Central Tendency - Werkloosheid - Tim vervaet

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 01 Jun 2009 11:36:34 -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/01/t1243877822ziatswvyk7bq4hi.htm/, Retrieved Mon, 01 Jun 2009 19:37:04 +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/01/t1243877822ziatswvyk7bq4hi.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 «

517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 556.263888888889 4.80882539347478 115.675626244134 Geometric Mean 554.777760333594 Harmonic Mean 553.282958280402 Quadratic Mean 557.737729582642 Winsorized Mean ( 1 / 24 ) 556.375 4.77545225594669 116.507289818921 Winsorized Mean ( 2 / 24 ) 556.652777777778 4.69188189960786 118.641685721949 Winsorized Mean ( 3 / 24 ) 556.569444444444 4.62514333360306 120.335610012516 Winsorized Mean ( 4 / 24 ) 556.847222222222 4.55215213862643 122.326144923233 Winsorized Mean ( 5 / 24 ) 556.986111111111 4.52762746133349 123.019421511121 Winsorized Mean ( 6 / 24 ) 556.486111111111 4.4031480173905 126.383693873846 Winsorized Mean ( 7 / 24 ) 556.777777777778 4.3195076582083 128.898435153771 Winsorized Mean ( 8 / 24 ) 556.777777777778 4.28129745657406 130.048842301959 Winsorized Mean ( 9 / 24 ) 556.902777777778 4.26095934493754 130.698918411281 Winsorized Mean ( 10 / 24 ) 555.097222222222 3.91673707469540 141.724402643338 Winsorized Mean ( 11 / 24 ) 554.944444444444 3.84606422858823 144.288917569155 Winsorized Mean ( 12 / 24 ) 554.944444444444 3.84606422858823 144.288917569155 Winsorized Mean ( 13 / 24 ) 554.944444444444 3.79011609366753 146.418851225068 Winsorized Mean ( 14 / 24 ) 555.527777777778 3.69631484534586 150.292331963350 Winsorized Mean ( 15 / 24 ) 555.736111111111 3.60050167428865 154.349632741362 Winsorized Mean ( 16 / 24 ) 555.513888888889 3.50189938711980 158.632167141096 Winsorized Mean ( 17 / 24 ) 555.277777777778 3.46840322060641 160.096085276006 Winsorized Mean ( 18 / 24 ) 555.277777777778 3.39452185840536 163.580557421607 Winsorized Mean ( 19 / 24 ) 557.125 3.0411842822839 183.193436598194 Winsorized Mean ( 20 / 24 ) 556.291666666667 2.84528255621935 195.513681216193 Winsorized Mean ( 21 / 24 ) 555.416666666667 2.64639817821957 209.876454434508 Winsorized Mean ( 22 / 24 ) 555.416666666667 2.64639817821957 209.876454434508 Winsorized Mean ( 23 / 24 ) 556.055555555556 2.37874068227804 233.760476582525 Winsorized Mean ( 24 / 24 ) 555.388888888889 2.11425924566634 262.687222499931 Trimmed Mean ( 1 / 24 ) 556.471428571429 4.6693007101237 119.176609757628 Trimmed Mean ( 2 / 24 ) 556.573529411765 4.54300087711612 122.512309477051 Trimmed Mean ( 3 / 24 ) 556.530303030303 4.44543293556446 125.191474283176 Trimmed Mean ( 4 / 24 ) 556.515625 4.35827256783529 127.691789886472 Trimmed Mean ( 5 / 24 ) 556.41935483871 4.27897769629402 130.035581938326 Trimmed Mean ( 6 / 24 ) 556.283333333333 4.18944676758826 132.782050755969 Trimmed Mean ( 7 / 24 ) 556.241379310345 4.11453610351679 135.189330052278 Trimmed Mean ( 8 / 24 ) 556.142857142857 4.04258408512961 137.571129117287 Trimmed Mean ( 9 / 24 ) 556.037037037037 3.96128741919145 140.367758810728 Trimmed Mean ( 10 / 24 ) 555.903846153846 3.86326041150184 143.894997214992 Trimmed Mean ( 11 / 24 ) 556.02 3.81677179548051 145.678083415516 Trimmed Mean ( 12 / 24 ) 556.166666666667 3.76931589506436 147.551089415171 Trimmed Mean ( 13 / 24 ) 556.326086956522 3.70481529562692 150.162975091686 Trimmed Mean ( 14 / 24 ) 556.5 3.63045900102722 153.286402585056 Trimmed Mean ( 15 / 24 ) 556.619047619048 3.55183163900186 156.713240995699 Trimmed Mean ( 16 / 24 ) 556.725 3.46687391515609 160.584149762751 Trimmed Mean ( 17 / 24 ) 556.868421052632 3.37301040932014 165.095375784764 Trimmed Mean ( 18 / 24 ) 557.055555555556 3.2498948565274 171.407254741399 Trimmed Mean ( 19 / 24 ) 557.264705882353 3.09686427098229 179.944827128506 Trimmed Mean ( 20 / 24 ) 557.28125 2.98491988565695 186.698896904346 Trimmed Mean ( 21 / 24 ) 557.4 2.87821783939897 193.661505522597 Trimmed Mean ( 22 / 24 ) 557.642857142857 2.77708608168063 200.801430255048 Trimmed Mean ( 23 / 24 ) 557.923076923077 2.61647036286737 213.235007298784 Trimmed Mean ( 24 / 24 ) 558.166666666667 2.47206616236522 225.789533938940 Median 561 Midrange 549 Midmean - Weighted Average at Xnp 554.947368421053 Midmean - Weighted Average at X(n+1)p 557.055555555556 Midmean - Empirical Distribution Function 554.947368421053 Midmean - Empirical Distribution Function - Averaging 557.055555555556 Midmean - Empirical Distribution Function - Interpolation 557.055555555556 Midmean - Closest Observation 554.947368421053 Midmean - True Basic - Statistics Graphics Toolkit 557.055555555556 Midmean - MS Excel (old versions) 555.846153846154 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243877822ziatswvyk7bq4hi/1d5311243877792.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243877822ziatswvyk7bq4hi/1d5311243877792.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243877822ziatswvyk7bq4hi/2de351243877792.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243877822ziatswvyk7bq4hi/2de351243877792.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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