Centrummaten aantal stuks product Y

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 16 Aug 2010 11:23:24 +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/16/t128195778722sseh2borfuho1.htm/, Retrieved Mon, 16 Aug 2010 13:23:08 +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/16/t128195778722sseh2borfuho1.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:

Sebastien Delforge

Dataseries X:

» Textbox « » Textfile « » CSV «

152 151 150 148 146 145 146 148 149 149 150 152 154 164 167 162 164 172 169 174 181 181 172 181 183 200 199 190 197 194 190 195 204 197 185 193 192 211 210 197 191 182 170 166 175 163 153 171 165 184 179 163 163 148 132 127 130 118 113 137 133 155 151 132 134 118 102 98 91 77 74 102 98 113 114 96 102 90 72 67 62 48 43 75

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 148.107142857143 4.43998088415015 33.3576082243633 Geometric Mean 141.057180038355 Harmonic Mean 131.917557089629 Quadratic Mean 153.53156182424 Winsorized Mean ( 1 / 28 ) 148.154761904762 4.42134984981288 33.5089434080934 Winsorized Mean ( 2 / 28 ) 148.345238095238 4.31243562143135 34.399409317095 Winsorized Mean ( 3 / 28 ) 148.380952380952 4.24871837048669 34.9236968521299 Winsorized Mean ( 4 / 28 ) 148.571428571429 4.18807303438379 35.4748896095334 Winsorized Mean ( 5 / 28 ) 148.571428571429 4.14504265062817 35.8431603952044 Winsorized Mean ( 6 / 28 ) 148.642857142857 4.1296280165553 35.9942485247973 Winsorized Mean ( 7 / 28 ) 148.809523809524 4.09411217494064 36.3472023850156 Winsorized Mean ( 8 / 28 ) 149.857142857143 3.81883722413606 39.2415633507514 Winsorized Mean ( 9 / 28 ) 149.857142857143 3.78351888626072 39.607874933921 Winsorized Mean ( 10 / 28 ) 150.333333333333 3.65769778790823 41.1005342842461 Winsorized Mean ( 11 / 28 ) 150.464285714286 3.59289660751495 41.8782676349697 Winsorized Mean ( 12 / 28 ) 150.321428571429 3.57315004409323 42.0697218746592 Winsorized Mean ( 13 / 28 ) 150.785714285714 3.44446438370071 43.7762442832145 Winsorized Mean ( 14 / 28 ) 150.785714285714 3.44446438370071 43.7762442832145 Winsorized Mean ( 15 / 28 ) 149.892857142857 3.32638480547706 45.0617910760207 Winsorized Mean ( 16 / 28 ) 151.797619047619 2.95329778437352 51.3993610298325 Winsorized Mean ( 17 / 28 ) 151.595238095238 2.92692209221778 51.7933970631831 Winsorized Mean ( 18 / 28 ) 151.595238095238 2.86541282574913 52.9051998137844 Winsorized Mean ( 19 / 28 ) 152.27380952381 2.69555589244042 56.4906889710042 Winsorized Mean ( 20 / 28 ) 152.27380952381 2.69555589244042 56.4906889710042 Winsorized Mean ( 21 / 28 ) 154.52380952381 2.36448406810891 65.3520197526204 Winsorized Mean ( 22 / 28 ) 154.785714285714 2.18533627050747 70.8292432494935 Winsorized Mean ( 23 / 28 ) 154.238095238095 1.96772721345728 78.3838807448826 Winsorized Mean ( 24 / 28 ) 153.952380952381 1.93170134805549 79.697817215562 Winsorized Mean ( 25 / 28 ) 153.654761904762 1.81751329424619 84.5412038476946 Winsorized Mean ( 26 / 28 ) 153.964285714286 1.77535290008568 86.7232006137232 Winsorized Mean ( 27 / 28 ) 154.607142857143 1.60687509722049 96.2160301846584 Winsorized