trimmed mean plot

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 11:15:50 -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/t1208366199v4x3j0pnxyvyohn.htm/, Retrieved Wed, 16 Apr 2008 19:16:41 +0200

User-defined keywords:

opgave 5 oef 2

Dataseries X:

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4.07 4.08 4.09 4.08 4.09 4.12 4.14 4.14 4.14 4.14 4.14 4.23 4.29 4.32 4.33 4.35 4.35 4.35 4.35 4.36 4.36 4.38 4.4 4.4 4.4 4.43 4.44 4.46 4.47 4.49 4.49 4.57 4.62 4.64 4.66 4.67 4.68 4.72 4.74 4.75 4.76 4.77 4.76 4.77 4.77 4.78 4.81 4.81 4.85 4.92 4.96 4.95 4.96 4.97 5 5 5.01 5.01 5.02 5.04 5.04 5.19 5.22 5.22 5.22 5.24 5.28 5.34 5.36 5.38 5.39 5.41 5.44 5.51 5.55 5.56 5.57 5.58 5.58 5.59 5.61 5.63 5.64 5.64

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 4.79809523809524 0.0527962983190362 90.8793872081983 Geometric Mean 4.77418715143325 Harmonic Mean 4.75055700772139 Quadratic Mean 4.82214435603873 Winsorized Mean ( 1 / 28 ) 4.79821428571428 0.0527766488317794 90.9154785672001 Winsorized Mean ( 2 / 28 ) 4.79797619047619 0.052731140163207 90.989426278781 Winsorized Mean ( 3 / 28 ) 4.79761904761905 0.0525384374352335 91.3163634440649 Winsorized Mean ( 4 / 28 ) 4.79666666666667 0.0523627987110185 91.6044746412174 Winsorized Mean ( 5 / 28 ) 4.79785714285714 0.051968996292891 92.3215279320963 Winsorized Mean ( 6 / 28 ) 4.79928571428571 0.0517470972005474 92.7450228886452 Winsorized Mean ( 7 / 28 ) 4.79845238095238 0.0515962896902456 92.9999503793689 Winsorized Mean ( 8 / 28 ) 4.7975 0.0514254288021146 93.2904228851609 Winsorized Mean ( 9 / 28 ) 4.79642857142857 0.0512347938224089 93.6166267801145 Winsorized Mean ( 10 / 28 ) 4.79166666666667 0.0504039429803573 95.0653140079539 Winsorized Mean ( 11 / 28 ) 4.79428571428571 0.0470876691521407 101.816161228863 Winsorized Mean ( 12 / 28 ) 4.79857142857143 0.045183422589615 106.202035028536 Winsorized Mean ( 13 / 28 ) 4.80011904761905 0.0440617408476960 108.940748941608 Winsorized Mean ( 14 / 28 ) 4.80011904761905 0.0435759879452551 110.155139882301 Winsorized Mean ( 15 / 28 ) 4.80011904761905 0.0425467560457641 112.819859696376 Winsorized Mean ( 16 / 28 ) 4.79630952380952 0.0419472867308743 114.341353103044 Winsorized Mean ( 17 / 28 ) 4.78416666666667 0.0400935539396064 119.325083375575 Winsorized Mean ( 18 / 28 ) 4.77559523809524 0.0388372123685204 122.964418578253 Winsorized Mean ( 19 / 28 ) 4.77333333333333 0.0378920823694322 125.971787108328 Winsorized Mean ( 20 / 28 ) 4.77333333333333 0.0378920823694322 125.971787108328 Winsorized Mean ( 21 / 28 ) 4.77833333333333 0.0372412986342114 128.307376718162 Winsorized Mean ( 22 / 28 ) 4.77571428571429 0.0354547078467628 134.699016738629 Winsorized Mean ( 23 / 28 ) 4.73464285714286 0.0300155087225223 157.739883768493 Winsorized Mean ( 24 / 28 ) 4.73464285714286 0.0300155087225223 157.739883768493 Winsorized Mean ( 25 / 28 ) 4.73761904761905 0.0281014365421422 168.589923882158 Winsorized Mean ( 26 / 28 ) 4.73761904761905 0.0273209074968090 173.406357317098 Winsorized Mean ( 27 / 28 ) 4.74404761904762 0.0264835864515613 179.131615263836 Winsorized Mean ( 28 / 28 ) 4.74404761904762 