Centrummaten Lederen Laarzen - Christine Van Bergen

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 08:21:20 -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/t1208614972oo6modxmdoasgmc.htm/, Retrieved Sat, 19 Apr 2008 16:22:54 +0200

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Dataseries X:

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101.31 101.31 101.39 101.26 101.26 101.25 101.25 101.22 101.29 101.26 101.32 101.34 101.34 101.34 101.34 101.34 101.34 101.34 101.34 101.31 102.19 102.16 102.31 102.32 102.32 102.32 102.36 102.36 102.37 102.37 102.37 102.37 103.45 103.93 104 103.92 103.92 103.9 103.91 103.84 103.8 103.81 103.81 103.81 104.51 105.14 105.15 105.23 105.23 105.22 105.13 105 105.01 105.01 105.01 105.01 105.57 106.05 106.09 106.2 106.19 106.2 106.09 106.23 106.23 106.22 106.22 106.61 106.95 107.74 107.8 107.8

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 103.679305555556 0.239793723820945 432.368720513191 Geometric Mean 103.659683051457 Harmonic Mean 103.640129176699 Quadratic Mean 103.698992153305 Winsorized Mean ( 1 / 24 ) 103.679722222222 0.239733891025751 432.47836915593 Winsorized Mean ( 2 / 24 ) 103.678055555556 0.239332963801820 433.195887054683 Winsorized Mean ( 3 / 24 ) 103.645555555556 0.232027692556349 446.694764808664 Winsorized Mean ( 4 / 24 ) 103.626666666667 0.228394495081233 453.717882428863 Winsorized Mean ( 5 / 24 ) 103.600277777778 0.223780731553548 462.954415505553 Winsorized Mean ( 6 / 24 ) 103.602777777778 0.223414359051271 463.724794671778 Winsorized Mean ( 7 / 24 ) 103.60375 0.222970892005063 464.651457723223 Winsorized Mean ( 8 / 24 ) 103.60375 0.222970892005063 464.651457723223 Winsorized Mean ( 9 / 24 ) 103.60125 0.222558738136633 465.500707217334 Winsorized Mean ( 10 / 24 ) 103.602638888889 0.222357636143121 465.927955908854 Winsorized Mean ( 11 / 24 ) 103.604166666667 0.221665762114713 467.389125313141 Winsorized Mean ( 12 / 24 ) 103.5875 0.21895493976947 473.099625471175 Winsorized Mean ( 13 / 24 ) 103.5875 0.21895493976947 473.099625471175 Winsorized Mean ( 14 / 24 ) 103.579722222222 0.21770741124294 475.774901877996 Winsorized Mean ( 15 / 24 ) 103.479722222222 0.202418376700885 511.217034287034 Winsorized Mean ( 16 / 24 ) 103.404166666667 0.191848428818332 538.988863779456 Winsorized Mean ( 17 / 24 ) 103.404166666667 0.191848428818332 538.988863779456 Winsorized Mean ( 18 / 24 ) 103.401666666667 0.191513717295558 539.917809161886 Winsorized Mean ( 19 / 24 ) 103.396388888889 0.187061987662668 552.738641243058 Winsorized Mean ( 20 / 24 ) 103.6075 0.156392822049902 662.482450549684 Winsorized Mean ( 21 / 24 ) 103.613333333333 0.154853659020541 669.104843816374 Winsorized Mean ( 22 / 24 ) 103.613333333333 0.145144685247901 713.862399827913 Winsorized Mean ( 23 / 24 ) 103.616527777778 0.144741169847813 715.874604901458 Winsorized Mean ( 24 / 24 ) 103.616527777778 0.144741169847813 715.874604901458 Trimmed Mean ( 1 / 24 ) 103.655571428571 0.236817025900346 437.703205816757 Trimmed Mean ( 2 / 24 ) 103.63 0.233249180025227 444.288807312386 Trimmed Mean ( 3 / 24 ) 103.603787878788 0.229150734193505 452.120689219787 Trimmed Mean ( 4 / 24 ) 103.588125 0.227435002379888 455.462544973510 Trimmed Mean ( 5 / 24 ) 103.576935483871 0.226486696348668 457.320174445999 Trimmed Mean ( 6 / 24 ) 103.571333333333 0.226489728214807 457.289317929263 Trimmed Mean ( 7 / 24 ) 103.564827586207 0.226308154081352 457.627468204163 Trimmed Mean ( 8 / 24 ) 103.557678571429 0.225904386030938 458.413758098731 Trimmed Mean ( 9 / 24 ) 103.55 0.225115701286601 459.985684730927 Trimmed Mean ( 10 / 24 ) 103.542115384615 0.223939150951084 462.367187447417 Trimmed Mean ( 11 / 24 ) 103.5334 0.222223019068866 465.898629376084 Trimmed Mean ( 12 / 24 ) 103.52375 0.219924556898384 470.7239221486 Trimmed Mean ( 13 / 24 ) 103.515434782609 0.217315573765743 476.33693705815 Trimmed Mean ( 14 / 24 ) 103.506363636364 0.213687817113609 484.381211032417 Trimmed Mean ( 15 / 24 ) 103.497380952381 0.209011294429389 495.176020199931 Trimmed Mean ( 16 / 24 ) 103.4995 0.206118882176630 502.134976218761 Trimmed Mean ( 17 / 24 ) 103.510789473684 0.204177000994897 506.965960756136 Trimmed Mean ( 18 / 24 ) 103.523333333333 0.201068573945735 514.865805738855 Trimmed Mean ( 19 / 24 ) 103.537647058824 0.196419400506823 527.125359265246 Trimmed Mean ( 20 / 24 ) 103.554375 0.190675760031814 543.091450023445 Trimmed Mean ( 21 / 24 ) 103.548 0.190603035761185 543.265219184337 Trimmed Mean ( 22 / 24 ) 103.54 0.189883004915015 545.283133929447 Trimmed Mean ( 23 / 24 ) 103.530769230769 0.190473033081749 543.545548446928 Trimmed Mean ( 24 / 24 ) 103.519583333333 0.189989014906189 544.87141472073 Median 103.81 Midrange 104.51 Midmean - Weighted Average at Xnp 103.167906976744 Midmean - Weighted Average at X(n+1)p 103.167906976744 Midmean - Empirical Distribution Function 103.167906976744 Midmean - Empirical Distribution Function - Averaging 103.167906976744 Midmean - Empirical Distribution Function - Interpolation 103.167906976744 Midmean - Closest Observation 103.167906976744 Midmean - True Basic - Statistics Graphics Toolkit 103.167906976744 Midmean - MS Excel (old versions) 103.259555555556 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208614972oo6modxmdoasgmc/1nuwq1208614877.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208614972oo6modxmdoasgmc/1nuwq1208614877.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208614972oo6modxmdoasgmc/2r57d1208614877.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/19/t1208614972oo6modxmdoasgmc/2r57d1208614877.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')

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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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