opgave 5 - oef 2/blog - Van Mechelen Wout

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 05 Jun 2009 03:22:44 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/05/t12441937984x231x52y1um3ib.htm/, Retrieved Fri, 05 Jun 2009 11:23:20 +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/2009/Jun/05/t12441937984x231x52y1um3ib.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

» Textbox « » Textfile « » CSV «

20.050 19.260 19.280 19.100 18.955 18.265 17.760 18.760 19.280 18.920 18.950 18.490 18.470 18.570 18.900 18.485 18.635 18.865 18.860 18.400 18.515 18.950 18.830 18.840 19.200 19.340 20.780 20.270 20.270 20.270 20.250 20.310 19.660 19.760 19.750 19.470 19.320 19.360 19.600 20.140 19.660 19.790 19.670 19.590 19.340 19.330 19.430 19.520 19.400 19.910 19.800 19.830 20.100 20.260 20.310 20.450 19.990 20.095 20.365 19.740 20.100 19.910 20.060 20.440 20.740 21.480 21.050 21.850 22.490 21.660 21.650 21.680 23.020 23.100 22.650 22.440 22.910 22.980 22.535

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 19.9805696202532 0.140988707141953 141.717517844433 Geometric Mean 19.9431335192693 Harmonic Mean 19.9070126490824 Quadratic Mean 20.0193314564204 Winsorized Mean ( 1 / 26 ) 19.9859493670886 0.139552510709369 143.214545302672 Winsorized Mean ( 2 / 26 ) 19.9883544303797 0.138750384776229 144.059812609645 Winsorized Mean ( 3 / 26 ) 19.9883544303797 0.137638181769485 145.223906429221 Winsorized Mean ( 4 / 26 ) 19.9759493670886 0.134054264735514 149.013904231250 Winsorized Mean ( 5 / 26 ) 19.9689873417722 0.132172334334918 151.082958792055 Winsorized Mean ( 6 / 26 ) 19.9674683544304 0.131054194244577 152.360391588586 Winsorized Mean ( 7 / 26 ) 19.9679113924051 0.129280384371126 154.454300933102 Winsorized Mean ( 8 / 26 ) 19.9147468354430 0.114505445584912 173.91964839502 Winsorized Mean ( 9 / 26 ) 19.9096202531646 0.108387601772736 183.689092917753 Winsorized Mean ( 10 / 26 ) 19.9159493670886 0.106676355499701 186.695067278939 Winsorized Mean ( 11 / 26 ) 19.9159493670886 0.106203404963374 187.526467479616 Winsorized Mean ( 12 / 26 ) 19.8931645569620 0.100486813166586 197.967911709801 Winsorized Mean ( 13 / 26 ) 19.8232278481013 0.0867419422224803 228.531058219305 Winsorized Mean ( 14 / 26 ) 19.781582278481 0.0775425642610736 255.106114518983 Winsorized Mean ( 15 / 26 ) 19.7777848101266 0.0757446933812892 261.111160759048 Winsorized Mean ( 16 / 26 ) 19.7251265822785 0.0658762360060941 299.427043470634 Winsorized Mean ( 17 / 26 ) 19.7229746835443 0.0655736130311596 300.776086170092 Winsorized Mean ( 18 / 26 ) 19.7070253164557 0.0630585730369616 312.519366794178 Winsorized Mean ( 19 / 26 ) 19.7286708860759 0.0561151523949517 351.574753770976 Winsorized Mean ( 20 / 26 ) 19.7539873417722 0.0525837903973402 375.666858408354 Winsorized Mean ( 21 / 26 ) 19.7593037974684 0.0490333145710368 402.977118115116 Winsorized Mean ( 22 / 26 ) 19.7648734177215 0.0483113897755755 409.114155265182 Winsorized Mean ( 23 / 26 ) 19.7648734177215 0.0483113897755755 409.114155265182 Winsorized Mean ( 24 / 26 ) 19.7739873417722 0.0463585874273645 426.544216273941 Winsorized Mean ( 25 / 26 ) 19.7739873417722 