function 16.5291304347826 Midmean - Empirical Distribution Function - Averaging 16.5291304347826 Midmean - Empirical Distribution Function - Interpolation 16.5406818181818 Midmean - Closest Observation 16.5291304347826 Midmean - True Basic - Statistics Graphics Toolkit 16.5291304347826 Midmean - MS Excel (old versions) 16.5291304347826 Number of observations 90

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/17/t13056439818a6rep1g8fysngh/1eh3j1305644181.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t13056439818a6rep1g8fysngh/1eh3j1305644181.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t13056439818a6rep1g8fysngh/2edzl1305644181.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t13056439818a6rep1g8fysngh/2edzl1305644181.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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