Uitvoer per gewest (2002-2007) - Brussels Gewest - Central Tendency

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Sun, 07 Dec 2008 11:00:53 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/07/t12286729214plnfnvm3q6xtmv.htm/, Retrieved Sun, 07 Dec 2008 18:02:05 +0000

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/2008/Dec/07/t12286729214plnfnvm3q6xtmv.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

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Dataseries X:

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691.2 646.6 680.2 668.9 611.4 640.8 549.8 541.8 628.6 686.5 611.8 588.4 566.9 563.7 569.9 635.4 590.8 634.3 576.1 351.6 507.5 586.2 666.4 693.6 650.6 654.8 733.5 648.1 678.1 816.2 591 563.5 742.5 694.4 728.6 749 538.9 568.5 692.8 580.5 506.9 612.8 442.9 523.3 596.7 533.7 523.1 559.2 430.7 538.2 612.4 428 522.4 531.1 425.9 410.3 551 555.6 460.2 288.9 392.3 400.5 399 354.9 337.6 379.2 334.1 321.6 449.8 485.5 428.3 404.7

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 553.613888888889 13.9763144019708 39.6108639922141 Geometric Mean 539.955027454091 Harmonic Mean 525.120683939045 Quadratic Mean 566.001140310983 Winsorized Mean ( 1 / 24 ) 553.134722222222 13.6431819231424 40.5429411803094 Winsorized Mean ( 2 / 24 ) 553.301388888889 13.5260074492020 40.9064826384917 Winsorized Mean ( 3 / 24 ) 553.072222222222 13.4204251030322 41.2112297469074 Winsorized Mean ( 4 / 24 ) 553.577777777778 13.1974228085652 41.9459000297015 Winsorized Mean ( 5 / 24 ) 551.431944444444 12.7376881896297 43.2913678082801 Winsorized Mean ( 6 / 24 ) 553.390277777778 12.3048523069663 44.9733376697648 Winsorized Mean ( 7 / 24 ) 554.586111111111 12.0444432128079 46.0449770331741 Winsorized Mean ( 8 / 24 ) 555.152777777778 11.8761530981579 46.7451685061123 Winsorized Mean ( 9 / 24 ) 554.752777777778 11.7476540081714 47.2224307416532 Winsorized Mean ( 10 / 24 ) 554.461111111111 11.5037543296040 48.198274687095 Winsorized Mean ( 11 / 24 ) 554.995833333333 11.2988347892981 49.119740546964 Winsorized Mean ( 12 / 24 ) 556.0625 10.6067421492159 52.425381156372 Winsorized Mean ( 13 / 24 ) 555.990277777778 10.4740169908109 53.0828122835355 Winsorized Mean ( 14 / 24 ) 553.793055555555 10.1380670864987 54.6251125417257 Winsorized Mean ( 15 / 24 ) 553.418055555555 9.9292482080995 55.736148795648 Winsorized Mean ( 16 / 24 ) 555.573611111111 9.3870763623845 59.1849463734398 Winsorized Mean ( 17 / 24 ) 556.848611111111 9.06455762741103 61.4314160712281 Winsorized Mean ( 18 / 24 ) 557.998611111111 8.4345001171588 66.1566901843941 Winsorized Mean ( 19 / 24 ) 563.25 7.1779785712502 78.469167107293 Winsorized Mean ( 20 / 24 ) 568.888888888889 6.26352856810415 90.8256237204456 Winsorized Mean ( 21 / 24 ) 567.401388888889 5.99722663246313 94.6106298230472 Winsorized Mean ( 22 / 24 ) 567.126388888889 4.68941762780953 120.937488170316 Winsorized Mean ( 23 / 24 ) 567.222222222222 4.64190792278603 122.195922809641 Winsorized Mean ( 24 / 24 ) 567.088888888889 4.6056004366068 123.130283813047 Trimmed Mean ( 1 / 24 ) 553.644285714286 13.3401092982747 41.5022301043584 Trimmed Mean ( 2 / 24 ) 554.183823529412 12.9792790238312 42.6975814690383 Trimmed Mean ( 3 / 24 ) 554.665151515151 12.6232503677988 43.9399627951667 Trimmed Mean ( 4 / 24 ) 555.2625 12.244149983946 45.3492076402229 Trimmed Mean ( 5 / 24 ) 555.751612903226 11.8707020927672 46.8170802838903 Trimmed Mean ( 6 / 24 ) 556.788333333333 11.5629678935207 48.1527180963053 Trimmed Mean ( 7 / 24 ) 557.491379310345 11.3117588370864 49.2842348691675 Trimmed Mean ( 8 / 24 ) 558.025 11.0695793072258 50.4106781759758 Trimmed Mean ( 9 / 24 ) 558.503703703704 10.8088773990952 51.6708334346038 Trimmed Mean ( 10 / 24 ) 559.080769230769 10.5112013937289 53.189045503811 Trimmed Mean ( 11 / 24 ) 559.746 10.1916681496931 54.9219216892236 Trimmed Mean ( 12 / 24 ) 560.39375 9.83281856729766 56.9921784038381 Trimmed Mean ( 13 / 24 ) 560.958695652174 9.53617499762778 58.8242870744002 Trimmed Mean ( 14 / 24 ) 561.584090909091 9.17961130277301 61.1773279266678 Trimmed Mean ( 15 / 24 ) 562.538095238095 8.78633319507504 64.0242161034153 Trimmed Mean ( 16 / 24 ) 563.6325 8.31101014217486 67.8175685455856 Trimmed Mean ( 17 / 24 ) 564.586842105263 7.82126089074454 72.1861666542001 Trimmed Mean ( 18 / 24 ) 565.497222222222 7.24163390985096 78.0897279898344 Trimmed Mean ( 19 / 24 ) 566.379411764706 6.62810923831797 85.451128127218 Trimmed Mean ( 20 / 24 ) 566.75 6.18773826520722 91.5924325996068 Trimmed Mean ( 21 / 24 ) 566.493333333333 5.85601161462743 96.7370576790386 Trimmed Mean ( 22 / 24 ) 566.382142857143 5.45508367719232 103.826481200496 Trimmed Mean ( 23 / 24 ) 566.288461538462 5.32161434998261 106.412908620541 Trimmed Mean ( 24 / 24 ) 566.166666666667 5.11034992231475 110.788238628133 Median 565.3 Midrange 552.55 Midmean - Weighted Average at Xnp 562.37027027027 Midmean - Weighted Average at X(n+1)p 565.497222222222 Midmean - Empirical Distribution Function 562.37027027027 Midmean - Empirical Distribution Function - Averaging 565.497222222222 Midmean - Empirical Distribution Function - Interpolation 565.497222222222 Midmean - Closest Observation 562.37027027027 Midmean - True Basic - Statistics Graphics Toolkit 565.497222222222 Midmean - MS Excel (old versions) 564.586842105263 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t12286729214plnfnvm3q6xtmv/193sw1228672851.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t12286729214plnfnvm3q6xtmv/193sw1228672851.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t12286729214plnfnvm3q6xtmv/26lgg1228672851.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t12286729214plnfnvm3q6xtmv/26lgg1228672851.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')

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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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