centrummaten vruchtensappen-sanne peelmans

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

Title produced by software: Central Tendency

Date of computation: Tue, 15 Apr 2008 05:12:22 -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/15/t1208258045xchpf5teeaxp995.htm/, Retrieved Tue, 15 Apr 2008 13:14:07 +0200

User-defined keywords:

Dataseries X:

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1,08 1,08 1,09 1,1 1,1 1,11 1,1 1,1 1,11 1,11 1,11 1,11 1,11 1,12 1,11 1,11 1,12 1,12 1,11 1,12 1,11 1,11 1,1 1,1 1,1 1,11 1,1 1,1 1,09 1,1 1,1 1,11 1,13 1,13 1,13 1,13 1,14 1,14 1,14 1,15 1,15 1,15 1,15 1,15 1,15 1,14 1,14 1,14 1,13 1,12 1,13 1,13 1,13 1,12 1,13 1,12 1,12 1,11 1,11 1,11 1,11 1,14 1,15 1,15 1,16 1,15 1,16 1,13 1,13 1,12 1,12 1,11 1,11

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.12068493150685 0.00224395659822933 499.423621825469 Geometric Mean 1.12052348230917 Harmonic Mean 1.12036233990535 Quadratic Mean 1.12084667117049 Winsorized Mean ( 1 / 24 ) 1.12068493150685 0.00224395659822933 499.423621825469 Winsorized Mean ( 2 / 24 ) 1.12068493150685 0.00212193701824764 528.142410387064 Winsorized Mean ( 3 / 24 ) 1.12068493150685 0.00212193701824764 528.142410387064 Winsorized Mean ( 4 / 24 ) 1.12123287671233 0.00202669781015270 553.231404847599 Winsorized Mean ( 5 / 24 ) 1.12123287671233 0.00202669781015270 553.231404847599 Winsorized Mean ( 6 / 24 ) 1.12123287671233 0.00202669781015270 553.231404847599 Winsorized Mean ( 7 / 24 ) 1.12123287671233 0.00202669781015270 553.231404847599 Winsorized Mean ( 8 / 24 ) 1.12123287671233 0.00202669781015270 553.231404847599 Winsorized Mean ( 9 / 24 ) 1.12123287671233 0.00202669781015270 553.231404847599 Winsorized Mean ( 10 / 24 ) 1.12123287671233 0.00202669781015270 553.231404847599 Winsorized Mean ( 11 / 24 ) 1.11972602739726 0.00175532027479683 637.904115547723 Winsorized Mean ( 12 / 24 ) 1.11972602739726 0.00175532027479683 637.904115547723 Winsorized Mean ( 13 / 24 ) 1.11972602739726 0.00175532027479683 637.904115547723 Winsorized Mean ( 14 / 24 ) 1.11972602739726 0.00175532027479683 637.904115547723 Winsorized Mean ( 15 / 24 ) 1.12178082191781 0.00147715307028509 759.420837612521 Winsorized Mean ( 16 / 24 ) 1.12178082191781 0.00147715307028509 759.420837612521 Winsorized Mean ( 17 / 24 ) 1.12178082191781 0.00147715307028509 759.420837612521 Winsorized Mean ( 18 / 24 ) 1.11931506849315 0.00109183992705189 1025.16407466014 Winsorized Mean ( 19 / 24 ) 1.11931506849315 0.00109183992705189 1025.16407466014 Winsorized Mean ( 20 / 24 ) 1.11931506849315 0.00109183992705189 1025.16407466014 Winsorized Mean ( 21 / 24 ) 1.11931506849315 0.00109183992705189 1025.16407466014 Winsorized Mean ( 22 / 24 ) 1.11931506849315 0.00109183992705189 1025.16407466014 Winsorized Mean ( 23 / 24 ) 1.11931506849315 0.00109183992705189 1025.16407466014 Winsorized Mean ( 24 / 24 ) 1.11931506849315 0.00109183992705189 1025.16407466014 Trimmed Mean ( 1 / 24 ) 1.12070422535211 0.00216357204884471 517.987938488362 Trimmed Mean ( 2 / 24 ) 1.12072463768116 0.00206788911999769 541.965537147567 Trimmed Mean ( 3 / 24 ) 1.12074626865672 0.00203223049370602 551.485804453656 Trimmed Mean ( 4 / 24 ) 1.12076923076923 0.00198924623707472 563.414025815816 Trimmed Mean ( 5 / 24 ) 1.12063492063492 0.00197102690222877 568.55384336345 Trimmed Mean ( 6 / 24 ) 1.12049180327869 0.00194776359788213 575.27094381322 Trimmed Mean ( 7 / 24 ) 1.12033898305085 0.00191835243842719 584.01102978209 Trimmed Mean ( 8 / 24 ) 1.12017543859649 0.00188136934995852 595.404320061444 Trimmed Mean ( 9 / 24 ) 1.12 0.00183493960854392 610.374311386058 Trimmed Mean ( 10 / 24 ) 1.11981132075472 0.00177653153611741 630.335740170451 Trimmed Mean ( 11 / 24 ) 1.11960784313725 0.00170261124283077 657.582785178719 Trimmed Mean ( 12 / 24 ) 1.11959183673469 0.00167411220439791 668.76750183979 Trimmed Mean ( 13 / 24 ) 1.11957446808511 0.00163669323244843 684.046616610169 Trimmed Mean ( 14 / 24 ) 1.11955555555556 0.00158769114988710 705.14693971505 Trimmed Mean ( 15 / 24 ) 1.11953488372093 0.00152329596795578 734.942458505497 Trimmed Mean ( 16 / 24 ) 1.11926829268293 0.00149756892029352 747.390171841674 Trimmed Mean ( 17 / 24 ) 1.11897435897436 0.00145998686491751 766.427689085809 Trimmed Mean ( 18 / 24 ) 1.11864864864865 0.00140580959768712 795.73268705028 Trimmed Mean ( 19 / 24 ) 1.11857142857143 0.00142857142857141 783.000000000008 Trimmed Mean ( 20 / 24 ) 1.11848484848485 0.00145130636823241 770.674526734892 Trimmed Mean ( 21 / 24 ) 1.11838709677419 0.00147354989360221 758.974705661445 Trimmed Mean ( 22 / 24 ) 1.11827586206897 0.00149456861638206 748.22651152411 Trimmed Mean ( 23 / 24 ) 1.11814814814815 0.00151319335896175 738.932761980493 Trimmed Mean ( 24 / 24 ) 1.118 0.00152752523165193 731.902803851525 Median 1.12 Midrange 1.12 Midmean - Weighted Average at Xnp 1.118 Midmean - Weighted Average at X(n+1)p 1.118 Midmean - Empirical Distribution Function 1.118 Midmean - Empirical Distribution Function - Averaging 1.118 Midmean - Empirical Distribution Function - Interpolation 1.118 Midmean - Closest Observation 1.118 Midmean - True Basic - Statistics Graphics Toolkit 1.118 Midmean - MS Excel (old versions) 1.118 Number of observations 73

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208258045xchpf5teeaxp995/19itj1208257940.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208258045xchpf5teeaxp995/19itj1208257940.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208258045xchpf5teeaxp995/2oz941208257940.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208258045xchpf5teeaxp995/2oz941208257940.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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