Centrummaten: eigen reeks

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

Title produced by software: Central Tendency

Date of computation: Sat, 19 Apr 2008 07:25:26 -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/19/t1208611576bkra1a9hxh0rzpz.htm/, Retrieved Sat, 19 Apr 2008 15:26:19 +0200

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Dataseries X:

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66.2 66.2 66.08 66.31 66.39 66.37 66.23 66.27 66.27 66.27 66.28 66.28 66.28 66.26 66.13 65.86 65.9 65.94 65.94 65.91 65.95 65.91 66.08 66.47 66.47 66.56 66.78 67.08 67.28 67.27 67.27 67.26 67.37 67.5 67.63 67.64 67.64 67.71 67.87 67.93 68.33 68.39 68.39 68.58 68.44 68.49 68.52 68.54 68.54 68.54 68.62 68.75 68.71 68.72 68.72 68.72 68.92 68.9 69.12 69.09 69.09 69.1 69.16 68.83 68.52 68.53 68.53 68.51 68.38 68.44 68.41 68.42 68.42 68.45 68.63 68.84 68.72 68.37 68.37 68.47 68.69 68.46 68.17 68.17

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 67.6636904761905 0.120738165157440 560.416752962564 Geometric Mean 67.6547095983043 Harmonic Mean 67.6456898924684 Quadratic Mean 67.6726307921698 Winsorized Mean ( 1 / 28 ) 67.6636904761905 0.120583157014769 561.137161700809 Winsorized Mean ( 2 / 28 ) 67.6634523809524 0.120472450869329 561.650832972126 Winsorized Mean ( 3 / 28 ) 67.6630952380952 0.120421302911041 561.886423767395 Winsorized Mean ( 4 / 28 ) 67.6645238095238 0.120172519509512 563.06153924124 Winsorized Mean ( 5 / 28 ) 67.6544047619048 0.118799617612511 569.48335458935 Winsorized Mean ( 6 / 28 ) 67.6536904761905 0.118493457043307 570.948744043008 Winsorized Mean ( 7 / 28 ) 67.6595238095238 0.116042989734373 583.055675869771 Winsorized Mean ( 8 / 28 ) 67.6585714285714 0.115926651842841 583.632584509512 Winsorized Mean ( 9 / 28 ) 67.6553571428571 0.114037850208705 593.27106762394 Winsorized Mean ( 10 / 28 ) 67.660119047619 0.112303949662511 602.473192180216 Winsorized Mean ( 11 / 28 ) 67.660119047619 0.112303949662511 602.473192180216 Winsorized Mean ( 12 / 28 ) 67.6644047619048 0.111636544415648 606.113393388233 Winsorized Mean ( 13 / 28 ) 67.6690476190476 0.11092186845754 610.060473737429 Winsorized Mean ( 14 / 28 ) 67.6690476190476 0.110477451671437 612.514559263164 Winsorized Mean ( 15 / 28 ) 67.6654761904762 0.110074481220691 614.72446147452 Winsorized Mean ( 16 / 28 ) 67.6540476190476 0.108816076864906 621.728420728121 Winsorized Mean ( 17 / 28 ) 67.6540476190476 0.108288214142064 624.759103795839 Winsorized Mean ( 18 / 28 ) 67.6454761904762 0.107378185497108 629.974103932853 Winsorized Mean ( 19 / 28 ) 67.6364285714286 0.106441104045571 635.435240717448 Winsorized Mean ( 20 / 28 ) 67.6435714285714 0.105348047975251 642.096106464762 Winsorized Mean ( 21 / 28 ) 67.6585714285714 0.103074390480628 656.405253653061 Winsorized Mean ( 22 / 28 ) 67.6611904761905 0.102017430249143 663.231668460489 Winsorized Mean ( 23 / 28 ) 67.6830952380952 0.0987518166445793 685.385824158512 Winsorized Mean ( 24 / 28 ) 67.6802380952381 0.098457404373248 687.406280168276 Winsorized Mean ( 25 / 28 ) 67.7070238095238 0.0945152168295258 716.361090634166 Winsorized Mean ( 26 / 28 ) 67.7720238095238 0.0843822307433837 803.155157341438 Winsorized Mean ( 27 / 28 ) 