Central Tendency - Gemiddelde prijs Strip - Dellaert Kenny

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Thu, 07 May 2009 08:13:01 -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/May/07/t1241705919mu74d7qu3xg0sxi.htm/, Retrieved Thu, 07 May 2009 16:18:41 +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/May/07/t1241705919mu74d7qu3xg0sxi.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:

» Textbox « » Textfile « » CSV «

5,11 5,11 5,11 5,1 5,1 5,1 5,1 5,1 5,12 5,25 5,26 5,26 5,26 5,26 5,26 5,26 5,29 5,3 5,33 5,33 5,35 5,38 5,38 5,38 5,38 5,38 5,39 5,39 5,4 5,4 5,4 5,4 5,4 5,41 5,41 5,41 5,41 5,41 5,42 5,42 5,42 5,42 5,43 5,43 5,45 5,51 5,51 5,51 5,51 5,51 5,51 5,53 5,53 5,53 5,53 5,52 5,53 5,54 5,54 5,57 5,56 5,57 5,58 5,61 5,66 5,68 5,69 5,7 5,72 5,71 5,69 5,7 5,7

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 5.41821917808219 0.0199546121837308 271.527160146952 Geometric Mean 5.41555835197629 Harmonic Mean 5.41288232219603 Quadratic Mean 5.42086418324151 Winsorized Mean ( 1 / 24 ) 5.41808219178082 0.0199262887613157 271.906236865307 Winsorized Mean ( 2 / 24 ) 5.41780821917808 0.0198713964361343 272.643557617636 Winsorized Mean ( 3 / 24 ) 5.41780821917808 0.0198713964361343 272.643557617636 Winsorized Mean ( 4 / 24 ) 5.41780821917808 0.0198713964361343 272.643557617636 Winsorized Mean ( 5 / 24 ) 5.41780821917808 0.0195869122109576 276.603487105394 Winsorized Mean ( 6 / 24 ) 5.41780821917808 0.0195869122109576 276.603487105394 Winsorized Mean ( 7 / 24 ) 5.41684931506849 0.0194040557282113 279.160676043257 Winsorized Mean ( 8 / 24 ) 5.41575342465753 0.0187589834473486 288.701860623636 Winsorized Mean ( 9 / 24 ) 5.42561643835616 0.0145008086445510 374.159577672584 Winsorized Mean ( 10 / 24 ) 5.42287671232877 0.0135772207330195 399.409924826547 Winsorized Mean ( 11 / 24 ) 5.4213698630137 0.0133394892588492 406.41510014465 Winsorized Mean ( 12 / 24 ) 5.4213698630137 0.0133394892588492 406.41510014465 Winsorized Mean ( 13 / 24 ) 5.41958904109589 0.0130687771396985 414.697487237195 Winsorized Mean ( 14 / 24 ) 5.41575342465753 0.0125177466233282 432.646033477358 Winsorized Mean ( 15 / 24 ) 5.41575342465753 0.0125177466233282 432.646033477358 Winsorized Mean ( 16 / 24 ) 5.42013698630137 0.0111111945118948 487.808667240859 Winsorized Mean ( 17 / 24 ) 5.42246575342466 0.0107372465531577 505.014551596563 Winsorized Mean ( 18 / 24 ) 5.42986301369863 0.00961490857580248 564.733712327103 Winsorized Mean ( 19 / 24 ) 5.42986301369863 0.00961490857580248 564.733712327102 Winsorized Mean ( 20 / 24 ) 5.43534246575343 0.0088516485229935 614.048609322241 Winsorized Mean ( 21 / 24 ) 5.44109589041096 0.00733925052845777 741.36941766918 Winsorized Mean ( 22 / 24 ) 5.43808219178082 0.00689577091805431 788.611201909708 Winsorized Mean ( 23 / 24 ) 5.43808219178082 0.00689577091805431 788.611201909708 Winsorized Mean ( 24 / 24 ) 5.43808219178082 0.00689577091805431 788.611201909708 Trimmed Mean ( 1 / 24 ) 5.41845070422535 0.0195550586140094 277.086906829496 Trimmed Mean ( 2 / 24 ) 5.41884057971015 0.0191134900026214 283.508693544033 Trimmed Mean ( 3 / 24 ) 5.41940298507463 0.0186215135998084 291.029134448576 Trimmed Mean ( 4 / 24 ) 5.42 0.0180317561754043 300.580816825429 Trimmed Mean ( 5 / 24 ) 5.42063492063492 0.0173203203780002 312.963894566295 Trimmed Mean ( 6 / 24 ) 5.42131147540984 0.0165517493005747 327.537070370055 Trimmed Mean ( 7 / 24 ) 5.42203389830508 0.0156072853498499 347.40403451118 Trimmed Mean ( 8 / 24 ) 5.42298245614035 0.014483516065223 374.424444431812 Trimmed Mean ( 9 / 24 ) 5.42418181818182 0.0132514935543230 409.326073015544 Trimmed Mean ( 10 / 24 ) 5.42396226415094 0.0128724332277100 421.362625713607 Trimmed Mean ( 11 / 24 ) 5.42411764705882 0.0126092915339171 430.168311397098 Trimmed Mean ( 12 / 24 ) 5.42448979591837 0.0123237962683346 440.163864916878 Trimmed Mean ( 13 / 24 ) 5.42489361702128 0.0119545560287741 453.792981016089 Trimmed Mean ( 14 / 24 ) 5.42555555555556 0.0115363087577044 470.302561201144 Trimmed Mean ( 15 / 24 ) 5.42674418604651 0.0111106432378936 488.427543739161 Trimmed Mean ( 16 / 24 ) 5.4280487804878 0.0105415525780362 514.919291091652 Trimmed Mean ( 17 / 24 ) 5.42897435897436 0.0101526465028314 534.734894735115 Trimmed Mean ( 18 / 24 ) 5.42972972972973 0.0097220106183565 558.498642192146 Trimmed Mean ( 19 / 24 ) 5.42971428571429 0.00943340848677037 575.58350126882 Trimmed Mean ( 20 / 24 ) 5.42969696969697 0.00901897041599286 602.030688566045 Trimmed Mean ( 21 / 24 ) 5.42903225806452 0.00864291416791286 628.148348183301 Trimmed Mean ( 22 / 24 ) 5.42758620689655 0.00850463757019906 638.191358784677 Trimmed Mean ( 23 / 24 ) 5.4262962962963 0.00840817923838956 645.359255844742 Trimmed Mean ( 24 / 24 ) 5.4248 0.00820812605491248 660.9060294284 Median 5.41 Midrange 5.41 Midmean - Weighted Average at Xnp 5.4348717948718 Midmean - Weighted Average at X(n+1)p 5.4348717948718 Midmean - Empirical Distribution Function 5.4348717948718 Midmean - Empirical Distribution Function - Averaging 5.4348717948718 Midmean - Empirical Distribution Function - Interpolation 5.4348717948718 Midmean - Closest Observation 5.4315 Midmean - True Basic - Statistics Graphics Toolkit 5.4348717948718 Midmean - MS Excel (old versions) 5.4348717948718 Number of observations 73

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/07/t1241705919mu74d7qu3xg0sxi/1y1h61241705579.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/07/t1241705919mu74d7qu3xg0sxi/1y1h61241705579.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/07/t1241705919mu74d7qu3xg0sxi/2ddph1241705579.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/07/t1241705919mu74d7qu3xg0sxi/2ddph1241705579.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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