Central Tendency - Invoer/Uitvoer

*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, 20 Oct 2009 14:34:30 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/20/t1256071045ll3gipb6dder47i.htm/, Retrieved Tue, 20 Oct 2009 22:37:28 +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/2009/Oct/20/t1256071045ll3gipb6dder47i.htm/}, year = {2009}, } @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 = {2009}, 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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9904,642857 13710,15385 13747,69231 14517 15185,81818 11422,28571 13819,66667 12749 16217 13238 12391 14780,09091 10815,42857 14770,84615 11831 11931,3125 10611,94118 15923,18182 11094,875 16209,53846 10100 12149,6875 11644,35294 9249,947368 8980,777778 10244,52632 12457,5625 13307,46667 10839,625 11827,625 10925,94118 10675,3 9297,3 10433,21053 12261,41176 10911,22222 9334,421053 11655,05882 11080 9840,142857 7448,916667 8362,6 8465,64 8220,923077 10432,86364 8537,4 8535,464286 7997,464286 6301,413793 7595,566667 7200,483871 6152,482759 6064,259259 7269,909091 6578,44 7708,26087 6401,153846 7042,043478 8296,409091 9613,333333

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 10605.1846946167 349.744527209772 30.3226608839995 Geometric Mean 10259.5128486757 Harmonic Mean 9912.00034256587 Quadratic Mean 10940.1506036896 Winsorized Mean ( 1 / 20 ) 10606.5307272833 349.390074523699 30.3572754370385 Winsorized Mean ( 2 / 20 ) 10601.94987375 345.78813846728 30.6602474010346 Winsorized Mean ( 3 / 20 ) 10570.0686944 335.624920576011 31.4936944380033 Winsorized Mean ( 4 / 20 ) 10554.8392866667 327.046240809919 32.2732322515861 Winsorized Mean ( 5 / 20 ) 10592.7025131667 319.250284142786 33.1799313557668 Winsorized Mean ( 6 / 20 ) 10583.1619374667 310.75502078783 34.0562862367794 Winsorized Mean ( 7 / 20 ) 10509.9059913 292.696528761224 35.9071767464444 Winsorized Mean ( 8 / 20 ) 10524.1770867667 286.450415290714 36.7399610019271 Winsorized Mean ( 9 / 20 ) 10540.5438177667 281.423385646444 37.4543991557578 Winsorized Mean ( 10 / 20 ) 10492.2116549333 265.64516809532 39.497092042602 Winsorized Mean ( 11 / 20 ) 10532.4967250333 254.156905216655 41.4409229450404 Winsorized Mean ( 12 / 20 ) 10479.3884832333 229.603643094907 45.6412117071752 Winsorized Mean ( 13 / 20 ) 10432.5989946 216.571754971465 48.171558641036 Winsorized Mean ( 14 / 20 ) 10432.5122900333 211.550645653899 49.3144904275127 Winsorized Mean ( 15 / 20 ) 10425.8752300333 202.264092922453 51.5458531437438 Winsorized Mean ( 16 / 20 ) 10414.7019036333 194.669112101206 53.4995089422243 Winsorized Mean ( 17 / 20 ) 10353.3774392667 185.438601298133 55.8318352640147 Winsorized Mean ( 18 / 20 ) 10456.2970226667 159.564668334964 65.5301523311942 Winsorized Mean ( 19 / 20 ) 10540.4653095 146.34405943738 72.0252352573985 Winsorized Mean ( 20 / 20 ) 10498.7274601667 135.52724475785 77.465807549803 Trimmed Mean ( 1 / 20 ) 10586.7210761724 339.426281071847 31.1900452809413 Trimmed Mean ( 2 / 20 ) 10565.4964499821 327.1190409446 32.2986287177685 Trimmed Mean ( 3 / 20 ) 10545.2445478889 314.272539277028 33.5544574532277 Trimmed Mean ( 4 / 20 ) 10535.6967992308 303.299264799425 34.7369678136152 Trimmed Mean ( 5 / 20 ) 10529.954053 292.966701362438 35.9424945020392 Trimmed Mean ( 6 / 20 ) 10514.2669379583 282.560283373158 37.210703544181 Trimmed Mean ( 7 / 20 ) 10499.2897641522 271.964049105934 38.6054325881233 Trimmed Mean ( 8 / 20 ) 10497.2216679545 263.787273124163 39.7942688577458 Trimmed Mean ( 9 / 20 ) 10492.4082003095 254.795712712629 41.1796889696624 Trimmed Mean ( 10 / 20 ) 10484.3855974 244.222418936827 42.929660770054 Trimmed Mean ( 11 / 20 ) 10483.1499041053 234.579686760438 44.6890779371322 Trimmed Mean ( 12 / 20 ) 10475.6731130556 224.66730688063 46.6274922617980 Trimmed Mean ( 13 / 20 ) 10475.1267350882 218.051408217730 48.0397114639524 Trimmed Mean ( 14 / 20 ) 10481.2605438125 212.200959806148 49.3930873516664 Trimmed Mean ( 15 / 20 ) 10488.2245800667 204.915825554275 51.1830872588642 Trimmed Mean ( 16 / 20 ) 10497.1316300714 196.848411400954 53.3259656776713 Trimmed Mean ( 17 / 20 ) 10509.0205329231 186.925381728885 56.2204042903349 Trimmed Mean ( 18 / 20 ) 10531.9092231667 174.39823317032 60.389999552811 Trimmed Mean ( 19 / 20 ) 10543.3656171818 165.749024382772 63.610423388276 Trimmed Mean ( 20 / 20 ) 10543.8235605 157.029567554546 67.1454664538735 Median 10643.62059 Midrange 11140.6296295 Midmean - Weighted Average at Xnp 10419.6560452258 Midmean - Weighted Average at X(n+1)p 10488.2245800667 Midmean - Empirical Distribution Function 10419.6560452258 Midmean - Empirical Distribution Function - Averaging 10488.2245800667 Midmean - Empirical Distribution Function - Interpolation 10488.2245800667 Midmean - Closest Observation 10419.6560452258 Midmean - True Basic - Statistics Graphics Toolkit 10488.2245800667 Midmean - MS Excel (old versions) 10481.2605438125 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256071045ll3gipb6dder47i/1algx1256070868.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256071045ll3gipb6dder47i/1algx1256070868.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256071045ll3gipb6dder47i/25rwo1256070868.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256071045ll3gipb6dder47i/25rwo1256070868.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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