central tendency - verkocht aantal stuks - mattias debbaut

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 13 Aug 2010 12:15:20 +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/Aug/13/t1281701711x0d28v2996hs81c.htm/, Retrieved Fri, 13 Aug 2010 14:15:13 +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/Aug/13/t1281701711x0d28v2996hs81c.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:

mattias debbaut

Dataseries X:

» Textbox « » Textfile « » CSV «

376 375 374 372 370 369 370 372 373 373 374 376 371 374 369 363 357 366 362 366 361 362 358 363 360 360 348 345 332 333 323 327 332 337 336 337 343 337 326 321 309 302 293 287 292 292 289 302 310 295 276 264 257 243 227 226 226 229 224 240 244 226 208 199 193 180 167 164 166 173 169 191 193 166 143 147 139 129 115 108 106 116 108 135

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 279.892857142857 9.53659524360025 29.3493484826973 Geometric Mean 263.271552555214 Harmonic Mean 243.672098171498 Quadratic Mean 293.067540565879 Winsorized Mean ( 1 / 28 ) 279.916666666667 9.5313928321675 29.3678659137808 Winsorized Mean ( 2 / 28 ) 279.892857142857 9.52851531403653 29.3742359557889 Winsorized Mean ( 3 / 28 ) 280.107142857143 9.47080875890016 29.5758419357706 Winsorized Mean ( 4 / 28 ) 280.154761904762 9.46083047447063 29.6120686932019 Winsorized Mean ( 5 / 28 ) 280.928571428571 9.30378774237766 30.1950752970185 Winsorized Mean ( 6 / 28 ) 281.285714285714 9.21203613237175 30.5345865174428 Winsorized Mean ( 7 / 28 ) 281.619047619048 9.1488441683172 30.7819263764821 Winsorized Mean ( 8 / 28 ) 281.904761904762 9.0664756545156 31.0930920290243 Winsorized Mean ( 9 / 28 ) 282.333333333333 8.98804479968218 31.4120968047819 Winsorized Mean ( 10 / 28 ) 284.238095238095 8.61975840458531 32.9751811938132 Winsorized Mean ( 11 / 28 ) 284.369047619048 8.56010070533387 33.2202923082266 Winsorized Mean ( 12 / 28 ) 284.369047619048 8.56010070533387 33.2202923082266 Winsorized Mean ( 13 / 28 ) 284.369047619048 8.51576749171839 33.3932376495245 Winsorized Mean ( 14 / 28 ) 284.702380952381 8.46063036300414 33.6502563919234 Winsorized Mean ( 15 / 28 ) 284.880952380952 8.27985834109298 34.4065007691118 Winsorized Mean ( 16 / 28 ) 286.214285714286 8.06551400638532 35.486180482446 Winsorized Mean ( 17 / 28 ) 287.833333333333 7.64676318365115 37.6411988210546 Winsorized Mean ( 18 / 28 ) 288.261904761905 7.58162919667348 38.0211030220764 Winsorized Mean ( 19 / 28 ) 288.035714285714 7.55485668697241 38.1259004929111 Winsorized Mean ( 20 / 28 ) 289.464285714286 7.34051009646839 39.4338107175345 Winsorized Mean ( 21 / 28 ) 291.464285714286 6.98142043809834 41.7485651091481 Winsorized Mean ( 22 / 28 ) 295.392857142857 6.363848742221 46.4173284294253 Winsorized Mean ( 23 / 28 ) 295.940476190476 6.29015730658756 47.0481836567972 Winsorized Mean ( 24 / 28 ) 295.369047619048 6.22043851777239 47.4836374919791 Winsorized Mean ( 25 / 28 ) 295.071428571429 6.18443314647095 47.7119602691164 Winsorized Mean ( 26 / 28 ) 292.595238095238 5.81437668233976 50.322717993822 Winsorized Mean ( 27 / 28 ) 292.273809523810 5.61716978915383 52.0322191592214 Winsorized