Centrummaten Inktjet printer - Sanne Dangez

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

Title produced by software: Central Tendency

Date of computation: Sun, 20 Apr 2008 11:31:49 -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/20/t1208712770c9yqy92nw0a8kfi.htm/, Retrieved Sun, 20 Apr 2008 19:32:50 +0200

User-defined keywords:

Dataseries X:

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58,1 57,9 57,3 55,9 55 55,9 56,6 57,3 56,2 57,7 56,8 57,9 58,3 58,2 56,9 57,1 56,7 54,2 54,2 52,1 51,5 51,8 53 52,4 52,41 52,36 52,94 52,34 51,84 51,42 50,85 50,66 51,53 51,59 52,32 51,98 51,17 50,57 49,84 50,12 49,08 48,57 47,22 46,78 46,04 45,05 44,42 44,09 44,46 44,34 43,04 42,87 42,32 42,49 41,94 41,6 41,42 41,12 41,28 40,21 39,69 39,16 38,8 38,44 37,02 36,75 35,95 36,29 36,35 36,07 36,6 36,5

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 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 48.4569444444444 0.840768838262426 57.6340870869905 Geometric Mean 47.9145496583969 Harmonic Mean 47.3515472007045 Quadratic Mean 48.9720819844214 Winsorized Mean ( 1 / 24 ) 48.4572222222222 0.840193272306275 57.6738993508129 Winsorized Mean ( 2 / 24 ) 48.4605555555556 0.838482376191322 57.7955565097029 Winsorized Mean ( 3 / 24 ) 48.4547222222222 0.8366348911026 57.9162102101238 Winsorized Mean ( 4 / 24 ) 48.4630555555555 0.834944958942547 58.0434135645704 Winsorized Mean ( 5 / 24 ) 48.4561111111111 0.831353741583319 58.2857918204904 Winsorized Mean ( 6 / 24 ) 48.4352777777778 0.823712776134606 58.8011733957405 Winsorized Mean ( 7 / 24 ) 48.4615277777778 0.818506160089793 59.2072853458566 Winsorized Mean ( 8 / 24 ) 48.5970833333333 0.785192814390667 61.8919104233603 Winsorized Mean ( 9 / 24 ) 48.6170833333333 0.773277161163647 62.8714848634261 Winsorized Mean ( 10 / 24 ) 48.6531944444444 0.762328557046405 63.8218180267944 Winsorized Mean ( 11 / 24 ) 48.7188888888889 0.74602335307388 65.3047772407524 Winsorized Mean ( 12 / 24 ) 48.7888888888889 0.728938054183668 66.9314609230097 Winsorized Mean ( 13 / 24 ) 48.8809722222222 0.691481737813336 70.6901853645447 Winsorized Mean ( 14 / 24 ) 48.85375 0.677956558611132 72.0602955742212 Winsorized Mean ( 15 / 24 ) 48.8829166666667 0.673385521774158 72.5927645992086 Winsorized Mean ( 16 / 24 ) 48.7229166666667 0.638578368906687 76.2990402416628 Winsorized Mean ( 17 / 24 ) 48.6143055555556 0.600518419304894 80.9538958219252 Winsorized Mean ( 18 / 24 ) 48.7093055555556 0.585783997962334 83.1523321309428 Winsorized Mean ( 19 / 24 ) 48.4375 0.538989547211381 89.8672344400841 Winsorized Mean ( 20 / 24 ) 48.5263888888889 0.52072179295989 93.190624139341 Winsorized Mean ( 21 / 24 ) 48.4213888888889 0.495125547441344 97.7961834914714 Winsorized Mean ( 22 / 24 ) 48.7391666666667 0.446647779626613 109.122151480102 Winsorized Mean ( 23 / 24 ) 48.80625 0.433523677836533 112.580356033986 Winsorized Mean ( 24 / 24 ) 48.82625 0.428890160595044 113.843250524233 Trimmed Mean ( 1 / 24 ) 48.495 0.834085252902682 58.1415386871229 Trimmed Mean ( 2 / 24 ) 48.535 0.826411302508068 58.7298356795237 Trimmed Mean ( 3 / 24 ) 48.5756060606061 0.817923892048389 59.3889071255206 Trimmed Mean ( 4 / 24 ) 48.6209375 0.808171704470189 60.161642917051 Trimmed Mean ( 5 / 24 ) 48.6667741935484 0.796661157057454 61.0884235567652 Trimmed Mean ( 6 / 24 ) 48.7173333333333 0.783473104491401 62.1812453472269 Trimmed Mean ( 7 / 24 ) 48.7756896551724 0.769165649423722 63.4137648914982 Trimmed Mean ( 8 / 24 ) 48.8333928571429 0.752665233047225 64.8806278183423 Trimmed Mean ( 9 / 24 ) 48.8727777777778 0.740274016573136 66.0198476288804 Trimmed Mean ( 10 / 24 ) 48.9121153846154 0.727195916998805 67.2612623933307 Trimmed Mean ( 11 / 24 ) 48.9494 0.71286214770645 68.6660108935352 Trimmed Mean ( 12 / 24 ) 48.9808333333333 0.698010968012481 70.1720110112331 Trimmed Mean ( 13 / 24 ) 49.0058695652174 0.682478686194559 71.8057143124422 Trimmed Mean ( 14 / 24 ) 49.0215909090909 0.670349609267442 73.1283948425982 Trimmed Mean ( 15 / 24 ) 49.0421428571429 0.656842350999614 74.6634908399378 Trimmed Mean ( 16 / 24 ) 49.06125 0.639411306523631 76.728780832384 Trimmed Mean ( 17 / 24 ) 49.1013157894737 0.623622826504303 78.7355973877824 Trimmed Mean ( 18 / 24 ) 49.1586111111111 0.610361479257622 80.5401598588797 Trimmed Mean ( 19 / 24 ) 49.2114705882353 0.594931523247395 82.7178736800123 Trimmed Mean ( 20 / 24 ) 49.303125 0.58313381644616 84.5485609126084 Trimmed Mean ( 21 / 24 ) 49.3963333333333 0.56978731328056 86.6925819196169 Trimmed Mean ( 22 / 24 ) 49.5157142857143 0.554643559827435 89.2748386028677 Trimmed Mean ( 23 / 24 ) 49.6134615384615 0.547107060907346 90.6832777046972 Trimmed Mean ( 24 / 24 ) 49.71875 0.536600718053882 92.6550195093245 Median 50.755 Midrange 47.125 Midmean - Weighted Average at Xnp 49.1013157894737 Midmean - Weighted Average at X(n+1)p 49.2948648648649 Midmean - Empirical Distribution Function 49.1013157894737 Midmean - Empirical Distribution Function - Averaging 49.2948648648649 Midmean - Empirical Distribution Function - Interpolation 49.2948648648649 Midmean - Closest Observation 49.1013157894737 Midmean - True Basic - Statistics Graphics Toolkit 49.2948648648649 Midmean - MS Excel (old versions) 49.1013157894737 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208712770c9yqy92nw0a8kfi/1l4kg1208712704.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208712770c9yqy92nw0a8kfi/1l4kg1208712704.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208712770c9yqy92nw0a8kfi/2xhbm1208712704.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208712770c9yqy92nw0a8kfi/2xhbm1208712704.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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