Centrummaten - Eigen reeks - Kirsten Witvrouwen

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

Title produced by software: Central Tendency

Date of computation: Wed, 16 Apr 2008 11:50:46 -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/16/t1208368324erixrtakpxsqu8c.htm/, Retrieved Wed, 16 Apr 2008 19:52:06 +0200

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Dataseries X:

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77.5 77.7 76.6 77 76.5 77.6 77.8 76.9 76.9 77 77 76.3 76.5 77.1 76.4 75.4 75.4 75.5 75.5 75.8 75.7 75.9 76.1 76 76 75.89 74.87 74.9 74.79 74.64 74.09 74.33 73.93 73.78 72.85 71.51 71.5 71.5 71.31 70.85 70.62 70.07 68.83 68.82 68.4 68.21 67.75 67.7 67.42 66.27 64.8 62.69 62.75 62.31 62.4 61.75 61.69 60.39 59.9 59.62 58.97 58.54 58.32 56.03 53.63 53.61 53.48 53.48 52.81 52.8 52.57 52.36

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 69.0531944444444 0.970179686388367 71.1756754065887 Geometric Mean 68.5330632341875 Harmonic Mean 67.9773076118395 Quadratic Mean 69.5354033228957 Winsorized Mean ( 1 / 24 ) 69.0547222222222 0.969301532327312 71.2417342995636 Winsorized Mean ( 2 / 24 ) 69.0583333333333 0.96743303763936 71.3830628545031 Winsorized Mean ( 3 / 24 ) 69.0545833333333 0.966819033189865 71.4245178909012 Winsorized Mean ( 4 / 24 ) 69.0695833333333 0.955454349504307 72.2897785427079 Winsorized Mean ( 5 / 24 ) 69.0626388888889 0.954636695494985 72.3444208826264 Winsorized Mean ( 6 / 24 ) 69.0734722222222 0.952152371054293 72.5445572810358 Winsorized Mean ( 7 / 24 ) 69.0754166666667 0.951707754584848 72.5804915783193 Winsorized Mean ( 8 / 24 ) 69.3309722222222 0.891826960269023 77.7403860960968 Winsorized Mean ( 9 / 24 ) 69.6172222222222 0.834375832007632 83.4362880031087 Winsorized Mean ( 10 / 24 ) 69.6061111111111 0.823517104131046 84.522969543611 Winsorized Mean ( 11 / 24 ) 69.6565277777778 0.809367499716845 86.0629167864375 Winsorized Mean ( 12 / 24 ) 69.7648611111111 0.789487660797475 88.3672596486694 Winsorized Mean ( 13 / 24 ) 69.7973611111111 0.778220955611803 89.6883598517847 Winsorized Mean ( 14 / 24 ) 69.8731944444444 0.758980888107775 92.0618628733145 Winsorized Mean ( 15 / 24 ) 70.1023611111111 0.707458186056125 99.090465688031 Winsorized Mean ( 16 / 24 ) 70.0934722222222 0.702584212667048 99.7652252334899 Winsorized Mean ( 17 / 24 ) 70.2256944444444 0.680694774931675 103.167670783860 Winsorized Mean ( 18 / 24 ) 70.2231944444444 0.674036808479918 104.183026150769 Winsorized Mean ( 19 / 24 ) 70.2970833333333 0.661267823568848 106.306523359842 Winsorized Mean ( 20 / 24 ) 70.28875 0.655598853499381 107.213045942379 Winsorized Mean ( 21 / 24 ) 70.8575 0.5577253977784 127.047289369013 Winsorized Mean ( 22 / 24 ) 71.2455555555556 0.483145296468428 147.461966568500 Winsorized Mean ( 23 / 24 ) 71.6129166666667 0.431266488310592 166.052588382643 Winsorized Mean ( 24 / 24 ) 71.6729166666667 0.414344818973488 172.97891365996 Trimmed Mean ( 1 / 24 ) 69.1667142857143 0.960459640684712 72.0141808732383 Trimmed Mean ( 2 / 24 ) 69.2852941176471 0.949373377521619 72.980026360671 Trimmed Mean ( 3 / 24 ) 69.4090909090909 0.936747428531939 74.0958435486374 Trimmed Mean ( 4 / 24 ) 69.54203125 0.921299579756282 75.482538772455 Trimmed Mean ( 5 / 24 ) 69.6791935483871 0.906241192400888 76.8881332394385 Trimmed Mean ( 6 / 24 ) 69.8271666666667 0.887568413585526 78.67243313063 Trimmed Mean ( 7 / 24 ) 69.9831034482759 0.864867946128521 80.9176750757696 Trimmed Mean ( 8 / 24 ) 70.1498214285714 0.836399848883553 83.871155072791 Trimmed Mean ( 9 / 24 ) 70.2862962962963 0.816650463891648 86.0665601796827 Trimmed Mean ( 10 / 24 ) 70.3892307692308 0.8056257157189 87.3721250399994 Trimmed Mean ( 11 / 24 ) 70.502 0.793242171633066 88.8782802039582 Trimmed Mean ( 12 / 24 ) 70.6172916666667 0.779849318255084 90.5524824009247 Trimmed Mean ( 13 / 24 ) 70.7284782608696 0.7664160880604 92.2846993463628 Trimmed Mean ( 14 / 24 ) 70.8456818181818 0.750573522626249 94.388730327568 Trimmed Mean ( 15 / 24 ) 70.9647619047619 0.733396093668699 96.7618487709307 Trimmed Mean ( 16 / 24 ) 71.06825 0.722083691390267 98.4210706423356 Trimmed Mean ( 17 / 24 ) 71.1836842105263 0.7064694361125 100.759750630161 Trimmed Mean ( 18 / 24 ) 71.2963888888889 0.689684095245474 103.375428519216 Trimmed Mean ( 19 / 24 ) 71.4226470588235 0.666525739403676 107.156622522520 Trimmed Mean ( 20 / 24 ) 71.5559375 0.636325587970695 112.451768171384 Trimmed Mean ( 21 / 24 ) 71.708 0.592501690186251 121.025815095074 Trimmed Mean ( 22 / 24 ) 71.8121428571429 0.565147908050894 127.067873443629 Trimmed Mean ( 23 / 24 ) 71.8834615384615 0.550541814888596 130.568577344134 Trimmed Mean ( 24 / 24 ) 71.91875 0.545038328827712 131.951729256703 Median 71.505 Midrange 65.08 Midmean - Weighted Average at Xnp 71.0535135135135 Midmean - Weighted Average at X(n+1)p 71.2963888888889 Midmean - Empirical Distribution Function 71.0535135135135 Midmean - Empirical Distribution Function - Averaging 71.2963888888889 Midmean - Empirical Distribution Function - Interpolation 71.2963888888889 Midmean - Closest Observation 71.0535135135135 Midmean - True Basic - Statistics Graphics Toolkit 71.2963888888889 Midmean - MS Excel (old versions) 71.3071794871795 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208368324erixrtakpxsqu8c/1fwki1208368244.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208368324erixrtakpxsqu8c/1fwki1208368244.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208368324erixrtakpxsqu8c/243m81208368244.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208368324erixrtakpxsqu8c/243m81208368244.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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