prijs kaas

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 12:11:18 -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/t1208715137iokpgxps4ca7jvj.htm/, Retrieved Sun, 20 Apr 2008 20:12:19 +0200

User-defined keywords:

Dataseries X:

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6,8400 6,8600 6,8600 6,8400 6,9200 6,9300 6,9700 6,9400 7,0000 6,9200 6,9800 6,9700 6,9700 7,0000 6,9300 6,9400 6,9700 6,9700 6,9400 7,0200 7,0600 7,0200 7,0200 6,9800 6,9600 7,0200 7,0000 7,1300 7,0800 7,1100 7,0600 7,0300 7,1300 7,0900 7,1100 7,0500 7,0600 7,1100 7,0500 7,0600 7,0300 7,0200 7,0900 7,1100 7,1200 7,0300 7,0200 7,1000 7,1300 7,0800 6,9900 7,0400 6,9800 6,9100 6,8700 6,8100 6,8800 6,8200 6,7700 6,7500 6,6800 6,5900 6,6500 6,5600 6,6200 6,5700 6,5500 6,5700 6,5300 6,5700 6,4800 6,4900 6,5300 6,4800 6,4900 6,4800 6,5200 6,4600 6,4600 6,4900 6,5100 6,5100 6,5400 6,5400 6,5300

