Clélia Comes - prijs bruin brood centrummaten

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

Title produced by software: Central Tendency

Date of computation: Fri, 18 Apr 2008 09:55:04 -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/18/t1208534296smltjw537pj6t25.htm/, Retrieved Fri, 18 Apr 2008 17:58:19 +0200

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Dataseries X:

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1,43 1,43 1,43 1,43 1,43 1,43 1,44 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,48 1,57 1,58 1,58 1,58 1,58 1,59 1,6 1,6 1,61 1,61 1,61 1,62 1,63 1,63 1,64 1,64 1,64 1,64 1,64 1,65 1,65 1,65 1,65 1,65 1,66 1,66 1,67 1,68 1,68 1,68 1,68 1,69 1,7 1,7 1,71 1,72 1,73 1,74 1,74 1,75 1,75 1,75 1,76 1,79 1,83

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 2 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.57719512195122 0.0119245272780642 132.264792152604 Geometric Mean 1.57358321107291 Harmonic Mean 1.57001683134731 Quadratic Mean 1.58084224232589 Winsorized Mean ( 1 / 27 ) 1.57670731707317 0.0118062432486441 133.548605078440 Winsorized Mean ( 2 / 27 ) 1.57597560975610 0.0116532504561536 135.239143420614 Winsorized Mean ( 3 / 27 ) 1.57560975609756 0.0115835828038821 136.020934349389 Winsorized Mean ( 4 / 27 ) 1.57560975609756 0.0115835828038821 136.020934349389 Winsorized Mean ( 5 / 27 ) 1.57560975609756 0.0115835828038821 136.020934349389 Winsorized Mean ( 6 / 27 ) 1.57560975609756 0.0113392534101898 138.951807416322 Winsorized Mean ( 7 / 27 ) 1.57902439024390 0.0108943763564903 144.939401630200 Winsorized Mean ( 8 / 27 ) 1.57804878048780 0.0107199985399198 147.206063005641 Winsorized Mean ( 9 / 27 ) 1.57695121951220 0.0105319076488062 149.730824851179 Winsorized Mean ( 10 / 27 ) 1.57573170731707 0.0103317895046944 152.512951081816 Winsorized Mean ( 11 / 27 ) 1.57439024390244 0.0101213616716822 155.551228675812 Winsorized Mean ( 12 / 27 ) 1.57439024390244 0.0101213616716822 155.551228675812 Winsorized Mean ( 13 / 27 ) 1.57280487804878 0.00988380916126985 159.129425951675 Winsorized Mean ( 14 / 27 ) 1.57109756097561 0.00963970962909372 162.981834663760 Winsorized Mean ( 15 / 27 ) 1.57109756097561 0.00963970962909372 162.98183466376 Winsorized Mean ( 16 / 27 ) 1.57109756097561 0.00963970962909372 162.98183466376 Winsorized Mean ( 17 / 27 ) 1.57109756097561 0.00963970962909372 162.98183466376 Winsorized Mean ( 18 / 27 ) 1.56890243902439 0.00933985785880455 167.979262933366 Winsorized Mean ( 19 / 27 ) 1.56658536585366 0.0090370769487168 173.350893739607 Winsorized Mean ( 20 / 27 ) 1.56658536585366 0.0090370769487168 173.350893739607 Winsorized Mean ( 21 / 27 ) 1.56402439024390 0.00871762476334756 179.40946447015 Winsorized Mean ( 22 / 27 ) 1.56402439024390 0.00871762476334756 179.40946447015 Winsorized Mean ( 23 / 27 ) 1.56402439024390 0.00871762476334756 179.40946447015 Winsorized Mean ( 24 / 27 ) 1.56402439024390 0.00871762476334756 179.40946447015 Winsorized Mean ( 25 / 27 ) 1.56402439024390 0.00871762476334756 179.40946447015 Winsorized Mean ( 26 / 27 ) 1.56085365853659 0.00833866355189746 187.182712052390 Winsorized