Paper: Central Tendency Prijzen 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, 16 Dec 2008 09:45:52 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/16/t1229446000bar2td3paaw8hcv.htm/, Retrieved Tue, 16 Dec 2008 17:46:40 +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/2008/Dec/16/t1229446000bar2td3paaw8hcv.htm/}, year = {2008}, } @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 = {2008}, 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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1,3 1,4 1,3 1 0,8 0,7 0,6 0,8 0,9 1 1,2 1,3 1,3 1,4 1,4 1,8 1,9 2 2,4 2,5 2,5 2,3 1,7 1,1 0,7 0,2 0,3 1,1 1,6 2,2 3 3,8 4,6 5,1 5,3 5,5 5,7 5,9 6,1 6,1 6,3 6,5 6,7 6,6 6,5 6,4 6,3 6,3 6,3 6,2 6 5,6 5,3 5,1 4,5 4 3,5 3,5 3,3 3,1 2,9 2,5 2,6 2,8 2,8 2,9 3,1 3,3 3,5 3,4 3,5 3,7 3,8

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 3.29589041095890 0.234264599162393 14.0690929092286 Geometric Mean 2.57530720843188 Harmonic Mean 1.76042627308944 Quadratic Mean 3.84892797741689 Winsorized Mean ( 1 / 24 ) 3.29589041095890 0.233744243176771 14.1004131959150 Winsorized Mean ( 2 / 24 ) 3.3013698630137 0.231815785510916 14.241350543655 Winsorized Mean ( 3 / 24 ) 3.30547945205479 0.231161536709456 14.2994353606907 Winsorized Mean ( 4 / 24 ) 3.3 0.230123056221158 14.3401537168382 Winsorized Mean ( 5 / 24 ) 3.3 0.227796338850983 14.4866243972374 Winsorized Mean ( 6 / 24 ) 3.3 0.227796338850983 14.4866243972374 Winsorized Mean ( 7 / 24 ) 3.30958904109589 0.226356593444044 14.6211293903132 Winsorized Mean ( 8 / 24 ) 3.32054794520548 0.224760644749295 14.7737071537116 Winsorized Mean ( 9 / 24 ) 3.30821917808219 0.222512919473884 14.8675375160428 Winsorized Mean ( 10 / 24 ) 3.30821917808219 0.218108596949742 15.1677614928883 Winsorized Mean ( 11 / 24 ) 3.30821917808219 0.218108596949742 15.1677614928883 Winsorized Mean ( 12 / 24 ) 3.30821917808219 0.212917629944095 15.5375540247692 Winsorized Mean ( 13 / 24 ) 3.30821917808219 0.207386005296309 15.951988531509 Winsorized Mean ( 14 / 24 ) 3.26986301369863 0.200832409019518 16.2815505209662 Winsorized Mean ( 15 / 24 ) 3.24931506849315 0.197406349178179 16.4600332361160 Winsorized Mean ( 16 / 24 ) 3.22739726027397 0.193808857353405 16.6524755594060 Winsorized Mean ( 17 / 24 ) 3.20410958904110 0.183109435262655 17.4983314455919 Winsorized Mean ( 18 / 24 ) 3.20410958904110 0.183109435262655 17.4983314455919 Winsorized Mean ( 19 / 24 ) 3.15205479452055 0.174944104892202 18.0174964824496 Winsorized Mean ( 20 / 24 ) 3.20684931506849 0.167478942622439 19.1477762210258 Winsorized Mean ( 21 / 24 ) 3.09178082191781 0.141619699771016 21.8315730573988 Winsorized Mean ( 22 / 24 ) 3.09178082191781 0.133087007404152 23.2312746542482 Winsorized Mean ( 23 / 24 ) 2.96575342465753 0.106472768581095 27.8545722458477 Winsorized Mean ( 24 / 24 ) 2.93287671232877 0.0932063469652896 31.4664913691015 Trimmed Mean ( 1 / 24 ) 3.29154929577465 0.231900090182069 14.1938249924370 Trimmed Mean ( 2 / 24 ) 3.28695652173913 0.229615797600209 14.3150277815909 Trimmed Mean ( 3 / 24 ) 3.27910447761194 0.227978921334276 14.3833669289273 Trimmed Mean ( 4 / 24 ) 3.26923076923077 0.226171342860586 14.4546640077472 Trimmed Mean ( 5 / 24 ) 3.26031746031746 0.224230374943517 14.5400348241790 Trimmed Mean ( 6 / 24 ) 3.25081967213115 0.222438337385679 14.6144756804878 Trimmed Mean ( 7 / 24 ) 3.24067796610169 0.220104627424865 14.7233522712190 Trimmed Mean ( 8 / 24 ) 3.22807017543860 0.217452129176721 14.8449692705247 Trimmed Mean ( 9 / 24 ) 3.21272727272727 0.214398454462219 14.9848434345566 Trimmed Mean ( 10 / 24 ) 3.19811320754717 0.210991345994223 15.1575563086589 Trimmed Mean ( 11 / 24 ) 3.18235294117647 0.207557332166564 15.3324043432137 Trimmed Mean ( 12 / 24 ) 3.16530612244898 0.203070625017424 15.5872181029501 Trimmed Mean ( 13 / 24 ) 3.1468085106383 0.19837105048608 15.8632446767182 Trimmed Mean ( 14 / 24 ) 3.12666666666667 0.193411687361650 16.1658621012921 Trimmed Mean ( 15 / 24 ) 3.10930232558140 0.188389865587638 16.5046156590359 Trimmed Mean ( 16 / 24 ) 3.09268292682927 0.182475866894256 16.9484490166662 Trimmed Mean ( 17 / 24 ) 3.07692307692308 0.175390889392243 17.5432320777042 Trimmed Mean ( 18 / 24 ) 3.06216216216216 0.168519046220923 18.1710152699759 Trimmed Mean ( 19 / 24 ) 3.04571428571429 0.158900785976387 19.1673959760456 Trimmed Mean ( 20 / 24 ) 3.03333333333333 0.147944672978199 20.5031602170652 Trimmed Mean ( 21 / 24 ) 3.01290322580645 0.134303614910946 22.4335229383382 Trimmed Mean ( 22 / 24 ) 3.00344827586207 0.124220005708596 24.1784586848899 Trimmed Mean ( 23 / 24 ) 2.99259259259259 0.112207318032791 26.6702087266541 Trimmed Mean ( 24 / 24 ) 2.996 0.105115809150353 28.5018973284472 Median 3 Midrange 3.45 Midmean - Weighted Average at Xnp 2.95675675675676 Midmean - Weighted Average at X(n+1)p 3.07692307692308 Midmean - Empirical Distribution Function 3.07692307692308 Midmean - Empirical Distribution Function - Averaging 3.07692307692308 Midmean - Empirical Distribution Function - Interpolation 3.07692307692308 Midmean - Closest Observation 3.07692307692308 Midmean - True Basic - Statistics Graphics Toolkit 3.07692307692308 Midmean - MS Excel (old versions) 3.07692307692308 Number of observations 73

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229446000bar2td3paaw8hcv/1r5v01229445947.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229446000bar2td3paaw8hcv/1r5v01229445947.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229446000bar2td3paaw8hcv/2j3hh1229445947.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229446000bar2td3paaw8hcv/2j3hh1229445947.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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