Centrummaten verkoopprijzen scrabble - Cynthia D'Hooghe

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 05:23:04 -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/20/t12086906260kclu5ytv0tyh4f.htm/, Retrieved Sun, 20 Apr 2008 13:23:46 +0200

User-defined keywords:

Dataseries X:

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24,65 25,24 25,56 25,9 25,87 25,78 25,78 25,74 25,78 25,73 24,67 24,31 24,56 25 25,38 25,99 26,22 26,19 26,22 26,22 26,61 26,72 25,46 25,48 25,59 25,88 26 26,97 27,2 27,19 27,19 27,19 27,26 26,9 26,11 25,87 26,02 26,31 26,37 26,52 26,86 26,92 26,98 26,98 27,03 26,75 26,39 26,3 26,3 26,52 26,53 26,98 27,22 27,34 27,41 27,47 27,46 27,53 27,21 26,91 26,95 26,91 27,39 27,62 27,79 27,88 27,9 28,09 28,46 28,73 27,93 27,61

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 26.5552777777778 0.110272633442371 240.814760188490 Geometric Mean 26.5389313795381 Harmonic Mean 26.5224918923496 Quadratic Mean 26.5715287792529 Winsorized Mean ( 1 / 24 ) 26.555 0.108338389192243 245.111637693624 Winsorized Mean ( 2 / 24 ) 26.5472222222222 0.105361591826283 251.962994883301 Winsorized Mean ( 3 / 24 ) 26.5413888888889 0.103834410117243 255.612651518126 Winsorized Mean ( 4 / 24 ) 26.5580555555556 0.099156189308999 267.840623370399 Winsorized Mean ( 5 / 24 ) 26.5733333333333 0.0954013021436512 278.542669085589 Winsorized Mean ( 6 / 24 ) 26.5775 0.0917574774257487 289.649418724560 Winsorized Mean ( 7 / 24 ) 26.56875 0.0874060948149391 303.969077399611 Winsorized Mean ( 8 / 24 ) 26.5698611111111 0.0868232814452528 306.022309556049 Winsorized Mean ( 9 / 24 ) 26.5698611111111 0.083431513303962 318.463132920895 Winsorized Mean ( 10 / 24 ) 26.5656944444444 0.081396945220758 326.372130703372 Winsorized Mean ( 11 / 24 ) 26.5855555555556 0.0776886086217339 342.206612104494 Winsorized Mean ( 12 / 24 ) 26.5788888888889 0.0761285862304934 349.131518197598 Winsorized Mean ( 13 / 24 ) 26.5825 0.0744664774229378 356.972706645203 Winsorized Mean ( 14 / 24 ) 26.5727777777778 0.0730042826316344 363.989300625813 Winsorized Mean ( 15 / 24 ) 26.5561111111111 0.0705995328300398 376.15137163927 Winsorized Mean ( 16 / 24 ) 26.5672222222222 0.0663281376165504 400.542261201573 Winsorized Mean ( 17 / 24 ) 26.5648611111111 0.0660019659496275 402.485906728677 Winsorized Mean ( 18 / 24 ) 26.5648611111111 0.065288571261629 406.883786821717 Winsorized Mean ( 19 / 24 ) 26.5675 0.0641508120160309 414.141289331785 Winsorized Mean ( 20 / 24 ) 26.5925 0.0605652010953863 439.072264585046 Winsorized Mean ( 21 / 24 ) 26.5954166666667 0.0601575713607089 442.095916858058 Winsorized Mean ( 22 / 24 ) 26.5526388888889 0.05276101115358 503.262509727076 Winsorized Mean ( 23 / 24 ) 26.5654166666667 0.0467223584104052 568.580387858813 Winsorized Mean ( 24 / 24 ) 26.5920833333333 0.0431383014006211 616.437886285214 Trimmed Mean ( 1 / 24 ) 26.5562857142857 0.104149353544961 254.982722507457 Trimmed Mean ( 2 / 24 ) 26.5576470588235 0.0991425304123803 267.873403557059 Trimmed Mean ( 3 / 24 ) 26.5633333333333 0.0950924794217694 279.342104600253 Trimmed Mean ( 4 / 24 ) 26.5715625 0.0909275447286299 292.227867576342 Trimmed Mean ( 5 / 24 ) 26.5754838709677 0.087717901956238 302.965338640066 Trimmed Mean ( 6 / 24 ) 26.576 0.0850640171027075 312.423524131382 Trimmed Mean ( 7 / 24 ) 26.5756896551724 0.0828829129413938 320.641356728907 Trimmed Mean ( 8 / 24 ) 26.5769642857143 0.0813350133238652 326.759204918162 Trimmed Mean ( 9 / 24 ) 26.5781481481481 0.079535722177593 334.166176159218 Trimmed Mean ( 10 / 24 ) 26.5794230769231 0.0780659955277131 340.473760659178 Trimmed Mean ( 11 / 24 ) 26.5814 0.0766380360619228 346.843439183678 Trimmed Mean ( 12 / 24 ) 26.5808333333333 0.0755974040168698 351.61039825391 Trimmed Mean ( 13 / 24 ) 26.5810869565217 0.0745305619386165 356.646807230757 Trimmed Mean ( 14 / 24 ) 26.5809090909091 0.0734327569049504 361.976183535023 Trimmed Mean ( 15 / 24 ) 26.5819047619048 0.0722327169649862 368.003667573379 Trimmed Mean ( 16 / 24 ) 26.585 0.0710786851818426 374.022112704911 Trimmed Mean ( 17 / 24 ) 26.5871052631579 0.0703920214575795 377.700550611125 Trimmed Mean ( 18 / 24 ) 26.5897222222222 0.0693753147982118 383.273536121059 Trimmed Mean ( 19 / 24 ) 26.5926470588235 0.0679982552249807 391.078373567652 Trimmed Mean ( 20 / 24 ) 26.595625 0.0662274573637776 401.580040343602 Trimmed Mean ( 21 / 24 ) 26.596 0.064602409122012 411.687433355143 Trimmed Mean ( 22 / 24 ) 26.5960714285714 0.0621789942365027 427.734024249591 Trimmed Mean ( 23 / 24 ) 26.6015384615385 0.0607888965258328 437.605220391423 Trimmed Mean ( 24 / 24 ) 26.60625 0.0604416490078043 440.197288405625 Median 26.57 Midrange 26.52 Midmean - Weighted Average at Xnp 26.5518421052632 Midmean - Weighted Average at X(n+1)p 26.5897222222222 Midmean - Empirical Distribution Function 26.5518421052632 Midmean - Empirical Distribution Function - Averaging 26.5897222222222 Midmean - Empirical Distribution Function - Interpolation 26.5897222222222 Midmean - Closest Observation 26.5518421052632 Midmean - True Basic - Statistics Graphics Toolkit 26.5897222222222 Midmean - MS Excel (old versions) 26.5687179487180 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t12086906260kclu5ytv0tyh4f/1njtl1208690578.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t12086906260kclu5ytv0tyh4f/1njtl1208690578.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t12086906260kclu5ytv0tyh4f/2rsr21208690578.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t12086906260kclu5ytv0tyh4f/2rsr21208690578.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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