Paper invoer central tendency

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Tue, 30 Nov 2010 13:44:42 +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/Nov/30/t1291124636thyfp8wqq2harfu.htm/, Retrieved Tue, 30 Nov 2010 14:43:56 +0100

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/Nov/30/t1291124636thyfp8wqq2harfu.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:

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Dataseries X:

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14731798,37 16471559,62 15213975,95 17637387,4 17972385,83 16896235,55 16697955,94 19691579,52 15930700,75 17444615,98 17699369,88 15189796,81 15672722,75 17180794,3 17664893,45 17862884,98 16162288,88 17463628,82 16772112,17 19106861,48 16721314,25 18161267,85 18509941,2 17802737,97 16409869,75 17967742,04 20286602,27 19537280,81 18021889,62 20194317,23 19049596,62 20244720,94 21473302,24 19673603,19 21053177,29 20159479,84 18203628,31 21289464,94 20432335,71 17180395,07 15816786,32 15071819,75 14521120,61 15668789,39 14346884,11 13881008,13 15465943,69 14238232,92 13557713,21 16127590,29 16793894,2 16014007,43 16867867,15 16014583,21 15878594,85 18664899,14 17962530,06 17332692,2 19542066,35 17203555,19

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 17380113.2295 250529.221517466 69.3735969170699 Geometric Mean 17273958.7921661 Harmonic Mean 17168260.3231621 Quadratic Mean 17486322.2099290 Winsorized Mean ( 1 / 20 ) 17382437.5231667 248355.733180828 69.990079554598 Winsorized Mean ( 2 / 20 ) 17386468.7611667 243572.288513917 71.3811446583065 Winsorized Mean ( 3 / 20 ) 17360859.2416667 234978.407786339 73.8827852534117 Winsorized Mean ( 4 / 20 ) 17362759.4456667 230379.60308701 75.3658709929675 Winsorized Mean ( 5 / 20 ) 17376825.8148333 226051.987998693 76.870926766341 Winsorized Mean ( 6 / 20 ) 17405787.5818333 218510.505178241 79.6565252898722 Winsorized Mean ( 7 / 20 ) 17415487.21 215179.008863054 80.9348797636843 Winsorized Mean ( 8 / 20 ) 17356324.386 201723.872995351 86.0400116668393 Winsorized Mean ( 9 / 20 ) 17391423.0975 194616.696118000 89.3624413753032 Winsorized Mean ( 10 / 20 ) 17403307.9075 184758.599186498 94.1948465951123 Winsorized Mean ( 11 / 20 ) 17403151.6745 184471.816585403 94.340436369276 Winsorized Mean ( 12 / 20 ) 17345880.5225 163569.265523457 106.046086757127 Winsorized Mean ( 13 / 20 ) 17346864.9843333 159204.777226839 108.959450127662 Winsorized Mean ( 14 / 20 ) 17269260.2823333 141611.76972541 121.947916587859 Winsorized Mean ( 15 / 20 ) 17251347.4673333 131916.042396430 130.775204849537 Winsorized Mean ( 16 / 20 ) 17169817.5713333 119255.448385686 143.975120665382 Winsorized Mean ( 17 / 20 ) 17189834.1136667 112296.666908024 153.075194366595 Winsorized Mean ( 18 / 20 ) 17158430.2216667 104627.813040899 163.994923748998 Winsorized Mean ( 19 / 20 ) 17221154.6303333 90089.9971115463 191.155013680494 Winsorized Mean ( 20 / 20 ) 17240169.9903333 86756.9485392933 198.718031011949 Trimmed Mean ( 1 / 20 ) 17375444.4537931 240249.360723836 72.3225418849959 Trimmed Mean ( 2 / 20 ) 17367951.8794643 230250.940013911 75.4305362593307 Trimmed Mean ( 3 / 20 ) 17357664.7229630 221097.244770713 78.506924593129 Trimmed Mean ( 4 / 20 ) 17356436.0619231 213944.058893871 81.1260483308533 Trimmed Mean ( 5 / 20 ) 17354539.0468 206785.34306292 83.9253826685358 Trimmed Mean ( 6 / 20 ) 17348967.3547917 199210.572134591 87.0885875628647 Trimmed Mean ( 7 / 20 ) 17336615.1315217 191914.572553116 90.3350636738308 Trimmed Mean ( 8 / 20 ) 17321250.4409091 183420.647257553 94.434572660662 Trimmed Mean ( 9 / 20 ) 17314987.2364286 176414.304784777 98.149564784741 Trimmed Mean ( 10 / 20 ) 17302247.92625 169091.791723553 102.324588023393 Trimmed Mean ( 11 / 20 ) 17286291.0871053 162021.643304042 106.691246518631 Trimmed Mean ( 12 / 20 ) 17268584.9375 152302.644471533 113.383355866337 Trimmed Mean ( 13 / 20 ) 17257217.9397059 145446.964258277 118.649557436355 Trimmed Mean ( 14 / 20 ) 17244288.0775 136993.696215602 125.876507853039 Trimmed Mean ( 15 / 20 ) 17240720.6196667 130749.850486112 131.860346727494 Trimmed Mean ( 16 / 20 ) 17239202.4985714 124707.566381383 138.237021207279 Trimmed Mean ( 17 / 20 ) 17249209.94 119774.668431238 144.013840037492 Trimmed Mean ( 18 / 20 ) 17257941.6791667 114470.830168823 150.762789557081 Trimmed Mean ( 19 / 20 ) 17273019.1727273 108553.041069733 159.120546071403 Trimmed Mean ( 20 / 20 ) 17281208.311 105239.282392215 164.208724329712 Median 17268123.695 Midrange 17515507.725 Midmean - Weighted Average at Xnp 17198461.9141935 Midmean - Weighted Average at X(n+1)p 17240720.6196667 Midmean - Empirical Distribution Function 17198461.9141935 Midmean - Empirical Distribution Function - Averaging 17240720.6196667 Midmean - Empirical Distribution Function - Interpolation 17240720.6196667 Midmean - Closest Observation 17198461.9141935 Midmean - True Basic - Statistics Graphics Toolkit 17240720.6196667 Midmean - MS Excel (old versions) 17244288.0775 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124636thyfp8wqq2harfu/1n8b71291124678.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124636thyfp8wqq2harfu/1n8b71291124678.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124636thyfp8wqq2harfu/2yits1291124678.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/30/t1291124636thyfp8wqq2harfu/2yits1291124678.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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