0.0455374144642538 434.236057852921 Winsorized Mean ( 26 / 26 ) 19.7410759493671 0.0403969141063093 488.677820722051 Trimmed Mean ( 1 / 26 ) 19.9688961038961 0.135733514681013 147.118389668351 Trimmed Mean ( 2 / 26 ) 19.9509333333333 0.131229895700353 152.030398461101 Trimmed Mean ( 3 / 26 ) 19.9306849315068 0.126394478758152 157.686357247004 Trimmed Mean ( 4 / 26 ) 19.9092957746479 0.121132453892683 164.359716449619 Trimmed Mean ( 5 / 26 ) 19.8902173913043 0.116205982177908 171.163454914507 Trimmed Mean ( 6 / 26 ) 19.8716417910448 0.110895953822361 179.191765849963 Trimmed Mean ( 7 / 26 ) 19.8522307692308 0.104766913379431 189.489507029118 Trimmed Mean ( 8 / 26 ) 19.8315079365079 0.0977117637373596 202.959266908877 Trimmed Mean ( 9 / 26 ) 19.8180327868852 0.093176875010533 212.692610528578 Trimmed Mean ( 10 / 26 ) 19.804406779661 0.089119588547709 222.222825558255 Trimmed Mean ( 11 / 26 ) 19.7889473684211 0.084463953327364 234.288670952014 Trimmed Mean ( 12 / 26 ) 19.7723636363636 0.0786953652652635 251.251945647824 Trimmed Mean ( 13 / 26 ) 19.7573584905660 0.0728656889873159 271.147624693500 Trimmed Mean ( 14 / 26 ) 19.7495098039216 0.0690619578182193 285.967997836161 Trimmed Mean ( 15 / 26 ) 19.7458163265306 0.0664263867630352 297.258624000888 Trimmed Mean ( 16 / 26 ) 19.7422340425532 0.0634614410362378 311.090226130856 Trimmed Mean ( 17 / 26 ) 19.7441111111111 0.0618666472555989 319.139827143684 Trimmed Mean ( 18 / 26 ) 19.7463953488372 0.0598230885728514 330.079837399075 Trimmed Mean ( 19 / 26 ) 19.7506097560976 0.0576660368197652 342.499863790327 Trimmed Mean ( 20 / 26 ) 19.7529487179487 0.0564179619936488 350.118083318437 Trimmed Mean ( 21 / 26 ) 19.7529487179487 0.0554880545204527 355.985606067119 Trimmed Mean ( 22 / 26 ) 19.7521428571429 0.0549313114679764 359.578941942026 Trimmed Mean ( 23 / 26 ) 19.7507575757576 0.0541777907627984 364.554502826269 Trimmed Mean ( 24 / 26 ) 19.7491935483871 0.0529587467641335 372.916557794421 Trimmed Mean ( 25 / 26 ) 19.7463793103448 0.0516112890473187 382.598064780765 Trimmed Mean ( 26 / 26 ) 19.7431481481481 0.0497237010820625 397.057091859768 Median 19.75 Midrange 20.43 Midmean - Weighted Average at Xnp 19.7506097560976 Midmean - Weighted Average at X(n+1)p 19.7506097560976 Midmean - Empirical Distribution Function 19.7506097560976 Midmean - Empirical Distribution Function - Averaging 19.7506097560976 Midmean - Empirical Distribution Function - Interpolation 19.766875 Midmean - Closest Observation 19.7506097560976 Midmean - True Basic - Statistics Graphics Toolkit 19.7506097560976 Midmean - MS Excel (old versions) 19.7506097560976 Number of observations 79

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12441937984x231x52y1um3ib/13drz1244193762.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12441937984x231x52y1um3ib/13drz1244193762.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12441937984x231x52y1um3ib/26ul61244193762.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t12441937984x231x52y1um3ib/26ul61244193762.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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