Raf Mattheussen centrumaten roze garnalen

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

Title produced by software: Central Tendency

Date of computation: Wed, 13 Aug 2008 04:44:13 -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/Aug/13/t1218624388vpo8ihskibodc5j.htm/, Retrieved Wed, 13 Aug 2008 10:46:31 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

16,8 16,91 16,91 17,16 17,02 17,23 17,22 17,29 17,3 17,22 17,19 17,23 17,36 17,39 17,29 17,28 17,4 17,51 17,54 17,64 17,65 17,5 17,37 17,56 17,49 17,61 17,79 17,83 17,56 17,95 18,09 18,38 18,38 18,44 18,84 19,01 19,06 19,06 18,97 18,98 19,41 19,55 19,64 19,71 19,48 19,48 19,41 19,25 19,14 19,21 19,3 19,53 19,14 19,16 19,24 19,38 19,27 19,27 19,07 19,15 19,24 19,36 19,57 19,59 19,36 19,46 19,65 19,46 19,51 19,64 19,64 19,69 19,28 19,67 19,65 19,6 19,53 19,64 19,67 19,81 19,73 19,87 19,97 20,12 19,94 20,31 20,13 20,22 20,38 20,44 20,34 20,14 19,97 19,82 19,98 20,12

Text written by user:

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 18.8302083333333 0.109764598514222 171.550833221456 Geometric Mean 18.7992030743130 Harmonic Mean 18.7676234927864 Quadratic Mean 18.8605761112963 Winsorized Mean ( 1 / 32 ) 18.8307291666667 0.109452409428216 172.044903031730 Winsorized Mean ( 2 / 32 ) 18.8298958333333 0.109329745754917 172.230308442718 Winsorized Mean ( 3 / 32 ) 18.8323958333333 0.108574671611784 173.451096409205 Winsorized Mean ( 4 / 32 ) 18.8344791666667 0.107057624034220 175.928424870016 Winsorized Mean ( 5 / 32 ) 18.831875 0.106248045647661 177.244436687807 Winsorized Mean ( 6 / 32 ) 18.833125 0.105864373728842 177.898610615112 Winsorized Mean ( 7 / 32 ) 18.8323958333333 0.105770641549781 178.04936755035 Winsorized Mean ( 8 / 32 ) 18.8332291666667 0.105637215871161 178.282142437722 Winsorized Mean ( 9 / 32 ) 18.8201041666667 0.104024973257486 180.91909641815 Winsorized Mean ( 10 / 32 ) 18.8242708333333 0.103073145633062 182.630215830875 Winsorized Mean ( 11 / 32 ) 18.8254166666667 0.102892798567616 182.961460167647 Winsorized Mean ( 12 / 32 ) 18.8216666666667 0.102457807604796 183.701633937614 Winsorized Mean ( 13 / 32 ) 18.8135416666667 0.101179012278164 185.943124399594 Winsorized Mean ( 14 / 32 ) 18.815 0.0990229682730933 190.006423036224 Winsorized Mean ( 15 / 32 ) 18.815 0.0986151922390809 190.792103861495 Winsorized Mean ( 16 / 32 ) 18.805 0.096721929152325 194.423334654383 Winsorized Mean ( 17 / 32 ) 18.8032291666667 0.0960953125615839 195.672698963504 Winsorized Mean ( 18 / 32 ) 18.8163541666667 0.0931620593035433 201.974433662514 Winsorized Mean ( 19 / 32 ) 18.814375 0.0924775710716701 203.447979677352 Winsorized Mean ( 20 / 32 ) 18.8164583333333 0.0921662993512874 204.157685246918 Winsorized Mean ( 21 / 32 ) 18.8186458333333 0.090765943912784 207.331571976114 Winsorized Mean ( 22 / 32 ) 18.8232291666667 0.0900878585282347 208.943019338918 Winsorized Mean ( 23 / 32 ) 18.8208333333333 0.0898571803780705 209.452747728623 Winsorized Mean ( 24 / 32 ) 18.8333333333333 0.0880195934460582 213.967511050538 Winsorized Mean ( 25 / 32 ) 18.8411458333333 0.0868796139493765 216.864981056566 Winsorized Mean ( 26 / 32 ) 18.8438541666667 0.0864857723051646 217.883863026351 Winsorized Mean ( 27 / 32 ) 18.8719791666667 0.079724665968898 236.714433824395 Winsorized Mean ( 28 / 32 ) 18.8807291666667 0.0777816394685388 242.740180017722 Winsorized Mean ( 29 / 32 ) 18.9109375 0.07207879431886 262.364786740776 Winsorized Mean ( 30 / 32 ) 18.9484375 0.0653800173555185 289.820013307180 Winsorized Mean ( 31 / 32 ) 19.035625 0.0520342356303193 365.828858047226 Winsorized Mean ( 32 / 32 ) 19.035625 0.0520342356303193 365.828858047226 Trimmed Mean ( 1 / 32 ) 18.8346808510638 0.108632828059182 173.379273904227 Trimmed Mean ( 2 / 32 ) 18.8388043478261 0.107678877320068 174.953573223363 Trimmed Mean ( 3 / 32 ) 18.8435555555556 0.106642824010276 176.697829698694 Trimmed Mean ( 4 / 32 ) 18.8476136363636 0.105750291718225 178.227533277958 Trimmed Mean ( 5 / 32 ) 18.8512790697674 0.105190439833328 179.210953957763 Trimmed Mean ( 6 / 32 ) 18.8557142857143 0.104724221303678 180.051129060552 Trimmed Mean ( 7 / 32 ) 18.8601219512195 0.104232977109389 180.941986636595 Trimmed Mean ( 8 / 32 ) 18.864875 0.103638703267039 182.025386321093 Trimmed Mean ( 9 / 32 ) 18.8697435897436 0.102931551241872 183.323221714621 Trimmed Mean ( 10 / 32 ) 18.8767105263158 0.102347771109850 184.436947884829 Trimmed Mean ( 11 / 32 ) 18.8835135135135 0.101779507824386 185.533551076862 Trimmed Mean ( 12 / 32 ) 18.8905555555556 0.101086021582344 186.876041413573 Trimmed Mean ( 13 / 32 ) 18.8984285714286 0.100278006050609 188.460354525705 Trimmed Mean ( 14 / 32 ) 18.9076470588235 0.099454419887088 190.113693089655 Trimmed Mean ( 15 / 32 ) 18.9172727272727 0.0987456400039634 191.575777183817 Trimmed Mean ( 16 / 32 ) 18.9275 0.0978853800066569 193.363911941832 Trimmed Mean ( 17 / 32 ) 18.9393548387097 0.0970426999540423 195.165167989751 Trimmed Mean ( 18 / 32 ) 18.9521666666667 0.0960267417046447 197.363425335819 Trimmed Mean ( 19 / 32 ) 18.9646551724138 0.0951825753844705 199.245030887323 Trimmed Mean ( 20 / 32 ) 18.9782142857143 0.0941441651959657 201.586728675221 Trimmed Mean ( 21 / 32 ) 18.9925925925926 0.092811202449665 204.636855156499 Trimmed Mean ( 22 / 32 ) 19.0078846153846 0.0912843404414949 208.227221924958 Trimmed Mean ( 23 / 32 ) 19.024 0.0893902245488732 212.819691370155 Trimmed Mean ( 24 / 32 ) 19.0416666666667 0.0869072288722869 219.103369348585 Trimmed Mean ( 25 / 32 ) 19.0597826086957 0.0840304115241118 226.820055536996 Trimmed Mean ( 26 / 32 ) 19.0788636363636 0.0804586587140275 237.126294935828 Trimmed Mean ( 27 / 32 ) 19.0995238095238 0.0757218091354144 252.232798286262 Trimmed Mean ( 28 / 32 ) 19.11975 0.0711260054680857 268.815180526046 Trimmed Mean ( 29 / 32 ) 19.1413157894737 0.06526907982585 293.267743938574 Trimmed Mean ( 30 / 32 ) 19.1625 0.0588950842802772 325.366713269432 Trimmed Mean ( 31 / 32 ) 19.1826470588235 0.0521913878600775 367.544298884162 Trimmed Mean ( 32 / 32 ) 19.196875 0.0479928537607088 399.994447000697 Median 19.245 Midrange 18.62 Midmean - Weighted Average at Xnp 18.9952941176471 Midmean - Weighted Average at X(n+1)p 19.0538775510204 Midmean - Empirical Distribution Function 18.9952941176471 Midmean - Empirical Distribution Function - Averaging 19.0538775510204 Midmean - Empirical Distribution Function - Interpolation 19.0538775510204 Midmean - Closest Observation 18.9952941176471 Midmean - True Basic - Statistics Graphics Toolkit 19.0538775510204 Midmean - MS Excel (old versions) 18.9952941176471 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/13/t1218624388vpo8ihskibodc5j/137d51218624249.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/13/t1218624388vpo8ihskibodc5j/137d51218624249.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/13/t1218624388vpo8ihskibodc5j/2fqbs1218624249.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/13/t1218624388vpo8ihskibodc5j/2fqbs1218624249.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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