Omzet product Y

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 06 Aug 2010 13:54:48 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Aug/06/t1281102863fgswgl83qcboxnv.htm/, Retrieved Fri, 06 Aug 2010 15:54:23 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Aug/06/t1281102863fgswgl83qcboxnv.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Philippe De Vocht

Dataseries X:

» Textbox « » Textfile « » CSV «

31 30 29 27 25 24 25 27 28 28 29 31 31 27 25 16 20 21 25 24 28 27 23 36 37 30 27 22 22 25 33 35 35 29 25 34 31 29 21 19 18 25 23 22 20 15 17 25 26 26 23 24 24 42 40 45 47 40 39 49 55 54 48 44 48 62 57 60 56 57 54 62 65 68 69 67 72 82 72 77 79 78 76 79

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 38.3571428571429 2.02236795203832 18.9664510943635 Geometric Mean 34.5499008615466 Harmonic Mean 31.4839349367746 Quadratic Mean 42.5527683616248 Winsorized Mean ( 1 / 28 ) 38.3333333333333 2.01175071634915 19.0547134005247 Winsorized Mean ( 2 / 28 ) 38.3571428571429 2.00863332119908 19.0961398739742 Winsorized Mean ( 3 / 28 ) 38.3571428571429 1.99552301965104 19.2215987885975 Winsorized Mean ( 4 / 28 ) 38.3571428571429 1.97848749125513 19.3871040512920 Winsorized Mean ( 5 / 28 ) 38.3571428571429 1.95771733384808 19.5927891090121 Winsorized Mean ( 6 / 28 ) 38.0714285714286 1.89374863990838 20.1037390966895 Winsorized Mean ( 7 / 28 ) 38.1547619047619 1.88438749996760 20.2478322029932 Winsorized Mean ( 8 / 28 ) 37.8690476190476 1.82407402784706 20.7606966827679 Winsorized Mean ( 9 / 28 ) 37.8690476190476 1.79050371296946 21.1499408489043 Winsorized Mean ( 10 / 28 ) 37.75 1.76655963152307 21.3692192023279 Winsorized Mean ( 11 / 28 ) 37.4880952380952 1.71511571909783 21.8574728344362 Winsorized Mean ( 12 / 28 ) 37.2023809523809 1.61877075270998 22.9818712069639 Winsorized Mean ( 13 / 28 ) 37.2023809523809 1.61877075270998 22.9818712069639 Winsorized Mean ( 14 / 28 ) 36.8690476190476 1.55818308527097 23.6615632447558 Winsorized Mean ( 15 / 28 ) 36.5119047619048 1.44555960926598 25.2579724335579 Winsorized Mean ( 16 / 28 ) 36.5119047619048 1.44555960926598 25.2579724335579 Winsorized Mean ( 17 / 28 ) 36.3095238095238 1.41126687047916 25.7283186965168 Winsorized Mean ( 18 / 28 ) 36.0952380952381 1.37551107151687 26.2413286542532 Winsorized Mean ( 19 / 28 ) 36.0952380952381 1.31473172938737 27.4544511921512 Winsorized Mean ( 20 / 28 ) 36.0952380952381 1.31473172938737 27.4544511921512 Winsorized Mean ( 21 / 28 ) 34.8452380952381 1.11610723790325 31.2203316239571 Winsorized Mean ( 22 / 28 ) 34.5833333333333 1.07642663522117 32.1279056107967 Winsorized Mean ( 23 / 28 ) 34.5833333333333 1.07642663522117 32.1279056107967 Winsorized Mean ( 24 / 28 ) 34.2976190476191 1.03381992530284 33.1756219900406 Winsorized Mean ( 25 / 28 ) 33.7023809523809 0.94692481135846 35.5914012898569 Winsorized Mean ( 26 / 28 ) 33.3928571428571 0.90276204227637 36.9896557221823 Winsorized Mean ( 27 / 28 ) 33.0714285714286 0.777034411622909 42.5610861973999 Winsorized Mean ( 28 / 28 ) 32.4047619047619 0.686338921531583 