Opgave 5 Oefening 2 Stap 1

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 20 Oct 2010 11:25:09 +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/Oct/20/t1287574041u4l1b64ik9oopn8.htm/, Retrieved Wed, 20 Oct 2010 13:27:24 +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/Oct/20/t1287574041u4l1b64ik9oopn8.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 «

361,58 363,19 363,61 364,14 365,51 365,51 365,5 365,5 364,59 364,63 364,54 363,67 365,22 369,05 370,45 370,46 370,46 370,58 370,58 370,22 370,21 370,29 370,29 370,2 370,2 372,55 374,51 375,58 375,75 375,75 375,75 375,69 375,76 377,5 377,51 377,74 369,82 373,1 374,55 375,01 374,81 375,31 375,31 375,39 375,59 376,26 377,18 377,26 377,26 381,87 387,09 387,14 388,78 389,16 389,16 389,42 389,49 388,97 388,97 389,09 389,09 391,76 390,96 391,76 392,8 393,06 393,06 393,26 393,87 394,47 394,57 394,57 394,57 399,57 406,13 407,03 409,46 409,9 409,9 410,14 410,54 410,69 410,79 410,97

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 381.704523809524 1.55045577853490 246.188591183307 Geometric Mean 381.447006579910 Harmonic Mean 381.193362668583 Quadratic Mean 381.965794654069 Winsorized Mean ( 1 / 28 ) 381.721547619048 1.54708774117318 246.735551876057 Winsorized Mean ( 2 / 28 ) 381.729166666667 1.5451213842397 247.05448423685 Winsorized Mean ( 3 / 28 ) 381.725952380952 1.54361171391099 247.294024100004 Winsorized Mean ( 4 / 28 ) 381.729285714286 1.53622684144242 248.484973323253 Winsorized Mean ( 5 / 28 ) 381.738809523810 1.52979624340019 249.535721616978 Winsorized Mean ( 6 / 28 ) 381.742380952381 1.52931306148172 249.616897002449 Winsorized Mean ( 7 / 28 ) 381.709047619048 1.52076464916821 250.998106661557 Winsorized Mean ( 8 / 28 ) 381.53380952381 1.46343758560978 260.710680985300 Winsorized Mean ( 9 / 28 ) 381.467380952381 1.43934278843620 265.028861795205 Winsorized Mean ( 10 / 28 ) 380.686428571429 1.28917754141955 295.294027657544 Winsorized Mean ( 11 / 28 ) 380.032976190476 1.18231342089862 321.431669025317 Winsorized Mean ( 12 / 28 ) 380.032976190476 1.18231342089862 321.431669025317 Winsorized Mean ( 13 / 28 ) 380.580833333333 1.10720004748988 343.732674322172 Winsorized Mean ( 14 / 28 ) 380.6925 1.08888778906874 349.615914350166 Winsorized Mean ( 15 / 28 ) 380.653214285714 1.06461041173005 357.551654663165 Winsorized Mean ( 16 / 28 ) 380.537023809524 1.04741712729332 363.309911489502 Winsorized Mean ( 17 / 28 ) 380.498571428571 1.04127297174583 365.416736776157 Winsorized Mean ( 18 / 28 ) 380.500714285714 1.04101794076944 365.508315836014 Winsorized Mean ( 19 / 28 ) 380.457738095238 1.03061806218828 369.154929506497 Winsorized Mean ( 20 / 28 ) 380.210119047619 0.995436928461119 381.952997901534 Winsorized Mean ( 21 / 28 ) 380.250119047619 0.990651780062795 383.838324121838 Winsorized Mean ( 22 / 28 ) 380.043214285714 0.961335430893789 395.328417191879 Winsorized Mean ( 23 / 28 ) 379.640714285714 0.907448551679246 418.360593097189 Winsorized Mean ( 24 / 28 ) 379.655 0.900663895824375 421.527943731444 Winsorized Mean ( 25 / 28 ) 379.577619047619 0.890594115054431 426.207194311429 Winsorized Mean ( 26 / 28 ) 380.187380952381 0.819114380476344 464.144434543181 Winsorized