0.0256516443403034 184.941267550395 Trimmed Mean ( 1 / 28 ) 4.79670731707317 0.0523391572309505 91.6466288501234 Trimmed Mean ( 2 / 28 ) 4.795125 0.0518182051454281 92.5374583419563 Trimmed Mean ( 3 / 28 ) 4.79358974358974 0.0512276768010098 93.5742169649835 Trimmed Mean ( 4 / 28 ) 4.79210526315789 0.0506097264729394 94.6874365290276 Trimmed Mean ( 5 / 28 ) 4.79081081081081 0.0499350769750571 95.9407915442656 Trimmed Mean ( 6 / 28 ) 4.78916666666667 0.0492449841745703 97.2518673107779 Trimmed Mean ( 7 / 28 ) 4.78714285714286 0.0484753647523503 98.7541379337584 Trimmed Mean ( 8 / 28 ) 4.78514705882353 0.0475886920443737 100.552186943101 Trimmed Mean ( 9 / 28 ) 4.78318181818182 0.0465625674215981 102.725903725900 Trimmed Mean ( 10 / 28 ) 4.78125 0.0453685852958413 105.386799452137 Trimmed Mean ( 11 / 28 ) 4.77983870967742 0.0441042776257671 108.375853023492 Trimmed Mean ( 12 / 28 ) 4.778 0.0432387930028000 110.50262202487 Trimmed Mean ( 13 / 28 ) 4.77551724137931 0.0425319156444233 112.280793588131 Trimmed Mean ( 14 / 28 ) 4.77267857142857 0.0418520050811612 114.037035075696 Trimmed Mean ( 15 / 28 ) 4.76962962962963 0.0410790539893154 116.108555734273 Trimmed Mean ( 16 / 28 ) 4.76634615384615 0.0402874558455024 118.308442511846 Trimmed Mean ( 17 / 28 ) 4.7632 0.0393907064559909 120.921923685773 Trimmed Mean ( 18 / 28 ) 4.76104166666667 0.0386120451929634 123.304570966738 Trimmed Mean ( 19 / 28 ) 4.7595652173913 0.0378465711651703 125.759482850364 Trimmed Mean ( 20 / 28 ) 4.75818181818182 0.0370221816934637 128.522458713498 Trimmed Mean ( 21 / 28 ) 4.75666666666667 0.0359161927231854 132.437942499291 Trimmed Mean ( 22 / 28 ) 4.7545 0.0345723878261250 137.523043647197 Trimmed Mean ( 23 / 28 ) 4.75236842105263 0.0331929018842056 143.174237601503 Trimmed Mean ( 24 / 28 ) 4.75416666666667 0.0326364656310834 145.670389692526 Trimmed Mean ( 25 / 28 ) 4.75617647058824 0.0318026857515666 149.552666958449 Trimmed Mean ( 26 / 28 ) 4.758125 0.0310872779574933 153.056983840976 Trimmed Mean ( 27 / 28 ) 4.76033333333333 0.0302080271486663 157.585045521369 Trimmed Mean ( 28 / 28 ) 4.76214285714286 0.029124605239994 163.509267092261 Median 4.765 Midrange 4.855 Midmean - Weighted Average at Xnp 4.7595652173913 Midmean - Weighted Average at X(n+1)p 4.77772727272727 Midmean - Empirical Distribution Function 4.7595652173913 Midmean - Empirical Distribution Function - Averaging 4.77772727272727 Midmean - Empirical Distribution Function - Interpolation 4.77772727272727 Midmean - Closest Observation 4.7595652173913 Midmean - True Basic - Statistics Graphics Toolkit 4.77772727272727 Midmean - MS Excel (old versions) 4.7595652173913 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208366199v4x3j0pnxyvyohn/1nnz41208366148.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208366199v4x3j0pnxyvyohn/1nnz41208366148.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208366199v4x3j0pnxyvyohn/2ugl61208366148.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/16/t1208366199v4x3j0pnxyvyohn/2ugl61208366148.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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