Centrummaten cola

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 22 Nov 2009 04:32:23 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/22/t1258889591p62lu618fvm5kwv.htm/, Retrieved Sun, 22 Nov 2009 12:33:13 +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/2009/Nov/22/t1258889591p62lu618fvm5kwv.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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

1,25 1,25 1,26 1,26 1,26 1,26 1,27 1,27 1,29 1,31 1,32 1,32 1,33 1,33 1,32 1,32 1,31 1,3 1,31 1,29 1,3 1,3 1,32 1,31 1,35 1,35 1,36 1,37 1,37 1,37 1,32 1,32 1,31 1,31 1,34 1,31 1,26 1,27 1,24 1,25 1,27 1,25 1,26 1,27 1,26 1,26 1,28 1,27 1,28 1,27 1,26 1,27 1,27 1,28 1,27 1,26 1,3 1,31 1,28 1,29 1,31 1,29 1,29 1,32 1,3 1,29 1,31 1,29 1,33 1,35 1,32 1,33 1,34 1,34 1,33 1,33 1,35 1,32

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.29948717948718 0.00374822606903363 346.693917483535 Geometric Mean 1.29907237871019 Harmonic Mean 1.29865906173094 Quadratic Mean 1.29990334946438 Winsorized Mean ( 1 / 26 ) 1.29961538461538 0.00372391497133012 348.991691437891 Winsorized Mean ( 2 / 26 ) 1.29961538461538 0.00372391497133012 348.991691437891 Winsorized Mean ( 3 / 26 ) 1.29923076923077 0.00363489045186289 357.433266954417 Winsorized Mean ( 4 / 26 ) 1.29871794871795 0.00353074585779268 367.831047893622 Winsorized Mean ( 5 / 26 ) 1.29935897435897 0.00342533577835278 379.337693714753 Winsorized Mean ( 6 / 26 ) 1.29935897435897 0.00342533577835278 379.337693714753 Winsorized Mean ( 7 / 26 ) 1.29935897435897 0.00342533577835278 379.337693714753 Winsorized Mean ( 8 / 26 ) 1.29833333333333 0.00324089270161564 400.609786521501 Winsorized Mean ( 9 / 26 ) 1.29833333333333 0.00324089270161564 400.609786521501 Winsorized Mean ( 10 / 26 ) 1.29833333333333 0.00324089270161564 400.609786521501 Winsorized Mean ( 11 / 26 ) 1.29692307692308 0.00302232613863915 429.114204566631 Winsorized Mean ( 12 / 26 ) 1.29692307692308 0.00302232613863915 429.114204566631 Winsorized Mean ( 13 / 26 ) 1.29692307692308 0.00302232613863915 429.114204566631 Winsorized Mean ( 14 / 26 ) 1.29692307692308 0.00302232613863915 429.114204566631 Winsorized Mean ( 15 / 26 ) 1.29884615384615 0.00273712752849620 474.528914098405 Winsorized Mean ( 16 / 26 ) 1.29884615384615 0.00273712752849620 474.528914098405 Winsorized Mean ( 17 / 26 ) 1.29666666666667 0.00243918140973687 531.599110050017 Winsorized Mean ( 18 / 26 ) 1.29666666666667 0.00243918140973687 531.599110050017 Winsorized Mean ( 19 / 26 ) 1.29666666666667 0.00243918140973687 531.599110050017 Winsorized Mean ( 20 / 26 ) 1.29666666666667 0.00243918140973687 531.599110050017 Winsorized Mean ( 21 / 26 ) 1.29666666666667 0.00243918140973687 531.599110050017 Winsorized Mean ( 22 / 26 ) 1.29666666666667 0.00243918140973687 531.599110050017 Winsorized Mean ( 23 / 26 ) 1.29666666666667 0.00243918140973687 531.599110050017 Winsorized Mean ( 24 / 26 ) 1.29666666666667 0.00243918140973687 531.599110050017 Winsorized Mean ( 25 / 26 ) 1.29987179487179 0.00200310772323959 648.927553815995 Winsorized Mean ( 26 / 26 ) 