47.2139359843528 Trimmed Mean ( 1 / 28 ) 38.109756097561 1.98078743155585 19.2397000760586 Trimmed Mean ( 2 / 28 ) 37.875 1.9444317610597 19.478698485854 Trimmed Mean ( 3 / 28 ) 37.6153846153846 1.90353709436074 19.7607836100599 Trimmed Mean ( 4 / 28 ) 37.3421052631579 1.86100827525135 20.0655234905467 Trimmed Mean ( 5 / 28 ) 37.0540540540541 1.81654862440014 20.3980524145287 Trimmed Mean ( 6 / 28 ) 36.75 1.76978531539783 20.7652304944902 Trimmed Mean ( 7 / 28 ) 36.4857142857143 1.73166142377822 21.0697736778753 Trimmed Mean ( 8 / 28 ) 36.1911764705882 1.68766861453200 21.4444803671509 Trimmed Mean ( 9 / 28 ) 35.9242424242424 1.64894691350916 21.7861728172869 Trimmed Mean ( 10 / 28 ) 35.640625 1.60887407445406 22.1525261460217 Trimmed Mean ( 11 / 28 ) 35.3548387096774 1.56493449568236 22.5918968539713 Trimmed Mean ( 12 / 28 ) 35.0833333333333 1.52202134157786 23.0504871219237 Trimmed Mean ( 13 / 28 ) 34.8275862068966 1.48864179866735 23.3955450116171 Trimmed Mean ( 14 / 28 ) 34.5535714285714 1.44642857142857 23.8888888888889 Trimmed Mean ( 15 / 28 ) 34.2962962962963 1.40619315746712 24.3894632214480 Trimmed Mean ( 16 / 28 ) 34.0576923076923 1.37786133422919 24.7177937733081 Trimmed Mean ( 17 / 28 ) 33.8 1.34072779504572 25.2101881716022 Trimmed Mean ( 18 / 28 ) 33.5416666666667 1.29987667627451 25.8037299067465 Trimmed Mean ( 19 / 28 ) 33.2826086956522 1.25442715277592 26.5321175661744 Trimmed Mean ( 20 / 28 ) 33 1.20692154651838 27.3422908847683 Trimmed Mean ( 21 / 28 ) 32.6904761904762 1.14230653596642 28.6179542541260 Trimmed Mean ( 22 / 28 ) 32.475 1.10939316976814 29.2727599961582 Trimmed Mean ( 23 / 28 ) 32.2631578947368 1.07386130801737 30.0440640275075 Trimmed Mean ( 24 / 28 ) 32.0277777777778 1.02313408259622 31.3035977616019 Trimmed Mean ( 25 / 28 ) 31.7941176470588 0.964410741339992 32.9674030827184 Trimmed Mean ( 26 / 28 ) 31.59375 0.910134887867124 34.7132611013726 Trimmed Mean ( 27 / 28 ) 31.4 0.846357985181483 37.1001403067839 Trimmed Mean ( 28 / 28 ) 31.2142857142857 0.797411723825295 39.1445031238649 Median 30 Midrange 48.5 Midmean - Weighted Average at Xnp 32.3409090909091 Midmean - Weighted Average at X(n+1)p 32.3409090909091 Midmean - Empirical Distribution Function 32.3409090909091 Midmean - Empirical Distribution Function - Averaging 32.3409090909091 Midmean - Empirical Distribution Function - Interpolation 32.3409090909091 Midmean - Closest Observation 32.3409090909091 Midmean - True Basic - Statistics Graphics Toolkit 32.3409090909091 Midmean - MS Excel (old versions) 33.2826086956522 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/06/t1281102863fgswgl83qcboxnv/1w08c1281102885.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/06/t1281102863fgswgl83qcboxnv/1w08c1281102885.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/06/t1281102863fgswgl83qcboxnv/2w08c1281102885.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/06/t1281102863fgswgl83qcboxnv/2w08c1281102885.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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