Centrummaten GEmiddelde consumptieprijzen mineraalwater - Rebecca De Cauwer

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

Title produced by software: Central Tendency

Date of computation: Wed, 16 Apr 2008 10:40:42 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/16/t1208364122l4emgm07kmjnudw.htm/, Retrieved Wed, 16 Apr 2008 18:42:02 +0200

User-defined keywords:

Dataseries X:

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1,12 1,12 1,12 1,13 1,13 1,13 1,14 1,14 1,14 1,14 1,14 1,15 1,15 1,17 1,17 1,18 1,18 1,18 1,18 1,18 1,18 1,19 1,19 1,19 1,19 1,19 1,2 1,21 1,21 1,21 1,21 1,21 1,23 1,24 1,24 1,24 1,27 1,28 1,29 1,29 1,3 1,31 1,31 1,31 1,32 1,32 1,33 1,33 1,34 1,35 1,36 1,37 1,37 1,37 1,37 1,37 1,38 1,38 1,39 1,39 1,39 1,41 1,42 1,42 1,42 1,43 1,43 1,44 1,46 1,46 1,47 1,47 1,47 1,48 1,49 1,49 1,5 1,5 1,51 1,52 1,53 1,53 1,53 1,54

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.30630952380952 0.0142419666256113 91.7225519585472 Geometric Mean 1.29990869529583 Harmonic Mean 1.29357683624514 Quadratic Mean 1.31273750685534 Winsorized Mean ( 1 / 28 ) 1.30619047619048 0.0142189105472817 91.8629083323254 Winsorized Mean ( 2 / 28 ) 1.30619047619048 0.0142189105472817 91.8629083323254 Winsorized Mean ( 3 / 28 ) 1.30654761904762 0.0141639183128877 92.2447863779896 Winsorized Mean ( 4 / 28 ) 1.30607142857143 0.0140750568317729 92.7933325017283 Winsorized Mean ( 5 / 28 ) 1.30547619047619 0.0139680447966744 93.461626840358 Winsorized Mean ( 6 / 28 ) 1.30547619047619 0.0137381929298284 95.025320807785 Winsorized Mean ( 7 / 28 ) 1.30547619047619 0.0137381929298284 95.025320807785 Winsorized Mean ( 8 / 28 ) 1.30452380952381 0.0135785730708711 96.0722310595572 Winsorized Mean ( 9 / 28 ) 1.30452380952381 0.0135785730708711 96.0722310595572 Winsorized Mean ( 10 / 28 ) 1.30333333333333 0.0133859403953453 97.3658401905435 Winsorized Mean ( 11 / 28 ) 1.30333333333333 0.0129911631262458 100.324606862971 Winsorized Mean ( 12 / 28 ) 1.30333333333333 0.0129911631262458 100.324606862971 Winsorized Mean ( 13 / 28 ) 1.30642857142857 0.0125683933382771 103.945551055427 Winsorized Mean ( 14 / 28 ) 1.30476190476190 0.0123110809208123 105.982725087621 Winsorized Mean ( 15 / 28 ) 1.30654761904762 0.0120805933518203 108.152603187388 Winsorized Mean ( 16 / 28 ) 1.30273809523810 0.0115151016990431 113.133008225742 Winsorized Mean ( 17 / 28 ) 1.30071428571429 0.0112293486290860 115.831677212800 Winsorized Mean ( 18 / 28 ) 1.30071428571429 0.0112293486290860 115.831677212800 Winsorized Mean ( 19 / 28 ) 1.29845238095238 0.0109207414856351 118.897822337461 Winsorized Mean ( 20 / 28 ) 1.29845238095238 0.0109207414856351 118.897822337461 Winsorized Mean ( 21 / 28 ) 1.30095238095238 0.0105996609667946 122.735282291373 Winsorized Mean ( 22 / 28 ) 1.29833333333333 0.0102504961655003 126.660535487353 Winsorized Mean ( 23 / 28 ) 1.29285714285714 0.00955488332878033 135.308522183931 Winsorized Mean ( 24 / 28 ) 1.29285714285714 0.00955488332878033 135.308522183931 Winsorized Mean ( 25 / 28 ) 1.29285714285714 0.00955488332878033 135.308522183931 Winsorized Mean ( 26 / 28 ) 1.29285714285714 0.00878207411913313 147.215467020536 Winsorized Mean ( 27 / 28 ) 1.29607142857143 0.00837828014757757 