Mean ( 28 / 28 ) 156.940476190476 1.23062741304618 127.528831656692 Trimmed Mean ( 1 / 28 ) 148.621951219512 4.29310912757893 34.6187219571859 Trimmed Mean ( 2 / 28 ) 149.1125 4.14350925040935 35.987007869059 Trimmed Mean ( 3 / 28 ) 149.525641025641 4.03719488140973 37.0370134258737 Trimmed Mean ( 4 / 28 ) 149.947368421053 3.94078515361624 38.0501251846867 Trimmed Mean ( 5 / 28 ) 150.337837837838 3.84892783442987 39.0596665629889 Trimmed Mean ( 6 / 28 ) 150.75 3.75318070637566 40.1659317239683 Trimmed Mean ( 7 / 28 ) 151.171428571429 3.64353543800816 41.490313774489 Trimmed Mean ( 8 / 28 ) 151.588235294118 3.52173953932479 43.0435679871945 Trimmed Mean ( 9 / 28 ) 151.863636363636 3.44195195634113 44.1213701672555 Trimmed Mean ( 10 / 28 ) 152.15625 3.35330466223069 45.3750151943493 Trimmed Mean ( 11 / 28 ) 152.403225806452 3.27292465376493 46.5648439633764 Trimmed Mean ( 12 / 28 ) 152.65 3.18815117420811 47.8804145910415 Trimmed Mean ( 13 / 28 ) 152.931034482759 3.0877332843738 49.5285765958808 Trimmed Mean ( 14 / 28 ) 153.178571428571 2.99068978957024 51.2184754041585 Trimmed Mean ( 15 / 28 ) 153.444444444444 2.86971544116383 53.470264766814 Trimmed Mean ( 16 / 28 ) 153.826923076923 2.74063896308461 56.1281238240113 Trimmed Mean ( 17 / 28 ) 154.04 2.66036057092773 57.9019256574993 Trimmed Mean ( 18 / 28 ) 154.291666666667 2.56250900938277 60.2111704199748 Trimmed Mean ( 19 / 28 ) 154.565217391304 2.44942114307603 63.1027530027762 Trimmed Mean ( 20 / 28 ) 154.795454545455 2.34240700038417 66.0839275668434 Trimmed Mean ( 21 / 28 ) 155.047619047619 2.20045195995085 70.4617150792431 Trimmed Mean ( 22 / 28 ) 155.1 2.09969472750635 73.8678808724737 Trimmed Mean ( 23 / 28 ) 155.131578947368 2.00928536322847 77.2073403740455 Trimmed Mean ( 24 / 28 ) 155.222222222222 1.94083565340028 79.9770047248863 Trimmed Mean ( 25 / 28 ) 155.352941176471 1.85330189172081 83.8249514935874 Trimmed Mean ( 26 / 28 ) 155.53125 1.7609017433113 88.3247748437855 Trimmed Mean ( 27 / 28 ) 155.7 1.64012194668567 94.9319654642971 Trimmed Mean ( 28 / 28 ) 155.821428571429 1.52410401420222 102.238054043176 Median 152.5 Midrange 127 Midmean - Weighted Average at Xnp 154.565217391304 Midmean - Weighted Average at X(n+1)p 156.227272727273 Midmean - Empirical Distribution Function 154.565217391304 Midmean - Empirical Distribution Function - Averaging 156.227272727273 Midmean - Empirical Distribution Function - Interpolation 156.227272727273 Midmean - Closest Observation 154.565217391304 Midmean - True Basic - Statistics Graphics Toolkit 156.227272727273 Midmean - MS Excel (old versions) 154.565217391304 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t128195778722sseh2borfuho1/15owo1281957800.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t128195778722sseh2borfuho1/15owo1281957800.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t128195778722sseh2borfuho1/2gxvr1281957800.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t128195778722sseh2borfuho1/2gxvr1281957800.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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