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 15:00:05 -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/t1256072565yx5cxrx3niyr0hx.htm/, Retrieved Tue, 20 Oct 2009 23:02:48 +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/t1256072565yx5cxrx3niyr0hx.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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-379,8571429 918,1538462 924,0769231 671,3333333 -149,8181818 233,7857143 186,4166667 450,5333333 863,3636364 541,8461538 177,0666667 1096,363636 -398,7142857 820,6153846 651,8666667 129,4375 -576,8823529 -533,0909091 -15,1875 -321,1538462 61,58823529 468,4375 495,4705882 618,9473684 -405,6666667 479,7894737 413,8125 359,4 -147,5 179,3125 292,5882353 456 259,7 136,8947368 556 229,2777778 -28,52631579 348,7058824 95,55 -222,4761905 -669,6666667 -504,88 118,92 -308,3846154 -264,3181818 -54,44 -160,1428571 -128,1071429 -708,3448276 -287,9 -327,1612903 -611,2758621 -618,0740741 -585,7727273 -160,44 -187,173913 39,26923077 106,0869565 -48,04545455 505,3888889

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 84.7166388453333 58.2598938797798 1.45411591411662 Geometric Mean NaN Harmonic Mean -864.311004002335 Quadratic Mean 455.450993802143 Winsorized Mean ( 1 / 20 ) 82.4898296453333 57.3335668750766 1.43877023777483 Winsorized Mean ( 2 / 20 ) 84.0121468353333 56.9134561742097 1.47613855286131 Winsorized Mean ( 3 / 20 ) 81.6125469453333 56.1789553183155 1.45272453862676 Winsorized Mean ( 4 / 20 ) 80.4628724786667 55.1669858706786 1.45853305575342 Winsorized Mean ( 5 / 20 ) 68.7635660703333 52.381385343831 1.31274813789230 Winsorized Mean ( 6 / 20 ) 71.1960437903333 51.1076880966296 1.39305937016213 Winsorized Mean ( 7 / 20 ) 70.646731717 49.7261573403824 1.42071568557798 Winsorized Mean ( 8 / 20 ) 75.4821937036667 45.7101633926391 1.65132189651770 Winsorized Mean ( 9 / 20 ) 74.4019739236667 45.1490872664745 1.64791756441362 Winsorized Mean ( 10 / 20 ) 71.4686202403334 43.5473043321463 1.64117208484879 Winsorized Mean ( 11 / 20 ) 79.311171422 41.5897722356968 1.90698739518287 Winsorized Mean ( 12 / 20 ) 77.376437342 40.863230467689 1.89354675233478 Winsorized Mean ( 13 / 20 ) 77.6835097136667 39.9993265373158 1.94212044148280 Winsorized Mean ( 14 / 20 ) 79.5611699736667 38.7448601216714 2.05346385878846 Winsorized Mean ( 15 / 20 ) 84.0899578486667 37.5822351724155 2.23749219446072 Winsorized Mean ( 16 / 20 ) 85.455599982 34.2488522721838 2.49513762688641 Winsorized Mean ( 17 / 20 ) 80.0410369403333 30.2767384053915 2.64364793422002 Winsorized Mean ( 18 / 20 ) 84.8529755603333 28.5915177200063 2.96776744736986 Winsorized Mean ( 19 / 20 ) 67.1764825636667 25.8719227636949 2.59650135698198 Winsorized Mean ( 20 / 20 ) 59.655295897 23.76602337987 2.51010844109194 Trimmed Mean ( 1 / 20 ) 80.9479227986207 55.9857005992611 1.44586781860669 Trimmed Mean ( 2 / 20 ) 79.2958797485714 54.3195224447588 1.45980443456978 Trimmed Mean ( 3 / 20 ) 76.675731367037 52.5303218063163 1.4596470901082 Trimmed Mean ( 4 / 20 ) 74.7769561446154 50.6561747557683 1.47616665697997 Trimmed Mean ( 5 / 20 ) 73.0711812444 48.7074275665618 1.50020612656137 Trimmed Mean ( 6 / 20 ) 74.1480850379167 47.2281330015008 1.56999822617507 Trimmed Mean ( 7 / 20 ) 74.7898331352174 45.7333339107713 1.63534618493236 Trimmed Mean ( 8 / 20 ) 75.5969308140909 44.2062369969597 1.71009649202419 Trimmed Mean ( 9 / 20 ) 75.6174195838095 43.3426796764075 1.74464108237798 Trimmed Mean ( 10 / 20 ) 75.8199938605 42.309655890838 1.79202577435565 Trimmed Mean ( 11 / 20 ) 76.5070528531579 41.3187473151081 1.85163050248581 Trimmed Mean ( 12 / 20 ) 76.0821864033333 40.4527236434210 1.88076795703488 Trimmed Mean ( 13 / 20 ) 75.8918553829412 39.3928466062479 1.92653900190357 Trimmed Mean ( 14 / 20 ) 75.633443700625 38.0914764585738 1.98557395859622 Trimmed Mean ( 15 / 20 ) 75.0723399473333 36.5542922806515 2.05372160869518 Trimmed Mean ( 16 / 20 ) 73.7841088185714 34.6239208437935 2.13101540843540 Trimmed Mean ( 17 / 20 ) 72.10072067 32.8830483769994 2.19264101805209 Trimmed Mean ( 18 / 20 ) 70.9330271008333 31.6526875161108 2.24097960290827 Trimmed Mean ( 19 / 20 ) 68.8239440009091 30.2319901736634 2.27652706968875 Trimmed Mean ( 20 / 20 ) 69.084069491 29.0080762267466 2.38154605465707 Median 100.81847825 Midrange 194.0094042 Midmean - Weighted Average at Xnp 63.363554787742 Midmean - Weighted Average at X(n+1)p 75.0723399473333 Midmean - Empirical Distribution Function 63.363554787742 Midmean - Empirical Distribution Function - Averaging 75.0723399473333 Midmean - Empirical Distribution Function - Interpolation 75.0723399473333 Midmean - Closest Observation 63.363554787742 Midmean - True Basic - Statistics Graphics Toolkit 75.0723399473333 Midmean - MS Excel (old versions) 75.633443700625 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256072565yx5cxrx3niyr0hx/1s2go1256072400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256072565yx5cxrx3niyr0hx/1s2go1256072400.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256072565yx5cxrx3niyr0hx/2objb1256072400.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256072565yx5cxrx3niyr0hx/2objb1256072400.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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