Mean ( 27 / 27 ) 1.56085365853659 0.00833866355189746 187.182712052390 Trimmed Mean ( 1 / 27 ) 1.575875 0.011656602613698 135.191620768486 Trimmed Mean ( 2 / 27 ) 1.575 0.01148012224644 137.193661024682 Trimmed Mean ( 3 / 27 ) 1.57447368421053 0.0113653748355413 138.532490744336 Trimmed Mean ( 4 / 27 ) 1.57405405405405 0.0112573459811040 139.824613785183 Trimmed Mean ( 5 / 27 ) 1.57361111111111 0.0111265053764354 141.429052327952 Trimmed Mean ( 6 / 27 ) 1.57314285714286 0.0109686979003482 143.421112645733 Trimmed Mean ( 7 / 27 ) 1.57264705882353 0.0108417008777133 145.055381675059 Trimmed Mean ( 8 / 27 ) 1.57151515151515 0.0107833991904167 145.734672691313 Trimmed Mean ( 9 / 27 ) 1.57046875 0.0107423599823815 146.194016266046 Trimmed Mean ( 10 / 27 ) 1.56951612903226 0.0107207904280003 146.399292064607 Trimmed Mean ( 11 / 27 ) 1.56866666666667 0.0107210829483633 146.316064731701 Trimmed Mean ( 12 / 27 ) 1.56793103448276 0.0107458080592536 145.910947398001 Trimmed Mean ( 13 / 27 ) 1.56714285714286 0.0107592131637739 145.655898185883 Trimmed Mean ( 14 / 27 ) 1.56648148148148 0.0108001261976199 145.042886797629 Trimmed Mean ( 15 / 27 ) 1.56596153846154 0.0108717312848535 144.039757553909 Trimmed Mean ( 16 / 27 ) 1.5654 0.0109365890291186 143.134207185818 Trimmed Mean ( 17 / 27 ) 1.56479166666667 0.010992379627268 142.352404095015 Trimmed Mean ( 18 / 27 ) 1.56413043478261 0.0110360677331327 141.728962942729 Trimmed Mean ( 19 / 27 ) 1.56363636363636 0.0111167687989674 140.655652007588 Trimmed Mean ( 20 / 27 ) 1.56333333333333 0.0112394829750078 139.092993584276 Trimmed Mean ( 21 / 27 ) 1.563 0.0113578166916005 137.614476658695 Trimmed Mean ( 22 / 27 ) 1.56289473684211 0.0115258870903733 135.598650636398 Trimmed Mean ( 23 / 27 ) 1.56277777777778 0.0116945999688033 133.632427098547 Trimmed Mean ( 24 / 27 ) 1.56264705882353 0.0118615665064703 131.740361441394 Trimmed Mean ( 25 / 27 ) 1.5625 0.0120231631284327 129.957481513742 Trimmed Mean ( 26 / 27 ) 1.56233333333333 0.0121738681253782 128.334997327301 Trimmed Mean ( 27 / 27 ) 1.5625 0.0123937281459009 126.071830978217 Median 1.58 Midrange 1.63 Midmean - Weighted Average at Xnp 1.54148148148148 Midmean - Weighted Average at X(n+1)p 1.54571428571429 Midmean - Empirical Distribution Function 1.54571428571429 Midmean - Empirical Distribution Function - Averaging 1.54571428571429 Midmean - Empirical Distribution Function - Interpolation 1.54148148148148 Midmean - Closest Observation 1.54571428571429 Midmean - True Basic - Statistics Graphics Toolkit 1.54571428571429 Midmean - MS Excel (old versions) 1.54571428571429 Number of observations 82

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/18/t1208534296smltjw537pj6t25/13es61208534102.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/18/t1208534296smltjw537pj6t25/13es61208534102.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/18/t1208534296smltjw537pj6t25/2tqdl1208534102.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/18/t1208534296smltjw537pj6t25/2tqdl1208534102.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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