154.694209997999 Winsorized Mean ( 28 / 28 ) 1.29273809523810 0.00798261017031857 161.944284846181 Trimmed Mean ( 1 / 28 ) 1.30573170731707 0.0141229923391187 92.4543238404497 Trimmed Mean ( 2 / 28 ) 1.30525 0.0140072031650265 93.1841984886016 Trimmed Mean ( 3 / 28 ) 1.30474358974359 0.0138683745798006 94.0804982037303 Trimmed Mean ( 4 / 28 ) 1.30407894736842 0.0137256037243999 95.010680298905 Trimmed Mean ( 5 / 28 ) 1.30351351351351 0.0135845596308467 95.9555222205071 Trimmed Mean ( 6 / 28 ) 1.30305555555556 0.0134453028735633 96.915299551762 Trimmed Mean ( 7 / 28 ) 1.30257142857143 0.0133338804974982 97.688848255077 Trimmed Mean ( 8 / 28 ) 1.30205882352941 0.0131956287883124 98.6734959293998 Trimmed Mean ( 9 / 28 ) 1.30166666666667 0.0130599894932318 99.6682782433508 Trimmed Mean ( 10 / 28 ) 1.30125 0.0128916809031226 100.937186529711 Trimmed Mean ( 11 / 28 ) 1.30096774193548 0.012722290380411 102.258925322019 Trimmed Mean ( 12 / 28 ) 1.30066666666667 0.0125861251439575 103.341310513753 Trimmed Mean ( 13 / 28 ) 1.30034482758621 0.0124129528518480 104.757090686332 Trimmed Mean ( 14 / 28 ) 1.29964285714286 0.0122685435733024 105.932937302437 Trimmed Mean ( 15 / 28 ) 1.29907407407407 0.0121292495446182 107.102592728046 Trimmed Mean ( 16 / 28 ) 1.29826923076923 0.0119851628795496 108.323036058566 Trimmed Mean ( 17 / 28 ) 1.2978 0.0118985164570022 109.072421313185 Trimmed Mean ( 18 / 28 ) 1.2975 0.0118257892244087 109.717835772172 Trimmed Mean ( 19 / 28 ) 1.29717391304348 0.0117158921898703 110.719174606697 Trimmed Mean ( 20 / 28 ) 1.29704545454545 0.0116165822711877 111.654652312194 Trimmed Mean ( 21 / 28 ) 1.29690476190476 0.0114687278448138 113.08183256709 Trimmed Mean ( 22 / 28 ) 1.2965 0.011320222431447 114.529551680750 Trimmed Mean ( 23 / 28 ) 1.29631578947368 0.0111782470922637 115.967716474155 Trimmed Mean ( 24 / 28 ) 1.29666666666667 0.0111126982993359 116.683332143027 Trimmed Mean ( 25 / 28 ) 1.29705882352941 0.0109896192451037 118.025820058079 Trimmed Mean ( 26 / 28 ) 1.2975 0.0107856685078529 120.298523828662 Trimmed Mean ( 27 / 28 ) 1.298 0.0106716942174738 121.630171699884 Trimmed Mean ( 28 / 28 ) 1.29821428571429 0.0105791745538281 122.714137961220 Median 1.31 Midrange 1.33 Midmean - Weighted Average at Xnp 1.2878 Midmean - Weighted Average at X(n+1)p 1.3025 Midmean - Empirical Distribution Function 1.2878 Midmean - Empirical Distribution Function - Averaging 1.3025 Midmean - Empirical Distribution Function - Interpolation 1.3025 Midmean - Closest Observation 1.2878 Midmean - True Basic - Statistics Graphics Toolkit 1.3025 Midmean - MS Excel (old versions) 1.2878 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208364122l4emgm07kmjnudw/1rh7x1208364036.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208364122l4emgm07kmjnudw/1rh7x1208364036.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208364122l4emgm07kmjnudw/29yfk1208364036.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208364122l4emgm07kmjnudw/29yfk1208364036.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')

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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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