Taak 5 Eigen reeks

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 21 Apr 2010 16:52:07 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Apr/21/t12718687934bbk5o3tb8m4itg.htm/, Retrieved Wed, 21 Apr 2010 18:53:14 +0200

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/2010/Apr/21/t12718687934bbk5o3tb8m4itg.htm/}, year = {2010}, } @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 = {2010}, 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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

93.2 96 95.2 77.1 70.9 64.8 70.1 77.3 79.5 100.6 100.7 107.1 95.9 82.8 83.3 80 80.4 67.5 75.7 71.1 89.3 101.1 105.2 114.1 96.3 84.4 91.2 81.9 80.5 70.4 74.8 75.9 86.3 98.7 100.9 113.8 89.8 84.4 87.2 85.6 72 69.2 77.5 78.1 94.3 97.7 100.2 116.4 97.1 93 96 80.5 76.1 69.9 73.6 92.6 94.2 93.5 108.5 109.4 105.1 92.5 97.1

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 88.3412698412698 1.63806899124394 53.9301276768471 Geometric Mean 87.3994106792435 Harmonic Mean 86.4617422732407 Quadratic Mean 89.2778959116572 Winsorized Mean ( 1 / 21 ) 88.347619047619 1.61891953048939 54.5719644390924 Winsorized Mean ( 2 / 21 ) 88.3920634920635 1.60567398565826 55.0498197526857 Winsorized Mean ( 3 / 21 ) 88.215873015873 1.54937710482321 56.9363473496909 Winsorized Mean ( 4 / 21 ) 88.1714285714286 1.53455409324229 57.4573610403885 Winsorized Mean ( 5 / 21 ) 88.084126984127 1.50685616297631 58.4555640733123 Winsorized Mean ( 6 / 21 ) 87.9507936507936 1.46222248235174 60.14870836163 Winsorized Mean ( 7 / 21 ) 87.9619047619047 1.45594536298836 60.4156632508248 Winsorized Mean ( 8 / 21 ) 87.568253968254 1.34489196035681 65.1117387489039 Winsorized Mean ( 9 / 21 ) 87.768253968254 1.29877610944775 67.5776627933 Winsorized Mean ( 10 / 21 ) 87.9269841269841 1.26083264442241 69.7372363540475 Winsorized Mean ( 11 / 21 ) 88.0666666666667 1.23205397172661 71.4795525907436 Winsorized Mean ( 12 / 21 ) 88.0285714285714 1.21348547469409 72.5419242869493 Winsorized Mean ( 13 / 21 ) 87.7603174603175 1.15815976814674 75.7756571019121 Winsorized Mean ( 14 / 21 ) 87.7603174603175 1.08926366820724 80.5684794433265 Winsorized Mean ( 15 / 21 ) 87.6650793650794 1.06099239290831 82.62554939228 Winsorized Mean ( 16 / 21 ) 87.715873015873 1.05301655377071 83.2996145234133 Winsorized Mean ( 17 / 21 ) 87.6619047619048 0.997219453716484 87.906332387723 Winsorized Mean ( 18 / 21 ) 87.9761904761905 0.924682074827335 95.1420957225954 Winsorized Mean ( 19 / 21 ) 88.1269841269841 0.902582646883786 97.6386865305323 Winsorized Mean ( 20 / 21 ) 88.2222222222222 0.87978795926869 100.276687459505 Winsorized Mean ( 21 / 21 ) 88.0222222222222 0.842537326876961 104.472786444364 Trimmed Mean ( 1 / 21 ) 88.2672131147541 1.58019110919938 55.8585683724519 Trimmed Mean ( 2 / 21 ) 88.1813559322034 1.532807927836 57.529292699247 Trimmed Mean ( 3 / 21 ) 88.0649122807017 1.48326185635299 59.3724647495714 Trimmed Mean ( 4 / 21 ) 88.0072727272727 1.44916986464748 60.7294388837441 Trimmed Mean ( 5 / 21 ) 87.9584905660377 1.41222742970953 62.2835166033628 Trimmed Mean ( 6 / 21 ) 87.9274509803922 1.37509808115461 63.9426759337513 Trimmed Mean ( 7 / 21 ) 87.9224489795918 1.34162578202628 65.5342571359957 Trimmed Mean ( 8 / 21 ) 87.9148936170213 1.30029520139171 67.6114881627849 Trimmed Mean ( 9 / 21 ) 87.9755555555556 1.27686150722855 68.89984157053 Trimmed Mean ( 10 / 21 ) 88.0093023255814 1.25718230688783 70.0052027803743 Trimmed Mean ( 11 / 21 ) 88.0219512195122 1.23930799039725 71.0250816597234 Trimmed Mean ( 12 / 21 ) 88.0153846153846 1.22082988997799 72.0947163383846 Trimmed Mean ( 13 / 21 ) 88.0135135135135 1.19858626784805 73.431104522442 Trimmed Mean ( 14 / 21 ) 88.0485714285714 1.18015361077192 74.6077210838511 Trimmed Mean ( 15 / 21 ) 88.0878787878788 1.16949676415074 75.3211821426853 Trimmed Mean ( 16 / 21 ) 88.1451612903226 1.15777724295053 76.1330919458128 Trimmed Mean ( 17 / 21 ) 88.2034482758621 1.13877562327399 77.4546332685592 Trimmed Mean ( 18 / 21 ) 88.2777777777778 1.12294552302118 78.6126984506555 Trimmed Mean ( 19 / 21 ) 88.32 1.11691539518443 79.0749240101717 Trimmed Mean ( 20 / 21 ) 88.3478260869565 1.10717868785781 79.7954540272932 Trimmed Mean ( 21 / 21 ) 88.3666666666667 1.09116218805223 80.9839890295367 Median 89.3 Midrange 90.6 Midmean - Weighted Average at Xnp 88.0878787878788 Midmean - Weighted Average at X(n+1)p 88.0878787878788 Midmean - Empirical Distribution Function 88.0878787878788 Midmean - Empirical Distribution Function - Averaging 88.0878787878788 Midmean - Empirical Distribution Function - Interpolation 88.425 Midmean - Closest Observation 88.0878787878788 Midmean - True Basic - Statistics Graphics Toolkit 88.0878787878788 Midmean - MS Excel (old versions) 88.0878787878788 Number of observations 63

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Apr/21/t12718687934bbk5o3tb8m4itg/13bnd1271868723.png (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/21/t12718687934bbk5o3tb8m4itg/13bnd1271868723.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/21/t12718687934bbk5o3tb8m4itg/2e3mg1271868723.png (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/21/t12718687934bbk5o3tb8m4itg/2e3mg1271868723.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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