Mean ( 27 / 28 ) 380.341666666667 0.796525512788177 477.500921891767 Winsorized Mean ( 28 / 28 ) 380.811666666667 0.746834471528889 509.901030528337 Trimmed Mean ( 1 / 28 ) 381.593048780488 1.52750545677470 249.814524123674 Trimmed Mean ( 2 / 28 ) 381.458125 1.50447687503788 253.548679497248 Trimmed Mean ( 3 / 28 ) 381.312179487179 1.47857879724243 257.891010068812 Trimmed Mean ( 4 / 28 ) 381.159736842105 1.44871452969532 263.102032201105 Trimmed Mean ( 5 / 28 ) 380.998108108108 1.41601554547108 269.063506630754 Trimmed Mean ( 6 / 28 ) 380.825277777778 1.37914342238504 276.131743513081 Trimmed Mean ( 7 / 28 ) 380.641857142857 1.33529350675671 285.062314177950 Trimmed Mean ( 8 / 28 ) 380.453529411765 1.28497219636134 296.079191821502 Trimmed Mean ( 9 / 28 ) 380.281666666667 1.23868650982372 307.003962383336 Trimmed Mean ( 10 / 28 ) 380.10875 1.18833922934823 319.865523759979 Trimmed Mean ( 11 / 28 ) 380.030483870968 1.16138897375358 327.220674949857 Trimmed Mean ( 12 / 28 ) 380.030166666667 1.14967591826711 330.554168029789 Trimmed Mean ( 13 / 28 ) 380.029827586207 1.13471985107969 334.910707012490 Trimmed Mean ( 14 / 28 ) 379.96625 1.12880958336073 336.607923604576 Trimmed Mean ( 15 / 28 ) 379.885555555556 1.12324299217648 338.2042516192 Trimmed Mean ( 16 / 28 ) 379.802884615385 1.11907620328490 339.389653269833 Trimmed Mean ( 17 / 28 ) 379.7258 1.11530664182821 340.467621870836 Trimmed Mean ( 18 / 28 ) 379.64625 1.10986104750527 342.066469359711 Trimmed Mean ( 19 / 28 ) 379.559565217391 1.10111783151986 344.703858526649 Trimmed Mean ( 20 / 28 ) 379.469318181818 1.09007653385166 348.112546594327 Trimmed Mean ( 21 / 28 ) 379.395238095238 1.08110410709196 350.933120692479 Trimmed Mean ( 22 / 28 ) 379.30975 1.06802378535768 355.151032402307 Trimmed Mean ( 23 / 28 ) 379.236052631579 1.05509665575409 359.432522663562 Trimmed Mean ( 24 / 28 ) 379.195 1.04766433343679 361.943217782433 Trimmed Mean ( 25 / 28 ) 379.147647058824 1.03595418817832 365.988816286886 Trimmed Mean ( 26 / 28 ) 379.1025 1.01917829409838 371.968773467035 Trimmed Mean ( 27 / 28 ) 378.985666666667 1.00910597547126 375.565773941313 Trimmed Mean ( 28 / 28 ) 378.835 0.995055434365502 380.717482580822 Median 376.01 Midrange 386.275 Midmean - Weighted Average at Xnp 379.265333333333 Midmean - Weighted Average at X(n+1)p 379.682790697674 Midmean - Empirical Distribution Function 379.265333333333 Midmean - Empirical Distribution Function - Averaging 379.682790697674 Midmean - Empirical Distribution Function - Interpolation 379.682790697674 Midmean - Closest Observation 379.265333333333 Midmean - True Basic - Statistics Graphics Toolkit 379.682790697674 Midmean - MS Excel (old versions) 379.265333333333 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/20/t1287574041u4l1b64ik9oopn8/19jmo1287573907.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287574041u4l1b64ik9oopn8/19jmo1287573907.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287574041u4l1b64ik9oopn8/22s4q1287573907.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/20/t1287574041u4l1b64ik9oopn8/22s4q1287573907.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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