67.8620238095238 0.0703810584983637 964.208627397975 Winsorized Mean ( 28 / 28 ) 67.9153571428571 0.061801564265214 1098.92618334718 Trimmed Mean ( 1 / 28 ) 67.6674390243902 0.120311726368734 562.434278575654 Trimmed Mean ( 2 / 28 ) 67.671375 0.119933624014718 564.240225007254 Trimmed Mean ( 3 / 28 ) 67.675641025641 0.119496751076902 566.338753277807 Trimmed Mean ( 4 / 28 ) 67.6802631578947 0.118944919241980 569.005078898806 Trimmed Mean ( 5 / 28 ) 67.6847297297297 0.118319753107013 572.049281310731 Trimmed Mean ( 6 / 28 ) 67.6918055555556 0.117894333207250 574.173530771474 Trimmed Mean ( 7 / 28 ) 67.6994285714286 0.117385578968031 576.726963964338 Trimmed Mean ( 8 / 28 ) 67.7064705882353 0.117244063949634 577.483143345498 Trimmed Mean ( 9 / 28 ) 67.7140909090909 0.116990222784499 578.801281828679 Trimmed Mean ( 10 / 28 ) 67.72265625 0.116930874766190 579.168302515615 Trimmed Mean ( 11 / 28 ) 67.731129032258 0.11704453785327 578.678255940209 Trimmed Mean ( 12 / 28 ) 67.7401666666667 0.117030222487689 578.826265786112 Trimmed Mean ( 13 / 28 ) 67.7493103448276 0.116977684664881 579.16439822618 Trimmed Mean ( 14 / 28 ) 67.7585714285714 0.116876955104539 579.742784777084 Trimmed Mean ( 15 / 28 ) 67.7685185185185 0.116654808444196 580.932062915663 Trimmed Mean ( 16 / 28 ) 67.7796153846154 0.116260863369050 582.995974917723 Trimmed Mean ( 17 / 28 ) 67.7928 0.115767550351062 585.594147880128 Trimmed Mean ( 18 / 28 ) 67.8070833333333 0.115032742152569 589.458984150791 Trimmed Mean ( 19 / 28 ) 67.8234782608696 0.114019329402609 594.841932646181 Trimmed Mean ( 20 / 28 ) 67.8422727272727 0.112626655805472 602.3642648544 Trimmed Mean ( 21 / 28 ) 67.8621428571429 0.110820787260331 612.359328378771 Trimmed Mean ( 22 / 28 ) 67.8825 0.108739131493445 624.269286205326 Trimmed Mean ( 23 / 28 ) 67.9047368421053 0.105940707028530 640.969262398997 Trimmed Mean ( 24 / 28 ) 67.9272222222222 0.102788588020074 660.844005454735 Trimmed Mean ( 25 / 28 ) 67.9526470588235 0.0981816033749237 692.111808353082 Trimmed Mean ( 26 / 28 ) 67.9784375 0.0927460865349062 732.952084985445 Trimmed Mean ( 27 / 28 ) 68.0006666666667 0.0884046773263727 769.19761174651 Trimmed Mean ( 28 / 28 ) 68.0160714285714 0.0868745054962353 782.923264311633 Median 68.25 Midrange 67.51 Midmean - Weighted Average at Xnp 67.8577777777778 Midmean - Weighted Average at X(n+1)p 67.8929545454546 Midmean - Empirical Distribution Function 67.8577777777778 Midmean - Empirical Distribution Function - Averaging 67.8929545454546 Midmean - Empirical Distribution Function - Interpolation 67.8929545454546 Midmean - Closest Observation 67.8577777777778 Midmean - True Basic - Statistics Graphics Toolkit 67.8929545454546 Midmean - MS Excel (old versions) 67.8577777777778 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208611576bkra1a9hxh0rzpz/12u941208611524.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208611576bkra1a9hxh0rzpz/12u941208611524.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208611576bkra1a9hxh0rzpz/20g6x1208611524.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208611576bkra1a9hxh0rzpz/20g6x1208611524.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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