Centrummaten - Blue Jeans (D) - Versluys Alexia

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

Title produced by software: Central Tendency

Date of computation: Sun, 20 Apr 2008 03:57:48 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/20/t120868554370nimad32qjztql.htm/, Retrieved Sun, 20 Apr 2008 11:59:03 +0200

User-defined keywords:

Centrummaten - Blue Jeans (D) - Versluys Alexia

Dataseries X:

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44,13 44,13 44,17 44,14 44,15 44,14 44,14 44,14 44,19 44,29 44,29 44,29 44,29 44,27 44,26 44,33 44,32 44,34 44,34 44,34 44,37 44,47 44,51 44,51 44,51 44,52 44,7 44,84 44,9 44,95 44,94 44,94 44,91 45,28 45,36 45,34 45,34 45,34 45,44 45,62 45,75 45,77 45,77 45,77 46,09 46,25 46,35 46,34 46,34 46,28 46,59 46,42 46,29 46,29 46,29 46,3 46,52 46,66 46,67 46,72 46,72 46,72 46,76 46,89 47,04 47,02 47,02 47,18 47,22 47,8 47,88 47,91

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 45.4875 0.133439181870304 340.88563315842 Geometric Mean 45.4736780107095 Harmonic Mean 45.4599333154162 Quadratic Mean 45.5013943009809 Winsorized Mean ( 1 / 24 ) 45.4870833333333 0.133333250806899 341.153336156262 Winsorized Mean ( 2 / 24 ) 45.4851388888889 0.132739728073623 342.664095738248 Winsorized Mean ( 3 / 24 ) 45.4609722222222 0.127409509408536 356.809883604939 Winsorized Mean ( 4 / 24 ) 45.45875 0.126981314396215 357.995585540695 Winsorized Mean ( 5 / 24 ) 45.4490277777778 0.125182677114444 363.061637803347 Winsorized Mean ( 6 / 24 ) 45.4481944444444 0.124763207076209 364.275618666034 Winsorized Mean ( 7 / 24 ) 45.4501388888889 0.124479902824437 365.120295386078 Winsorized Mean ( 8 / 24 ) 45.4379166666667 0.121660707536230 373.480621532105 Winsorized Mean ( 9 / 24 ) 45.4304166666667 0.117756718108244 385.798936965161 Winsorized Mean ( 10 / 24 ) 45.42625 0.116687026643972 389.299918821326 Winsorized Mean ( 11 / 24 ) 45.4293055555556 0.116262937656382 390.746238408520 Winsorized Mean ( 12 / 24 ) 45.4293055555556 0.116262937656382 390.746238408520 Winsorized Mean ( 13 / 24 ) 45.4202777777778 0.114865365194954 395.42187238676 Winsorized Mean ( 14 / 24 ) 45.4183333333333 0.114567978057763 396.431307449924 Winsorized Mean ( 15 / 24 ) 45.41 0.111503980714502 407.25003456396 Winsorized Mean ( 16 / 24 ) 45.3966666666667 0.108908189500235 416.834279175751 Winsorized Mean ( 17 / 24 ) 45.3754166666667 0.105214762388981 431.264735445708 Winsorized Mean ( 18 / 24 ) 45.3579166666667 0.102801512242794 441.218379740772 Winsorized Mean ( 19 / 24 ) 45.3552777777778 0.102443536152658 442.734402590231 Winsorized Mean ( 20 / 24 ) 45.3636111111111 0.101286193622850 447.875564166497 Winsorized Mean ( 21 / 24 ) 45.3811111111111 0.0957340382826197 474.033185324743 Winsorized Mean ( 22 / 24 ) 45.3902777777778 0.0936929215334348 484.457918857617 Winsorized Mean ( 23 / 24 ) 45.3902777777778 0.0936929215334348 484.457918857617 Winsorized Mean ( 24 / 24 ) 45.3902777777778 0.0936929215334348 484.457918857617 Trimmed Mean ( 1 / 24 ) 45.4722857142857 0.131322965943531 346.263011862211 Trimmed Mean ( 2 / 24 ) 45.4566176470588 0.128885036040287 352.691197082413 Trimmed Mean ( 3 / 24 ) 45.4410606060606 0.126307082927166 359.766527363027 Trimmed Mean ( 4 / 24 ) 45.43359375 0.125573558564258 361.808602618767 Trimmed Mean ( 5 / 24 ) 45.4262903225806 0.124744950559781 364.153339423636 Trimmed Mean ( 6 / 24 ) 45.4208333333333 0.124183728399685 365.755110743225 Trimmed Mean ( 7 / 24 ) 45.4151724137931 0.123493031459573 367.754940315482 Trimmed Mean ( 8 / 24 ) 45.40875 0.122593738982308 370.400237214015 Trimmed Mean ( 9 / 24 ) 45.4038888888889 0.122016145117066 372.11377924886 Trimmed Mean ( 10 / 24 ) 45.3998076923077 0.121982273266644 372.183649939586 Trimmed Mean ( 11 / 24 ) 45.396 0.121958172823175 372.225976735638 Trimmed Mean ( 12 / 24 ) 45.3914583333333 0.121791441016623 372.698261507047 Trimmed Mean ( 13 / 24 ) 45.3865217391304 0.121353564721674 374.002377624631 Trimmed Mean ( 14 / 24 ) 45.3822727272727 0.120853581338069 375.514504616318 Trimmed Mean ( 15 / 24 ) 45.3778571428571 0.120025421094768 378.068718517792 Trimmed Mean ( 16 / 24 ) 45.374 0.119342106825456 380.201097558651 Trimmed Mean ( 17 / 24 ) 45.3713157894737 0.118714170189528 382.189554263303 Trimmed Mean ( 18 / 24 ) 45.3708333333333 0.118360074108025 383.328868921831 Trimmed Mean ( 19 / 24 ) 45.3723529411765 0.118027504289890 384.421861786862 Trimmed Mean ( 20 / 24 ) 45.374375 0.117207888011417 387.127315147768 Trimmed Mean ( 21 / 24 ) 45.3756666666667 0.115899960165151 391.507180865368 Trimmed Mean ( 22 / 24 ) 45.375 0.115079337712093 394.293197215991 Trimmed Mean ( 23 / 24 ) 45.3730769230769 0.113857899601983 398.506182545869 Trimmed Mean ( 24 / 24 ) 45.3708333333333 0.111320982348842 407.567669418841 Median 45.34 Midrange 46.02 Midmean - Weighted Average at Xnp 45.342972972973 Midmean - Weighted Average at X(n+1)p 45.342972972973 Midmean - Empirical Distribution Function 45.342972972973 Midmean - Empirical Distribution Function - Averaging 45.342972972973 Midmean - Empirical Distribution Function - Interpolation 45.342972972973 Midmean - Closest Observation 45.342972972973 Midmean - True Basic - Statistics Graphics Toolkit 45.342972972973 Midmean - MS Excel (old versions) 45.3713157894737 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t120868554370nimad32qjztql/1c9p61208685463.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t120868554370nimad32qjztql/1c9p61208685463.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t120868554370nimad32qjztql/2tp8g1208685463.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t120868554370nimad32qjztql/2tp8g1208685463.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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