Robuustheid- omzetprijs droge voeding Carrefour- Angelique Vigar

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 12 May 2009 05:42:06 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/May/12/t12421286451hbzjtyhnqlo77s.htm/, Retrieved Tue, 12 May 2009 13:44:09 +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/2009/May/12/t12421286451hbzjtyhnqlo77s.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

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831581 808744 899237 929532 883165 908232 955613 937590 849396 978630 868513 1156102 1505713 1415151 1545021 1681193 1457973 1638575 1688972 1563924 1596359 1722061 1549332 2264959 1420268 1415099 1597279 1605693 1575400 1654752 1553966 1570959 1642414 1664774 1551560 2304365 1644081 1425600 1569344 1456489 1610786 1601519 1496600 1486452 1637939 1605759 1504221 1993384 1507620 1477037 1679184 1504731 1570141 1734191 1657498 1652164 1610941 1813765 1711573 2165466 1492778 1385488 1470589 1514657 1641395 1606185 1581162 1517847 1630080 1604623 1548973 2125558

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1505943.29166667 37592.0303406872 40.0601744044862 Geometric Mean 1467952.80173725 Harmonic Mean 1424111.76858946 Quadratic Mean 1538895.58145458 Winsorized Mean ( 1 / 24 ) 1505713.16666667 37350.0632824714 40.3135372296225 Winsorized Mean ( 2 / 24 ) 1503444.33333333 36475.2895633260 41.2181603307946 Winsorized Mean ( 3 / 24 ) 1502578.04166667 35859.4556351121 41.9018642378777 Winsorized Mean ( 4 / 24 ) 1496049.04166667 33996.1577495080 44.0064154511201 Winsorized Mean ( 5 / 24 ) 1484691.61111111 31491.4995516436 47.1457895701769 Winsorized Mean ( 6 / 24 ) 1478810.02777778 30412.5566053217 48.6249823376904 Winsorized Mean ( 7 / 24 ) 1479701.55555556 29731.5941538285 49.7686584816044 Winsorized Mean ( 8 / 24 ) 1479431.55555556 29366.8013203995 50.3776880367245 Winsorized Mean ( 9 / 24 ) 1478859.30555556 28478.3355676571 51.9292745196492 Winsorized Mean ( 10 / 24 ) 1480975.69444444 27542.5820876302 53.7704014000043 Winsorized Mean ( 11 / 24 ) 1507782.54166667 20756.8834860717 72.6401216578788 Winsorized Mean ( 12 / 24 ) 1543611.875 12101.2455396093 127.558098870692 Winsorized Mean ( 13 / 24 ) 1547644.58333333 10967.1185065699 141.116792200815 Winsorized Mean ( 14 / 24 ) 1547120.75 10890.5674385546 142.060618854709 Winsorized Mean ( 15 / 24 ) 1547647.625 10634.8195258773 145.526458745649 Winsorized Mean ( 16 / 24 ) 1547036.29166667 10190.570564581 151.81056662751 Winsorized Mean ( 17 / 24 ) 1553935.93055556 8962.99155308775 173.372464020701 Winsorized Mean ( 18 / 24 ) 1554052.18055556 8870.91456418872 175.185114151494 Winsorized Mean ( 19 / 24 ) 1556637.23611111 8269.14873702797 188.246370408205 Winsorized Mean ( 20 / 24 ) 1558251.68055556 7984.80603453617 195.152101856419 Winsorized Mean ( 21 / 24 ) 1558705.51388889 7276.29845152804 214.216819756968 Winsorized Mean ( 22 / 24 ) 1554790.43055556 6227.79116836672 249.653591220739 Winsorized Mean ( 23 / 24 ) 1555961.83333333 6051.51538345797 257.119371717473 Winsorized Mean ( 24 / 24 ) 1556968.5 5510.1963745116 282.561345218482 Trimmed Mean ( 1 / 24 ) 1504497.25714286 35538.9363977935 42.3337727472414 Trimmed Mean ( 2 / 24 ) 1503209.82352941 33356.0889506653 45.065529887293 Trimmed Mean ( 3 / 24 ) 1503081.90909091 31300.7792819702 48.0205906552848 Trimmed Mean ( 4 / 24 ) 1503270.859375 29093.969405323 51.6695002470156 Trimmed Mean ( 5 / 24 ) 1505367.51612903 27150.5400163252 55.4452145417321 Trimmed Mean ( 6 / 24 ) 1510329.73333333 25621.8015429466 58.9470545543708 Trimmed Mean ( 7 / 24 ) 1516851.05172414 24028.777747064 63.1264339656009 Trimmed Mean ( 8 / 24 ) 1523674.42857143 22208.8913633890 68.6065055495376 Trimmed Mean ( 9 / 24 ) 1531048.24074074 19935.4862441229 76.8001453283892 Trimmed Mean ( 10 / 24 ) 1539077.30769231 17127.9511805614 89.8576421352144 Trimmed Mean ( 11 / 24 ) 1547443.94 13404.3921795199 115.443051745702 Trimmed Mean ( 12 / 24 ) 1552852.3125 10905.4295615996 142.392585613310 Trimmed Mean ( 13 / 24 ) 1554057.58695652 10488.0506167124 148.174112020415 Trimmed Mean ( 14 / 24 ) 1554864.81818182 10221.1352083530 152.122517361000 Trimmed Mean ( 15 / 24 ) 1555813.07142857 9880.97312671024 157.455450134046 Trimmed Mean ( 16 / 24 ) 1556792.925 9487.87142088333 164.082422277921 Trimmed Mean ( 17 / 24 ) 1557948.31578947 9065.48091321781 171.85501030816 Trimmed Mean ( 18 / 24 ) 1558420.36111111 8824.24299529002 176.606691581694 Trimmed Mean ( 19 / 24 ) 1558934.26470588 8503.39718453233 183.330759562964 Trimmed Mean ( 20 / 24 ) 1559206.28125 8217.02909166169 189.753043813879 Trimmed Mean ( 21 / 24 ) 1559320.83333333 7880.45633693586 197.871895568378 Trimmed Mean ( 22 / 24 ) 1559396.17857143 7603.90977962322 205.078206313055 Trimmed Mean ( 23 / 24 ) 1559975.92307692 7504.65605093533 207.867744036384 Trimmed Mean ( 24 / 24 ) 1560499.5 7372.48604389261 211.665304038483 Median 1566634 Midrange 1556554.5 Midmean - Weighted Average at Xnp 1555665.45945946 Midmean - Weighted Average at X(n+1)p 1558420.36111111 Midmean - Empirical Distribution Function 1555665.45945946 Midmean - Empirical Distribution Function - Averaging 1558420.36111111 Midmean - Empirical Distribution Function - Interpolation 1558420.36111111 Midmean - Closest Observation 1555665.45945946 Midmean - True Basic - Statistics Graphics Toolkit 1558420.36111111 Midmean - MS Excel (old versions) 1557948.31578947 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/12/t12421286451hbzjtyhnqlo77s/1y4w01242128524.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/12/t12421286451hbzjtyhnqlo77s/1y4w01242128524.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/12/t12421286451hbzjtyhnqlo77s/2lqu21242128524.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/12/t12421286451hbzjtyhnqlo77s/2lqu21242128524.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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