Mean ( 28 / 28 ) 295.273809523810 5.05061447698078 58.4629476016396 Trimmed Mean ( 1 / 28 ) 280.841463414634 9.4610163792318 29.6840690426368 Trimmed Mean ( 2 / 28 ) 281.8125 9.37548469211194 30.0584459635567 Trimmed Mean ( 3 / 28 ) 282.846153846154 9.2739071388891 30.4991358669174 Trimmed Mean ( 4 / 28 ) 283.855263157895 9.17652810444714 30.9327514640676 Trimmed Mean ( 5 / 28 ) 284.905405405405 9.0619483231626 31.4397517228364 Trimmed Mean ( 6 / 28 ) 285.833333333333 8.96982421672093 31.8661019912188 Trimmed Mean ( 7 / 28 ) 286.742857142857 8.88031031377031 32.2897339182188 Trimmed Mean ( 8 / 28 ) 287.647058823529 8.78443343207244 32.7450894867408 Trimmed Mean ( 9 / 28 ) 288.560606060606 8.68345501763556 33.2310820375711 Trimmed Mean ( 10 / 28 ) 289.46875 8.57422565658958 33.7603372705188 Trimmed Mean ( 11 / 28 ) 290.177419354839 8.51168121955128 34.0916690686563 Trimmed Mean ( 12 / 28 ) 290.916666666667 8.44016131217395 34.4681405848314 Trimmed Mean ( 13 / 28 ) 291.706896551724 8.34600398931422 34.9516842940897 Trimmed Mean ( 14 / 28 ) 292.553571428571 8.23194283781005 35.5388244540337 Trimmed Mean ( 15 / 28 ) 293.425925925926 8.0954560958797 36.2457559463845 Trimmed Mean ( 16 / 28 ) 294.346153846154 7.95328956745126 37.009359630355 Trimmed Mean ( 17 / 28 ) 295.2 7.81171281748485 37.7894076366015 Trimmed Mean ( 18 / 28 ) 295.958333333333 7.70764325068989 38.3980321490415 Trimmed Mean ( 19 / 28 ) 296.739130434783 7.57892034569471 39.1532193108941 Trimmed Mean ( 20 / 28 ) 297.613636363636 7.40858423798374 40.1714587839569 Trimmed Mean ( 21 / 28 ) 298.428571428571 7.22736306252594 41.2914874826105 Trimmed Mean ( 22 / 28 ) 299.125 7.06364722926387 42.3471034568034 Trimmed Mean ( 23 / 28 ) 299.5 6.97901243079894 42.9143812207989 Trimmed Mean ( 24 / 28 ) 299.861111111111 6.8668923654283 43.6676585497068 Trimmed Mean ( 25 / 28 ) 300.323529411765 6.71361197261053 44.7335250587898 Trimmed Mean ( 26 / 28 ) 300.875 6.49328902940219 46.3363017782839 Trimmed Mean ( 27 / 28 ) 301.766666666667 6.26276780157132 48.1842335893331 Trimmed Mean ( 28 / 28 ) 302.821428571429 5.96818140997772 50.7393136651587 Median 305.5 Midrange 241 Midmean - Weighted Average at Xnp 296.116279069767 Midmean - Weighted Average at X(n+1)p 298.428571428571 Midmean - Empirical Distribution Function 296.116279069767 Midmean - Empirical Distribution Function - Averaging 298.428571428571 Midmean - Empirical Distribution Function - Interpolation 298.428571428571 Midmean - Closest Observation 296.116279069767 Midmean - True Basic - Statistics Graphics Toolkit 298.428571428571 Midmean - MS Excel (old versions) 299.044444444444 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/13/t1281701711x0d28v2996hs81c/1lut51281701717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/13/t1281701711x0d28v2996hs81c/1lut51281701717.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/13/t1281701711x0d28v2996hs81c/2d3sq1281701717.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/13/t1281701711x0d28v2996hs81c/2d3sq1281701717.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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