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 6.85705882352941 0.0244140426192455 280.865358124837 Geometric Mean 6.8533578032775 Harmonic Mean 6.84960799075795 Quadratic Mean 6.86070867545123 Winsorized Mean ( 1 / 28 ) 6.85705882352941 0.0244140426192455 280.865358124837 Winsorized Mean ( 2 / 28 ) 6.8575294117647 0.0243250086767658 281.912722124318 Winsorized Mean ( 3 / 28 ) 6.85717647058824 0.0242787337432708 282.43550685541 Winsorized Mean ( 4 / 28 ) 6.85670588235294 0.0242191142857651 283.111339310332 Winsorized Mean ( 5 / 28 ) 6.85729411764706 0.0241113129620379 284.401522573389 Winsorized Mean ( 6 / 28 ) 6.85729411764706 0.0241113129620379 284.401522573389 Winsorized Mean ( 7 / 28 ) 6.85729411764706 0.0241113129620379 284.401522573389 Winsorized Mean ( 8 / 28 ) 6.85823529411765 0.0236596883647667 289.870060348332 Winsorized Mean ( 9 / 28 ) 6.85717647058823 0.0235329269082984 291.386468725665 Winsorized Mean ( 10 / 28 ) 6.85835294117647 0.0233280388503985 293.996121369599 Winsorized Mean ( 11 / 28 ) 6.85835294117647 0.0229552280460229 298.770847644213 Winsorized Mean ( 12 / 28 ) 6.85835294117647 0.0229552280460229 298.770847644213 Winsorized Mean ( 13 / 28 ) 6.85529411764706 0.0226145315539189 303.136684538534 Winsorized Mean ( 14 / 28 ) 6.85694117647059 0.0223343723551599 307.012933582011 Winsorized Mean ( 15 / 28 ) 6.85694117647059 0.0223343723551599 307.012933582011 Winsorized Mean ( 16 / 28 ) 6.85882352941176 0.0220182072383689 311.506902226789 Winsorized Mean ( 17 / 28 ) 6.85882352941176 0.0214707225351696 319.450056614389 Winsorized Mean ( 18 / 28 ) 6.86094117647059 0.0211216454943 324.829861306124 Winsorized Mean ( 19 / 28 ) 6.85870588235294 0.0208870433048683 328.371315281103 Winsorized Mean ( 20 / 28 ) 6.85635294117647 0.0206476693151144 332.064255608623 Winsorized Mean ( 21 / 28 ) 6.86129411764706 0.019837426243851 345.876225741424 Winsorized Mean ( 22 / 28 ) 6.86905882352941 0.0185855758123024 369.590853299394 Winsorized Mean ( 23 / 28 ) 6.87447058823529 0.0170232218084056 403.828996978754 Winsorized Mean ( 24 / 28 ) 6.88294117647059 0.0157063596901833 438.226381684898 Winsorized Mean ( 25 / 28 ) 6.90352941176471 0.0126221825570257 546.936267208567 Winsorized Mean ( 26 / 28 ) 6.90964705882353 0.0117459654660207 588.257055481059 Winsorized Mean ( 27 / 28 ) 6.92235294117647 0.00999250007105964 692.754855336458 Winsorized Mean ( 28 / 28 ) 6.92564705882353 0.00955515766810172 724.807198309624 Trimmed Mean ( 1 / 28 ) 6.85855421686747 0.0243137565559963 282.085337207015 Trimmed Mean ( 2 / 28 ) 6.86012345679012 0.0241864502848495 283.634984712384 Trimmed Mean ( 3 / 28 ) 6.86151898734177 0.0240806880997447 284.938659515071 Trimmed Mean ( 4 / 28 ) 6.86311688311688 0.0239640164715715 286.392595801233 Trimmed Mean ( 5 / 28 ) 6.86493333333333 0.0238337888194364 288.033656140102 Trimmed Mean ( 6 / 28 ) 6.86671232876712 0.0236982672128887 289.75588244834 Trimmed Mean ( 7 / 28 ) 6.86859154929577 0.0235247168912785 291.973398916534 Trimmed Mean ( 8 / 28 ) 6.87057971014493 0.0233061137586780 294.797312897638 Trimmed Mean ( 9 / 28 ) 6.87253731343284 0.0231295715919129 297.132062568586 Trimmed Mean ( 10 / 28 ) 6.87476923076923 0.0229266259513866 299.859614988548 Trimmed Mean ( 11 / 28 ) 6.87698412698413 0.0227079173308588 302.845215912368 Trimmed Mean ( 12 / 28 ) 6.87934426229508 0.0224957419801659 305.806506331753 Trimmed Mean ( 13 / 28 ) 6.88186440677966 0.0222197128376985 309.718872473623 Trimmed Mean ( 14 / 28 ) 6.88491228070175 0.0219179416427097 314.122210604197 Trimmed Mean ( 15 / 28 ) 6.888 0.0215812613568077 319.165774702377 Trimmed Mean ( 16 / 28 ) 6.89132075471698 0.0211430227708895 325.938293185079 Trimmed Mean ( 17 / 28 ) 6.89470588235294 0.0206413879704630 334.023365687375 Trimmed Mean ( 18 / 28 ) 6.89836734693878 0.0200940538019384 343.303915423642 Trimmed Mean ( 19 / 28 ) 6.90212765957447 0.0194535338368916 354.800712171138 Trimmed Mean ( 20 / 28 ) 6.90644444444444 0.0186410960020361 370.495621270878 Trimmed Mean ( 21 / 28 ) 6.91139534883721 0.0175856750930173 393.012796624538 Trimmed Mean ( 22 / 28 ) 6.91634146341463 0.0163824567738316 422.179747451702 Trimmed Mean ( 23 / 28 ) 6.92102564102564 0.0151144748873196 457.907118349978 Trimmed Mean ( 24 / 28 ) 6.92567567567568 0.0138228851270028 501.029677382363 Trimmed Mean ( 25 / 28 ) 6.93 0.0124549608758987 556.404798782633 Trimmed Mean ( 26 / 28 ) 6.93272727272727 0.0116715849530732 593.983362208391 Trimmed Mean ( 27 / 28 ) 6.93516129032258 0.0108545710874677 638.91619801815 Trimmed Mean ( 28 / 28 ) 6.93655172413793 0.0103304497785829 671.466574332396 Median 6.94 Midrange 6.795 Midmean - Weighted Average at Xnp 6.9140909090909 Midmean - Weighted Average at X(n+1)p 6.9140909090909 Midmean - Empirical Distribution Function 6.9140909090909 Midmean - Empirical Distribution Function - Averaging 6.9140909090909 Midmean - Empirical Distribution Function - Interpolation 6.9140909090909 Midmean - Closest Observation 6.89212765957446 Midmean - True Basic - Statistics Graphics Toolkit 6.9140909090909 Midmean - MS Excel (old versions) 6.9140909090909 Number of observations 85

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208715137iokpgxps4ca7jvj/1bqlz1208715076.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208715137iokpgxps4ca7jvj/1bqlz1208715076.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208715137iokpgxps4ca7jvj/2cj6b1208715076.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208715137iokpgxps4ca7jvj/2cj6b1208715076.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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