1.29987179487179 0.00200310772323959 648.927553815995 Trimmed Mean ( 1 / 26 ) 1.29934210526316 0.00364828980033395 356.151012220636 Trimmed Mean ( 2 / 26 ) 1.29905405405405 0.00355924584505214 364.980142032034 Trimmed Mean ( 3 / 26 ) 1.29875 0.00345402115342763 376.011015077650 Trimmed Mean ( 4 / 26 ) 1.29857142857143 0.00337010185496908 385.321122166304 Trimmed Mean ( 5 / 26 ) 1.29852941176471 0.00330790885806619 392.552959431848 Trimmed Mean ( 6 / 26 ) 1.29833333333333 0.00326443956240052 397.72013189872 Trimmed Mean ( 7 / 26 ) 1.298125 0.00321111505876618 404.259883636429 Trimmed Mean ( 8 / 26 ) 1.29790322580645 0.00314582224678471 412.579962880298 Trimmed Mean ( 9 / 26 ) 1.29783333333333 0.00310905063594562 417.437181089396 Trimmed Mean ( 10 / 26 ) 1.29775862068966 0.00306259662561768 423.744547301563 Trimmed Mean ( 11 / 26 ) 1.29767857142857 0.00300422939347323 431.950560848586 Trimmed Mean ( 12 / 26 ) 1.29777777777778 0.00297516703976634 436.203332596647 Trimmed Mean ( 13 / 26 ) 1.29788461538462 0.00293643747461926 441.992934160092 Trimmed Mean ( 14 / 26 ) 1.298 0.00288557283953202 449.824028774303 Trimmed Mean ( 15 / 26 ) 1.298125 0.00281926393114855 460.448199140813 Trimmed Mean ( 16 / 26 ) 1.29804347826087 0.00279093711371196 465.092341881708 Trimmed Mean ( 17 / 26 ) 1.29795454545455 0.00275073592794743 471.857197293041 Trimmed Mean ( 18 / 26 ) 1.29809523809524 0.00275263774326657 471.582300021354 Trimmed Mean ( 19 / 26 ) 1.29825 0.00274766800890855 472.491580420481 Trimmed Mean ( 20 / 26 ) 1.29842105263158 0.00273344794456443 475.012174720042 Trimmed Mean ( 21 / 26 ) 1.29861111111111 0.00270662848254141 479.789198808611 Trimmed Mean ( 22 / 26 ) 1.29882352941176 0.00266236414991068 487.845935521383 Trimmed Mean ( 23 / 26 ) 1.2990625 0.00259339168725983 500.912571896374 Trimmed Mean ( 24 / 26 ) 1.29933333333333 0.00248828673613514 522.179905741686 Trimmed Mean ( 25 / 26 ) 1.29964285714286 0.00232777926604166 558.318770212637 Trimmed Mean ( 26 / 26 ) 1.29961538461538 0.00225188941050838 577.122206157534 Median 1.3 Midrange 1.305 Midmean - Weighted Average at Xnp 1.29673913043478 Midmean - Weighted Average at X(n+1)p 1.29673913043478 Midmean - Empirical Distribution Function 1.29673913043478 Midmean - Empirical Distribution Function - Averaging 1.29673913043478 Midmean - Empirical Distribution Function - Interpolation 1.29673913043478 Midmean - Closest Observation 1.29673913043478 Midmean - True Basic - Statistics Graphics Toolkit 1.29673913043478 Midmean - MS Excel (old versions) 1.29673913043478 Number of observations 78

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/22/t1258889591p62lu618fvm5kwv/12l2o1258889541.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/22/t1258889591p62lu618fvm5kwv/12l2o1258889541.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/22/t1258889591p62lu618fvm5kwv/2gzkj1258889541.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/22/t1258889591p62lu618fvm5kwv/2gzkj1258889541.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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