Centrummaten - Omzetcijfers Carrefour Burcht - Jeroen Van Eeckhoven

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sat, 14 Mar 2009 03:01:51 -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/Mar/14/t1237021412pr407h9ql3jr8l4.htm/, Retrieved Sat, 14 Mar 2009 10:03:32 +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/2009/Mar/14/t1237021412pr407h9ql3jr8l4.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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2291180 1971664 2193270 2197733 2345324 2195121 2170583 2241521 2154945 2912568 2392562 3336621 4080642 3735329 4018383 4171360 3855698 4101316 4199346 3959646 3960841 4784025 4105467 5929558 4048642 3828808 4268127 4171816 4004783 4295447 3968177 3918480 4040260 4530715 4103330 6025506 4632308 4133863 4519182 4151573 4486595 4504699 4180443 4222193 4373727 4734738 4403232 5903985 4414074 4061816 4504697 3994176 4114925 4485120 4171230 4476075 4179369 4823185 4585751 6110454 4279575 3782118 4098678 4065616 4413733 4481214 4345018 4294488 4361269 4535031 4318397 6040168

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' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 4051270.95833333 108498.059292792 37.3395707235703 Geometric Mean 3930351.89394091 Harmonic Mean 3786576.75300653 Quadratic Mean 4153142.93368607 Winsorized Mean ( 1 / 24 ) 4052840.33333333 107580.605889993 37.6725925626183 Winsorized Mean ( 2 / 24 ) 4052867.44444444 107367.329589329 37.7476785531160 Winsorized Mean ( 3 / 24 ) 4049814.90277778 106118.079453774 38.1632887027693 Winsorized Mean ( 4 / 24 ) 4048497.01388889 105739.920941749 38.2873088785375 Winsorized Mean ( 5 / 24 ) 3973622.84722222 91170.6914121566 43.5844325152544 Winsorized Mean ( 6 / 24 ) 3974008.51388889 89752.4699154236 44.2774278817476 Winsorized Mean ( 7 / 24 ) 3974044.68055556 87847.9178430735 45.2377788583966 Winsorized Mean ( 8 / 24 ) 3968679.56944444 84904.6390018194 46.7427883340909 Winsorized Mean ( 9 / 24 ) 3968764.69444444 82690.6119996072 47.9953479418353 Winsorized Mean ( 10 / 24 ) 4033943.30555556 63109.0954892564 63.9201572179447 Winsorized Mean ( 11 / 24 ) 4098069.79166667 47497.9189411597 86.2789335411378 Winsorized Mean ( 12 / 24 ) 4162598.95833333 33498.1057768511 124.263711687540 Winsorized Mean ( 13 / 24 ) 4168431.98611111 31619.6091993806 131.830597899760 Winsorized Mean ( 14 / 24 ) 4177510.20833333 30096.6970956754 138.802945554235 Winsorized Mean ( 15 / 24 ) 4179341.04166667 28619.2648361743 146.032438834140 Winsorized Mean ( 16 / 24 ) 4192964.81944444 26434.1162467558 158.619443914984 Winsorized Mean ( 17 / 24 ) 4201762.31944444 24912.1666289821 168.663062591924 Winsorized Mean ( 18 / 24 ) 4200776.31944444 24668.7950296070 170.28704946483 Winsorized Mean ( 19 / 24 ) 4186350.83333333 21912.1271101059 191.051777506465 Winsorized Mean ( 20 / 24 ) 4193478.05555556 20906.4354840659 200.583119908302 Winsorized Mean ( 21 / 24 ) 4193508.97222222 20040.5341628624 209.251357181553 Winsorized Mean ( 22 / 24 ) 4188649.11111111 18179.1272379192 230.409802202944 Winsorized Mean ( 23 / 24 ) 4191657.95833333 16701.4584094362 250.975564862352 Winsorized Mean ( 24 / 24 ) 4189034.95833333 15576.0929363857 268.940033642696 Trimmed Mean ( 1 / 24 ) 4051562.72857143 103372.312816692 39.1938868172175 Trimmed Mean ( 2 / 24 ) 4050209.97058824 98340.8778713684 41.1854160574607 Trimmed Mean ( 3 / 24 ) 4048760.43939394 92398.5218290026 43.8184546597702 Trimmed Mean ( 4 / 24 ) 4048365.015625 85747.131190053 47.2128333559296 Trimmed Mean ( 5 / 24 ) 4048326.69354839 77588.8042868658 52.1766861953521 Trimmed Mean ( 6 / 24 ) 4066255.61666667 72726.0475564894 55.9119566274826 Trimmed Mean ( 7 / 24 ) 4085341.22413793 67037.7445195964 60.9409110257835 Trimmed Mean ( 8 / 24 ) 4105783.44642857 60284.0340987245 68.107310796499 Trimmed Mean ( 9 / 24 ) 4128634.09259259 52166.8348011253 79.1428904654098 Trimmed Mean ( 10 / 24 ) 4153229.38461538 41348.9876849969 100.443314749453 Trimmed Mean ( 11 / 24 ) 4170406.58 34013.5705482876 122.610079235270 Trimmed Mean ( 12 / 24 ) 4180270.6875 29810.0541430367 140.230227943966 Trimmed Mean ( 13 / 24 ) 4182575.69565217 28587.453246818 146.308090459850 Trimmed Mean ( 14 / 24 ) 4184356.02272727 27467.2848845043 152.339630229993 Trimmed Mean ( 15 / 24 ) 4185194.28571429 26380.1437740662 158.649411525523 Trimmed Mean ( 16 / 24 ) 4185896.675 25304.9416502701 165.418151634241 Trimmed Mean ( 17 / 24 ) 4185059.65789474 24411.3866640343 171.438833667760 Trimmed Mean ( 18 / 24 ) 4183094.63888889 23556.751718032 177.575189014148 Trimmed Mean ( 19 / 24 ) 4181014.44117647 22416.7820803154 186.512695095872 Trimmed Mean ( 20 / 24 ) 4180382.5 21631.7531833712 193.252135625029 Trimmed Mean ( 21 / 24 ) 4178811.03333333 20761.0898796743 201.280908543462 Trimmed Mean ( 22 / 24 ) 4177011.28571429 19728.6037364826 211.723614174989 Trimmed Mean ( 23 / 24 ) 4175546.38461538 18824.4056514268 221.815576116153 Trimmed Mean ( 24 / 24 ) 4173444.875 17928.5808044182 232.781664122100 Median 4171295 Midrange 4041059 Midmean - Weighted Average at Xnp 4177055.48648649 Midmean - Weighted Average at X(n+1)p 4183094.63888889 Midmean - Empirical Distribution Function 4177055.48648649 Midmean - Empirical Distribution Function - Averaging 4183094.63888889 Midmean - Empirical Distribution Function - Interpolation 4183094.63888889 Midmean - Closest Observation 4177055.48648649 Midmean - True Basic - Statistics Graphics Toolkit 4183094.63888889 Midmean - MS Excel (old versions) 4185059.65789474 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/14/t1237021412pr407h9ql3jr8l4/1wo7s1237021305.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/14/t1237021412pr407h9ql3jr8l4/1wo7s1237021305.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/14/t1237021412pr407h9ql3jr8l4/2ogp51237021305.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/14/t1237021412pr407h9ql3jr8l4/2ogp51237021305.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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