centrummaten- uitvoer België naar EU -Tessa Buck

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Thu, 12 Mar 2009 12:59:30 -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/Mar/12/t1236884622kgt3i6te34xz5ti.htm/, Retrieved Thu, 12 Mar 2009 20:03:45 +0100

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/Mar/12/t1236884622kgt3i6te34xz5ti.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 «

11025,1 10853,8 12252,6 11839,4 11669,1 11601,4 11178,4 9516,4 12102,8 12989 11610,2 10205,5 11356,2 11307,1 12648,6 11947,2 11714,1 12192,5 11268,8 9097,4 12639,8 13040,1 11687,3 11191,7 11391,9 11793,1 13933,2 12778,1 11810,3 13698,4 11956,6 10723,8 13938,9 13979,8 13807,4 12973,9 12509,8 12934,1 14908,3 13772,1 13012,6 14049,9 11816,5 11593,2 14466,2 13615,9 14733,9 13880,7 13527,5 13584 16170,2 13260,6 14741,9 15486,5 13154,5 12621,2 15031,6 15452,4 15428 13105,9 14716,8 14180 16202,2 14392,4 15140,6 15960,1 14351,3 13230,2 15202,1 17056 16077,7 13348,2 16707,5 16792,6 16831,3 17804,5 16370,2 17602,5 17065,6 14427,9 17818,5 18027,6

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 13559.5512195122 226.962540748187 59.7435646200155 Geometric Mean 13407.1822891627 Harmonic Mean 13256.3146478860 Quadratic Mean 13712.5453823026 Winsorized Mean ( 1 / 27 ) 13562.1109756098 225.168007781775 60.2310741619817 Winsorized Mean ( 2 / 27 ) 13578.5768292683 221.642712484048 61.2633579380399 Winsorized Mean ( 3 / 27 ) 13590.1487804878 216.594540383525 62.744650702754 Winsorized Mean ( 4 / 27 ) 13570.3 209.877628689649 64.658153823849 Winsorized Mean ( 5 / 27 ) 13580.1597560976 208.130876115178 65.2481746561353 Winsorized Mean ( 6 / 27 ) 13574.9353658537 203.140943712146 66.8252057797347 Winsorized Mean ( 7 / 27 ) 13572.7670731707 202.324339661139 67.0842029975382 Winsorized Mean ( 8 / 27 ) 13571.9865853659 199.621450669727 67.9886181561753 Winsorized Mean ( 9 / 27 ) 13539.1695121951 192.058251191964 70.4951202469433 Winsorized Mean ( 10 / 27 ) 13524.6695121951 187.530679908442 72.11977004935 Winsorized Mean ( 11 / 27 ) 13525.1658536585 186.094992023069 72.6788276601336 Winsorized Mean ( 12 / 27 ) 13541.0878048781 179.669532655763 75.3666334226073 Winsorized Mean ( 13 / 27 ) 13523.7439024390 176.279295131030 76.7177103379425 Winsorized Mean ( 14 / 27 ) 13444.3878048780 162.892800814007 82.5351871764365 Winsorized Mean ( 15 / 27 ) 13448.9243902439 160.442477059316 83.8239638077378 Winsorized Mean ( 16 / 27 ) 13447.7146341463 159.224436260409 84.4576055659752 Winsorized Mean ( 17 / 27 ) 13406.4378048780 151.434441833960 88.5296478299008 Winsorized Mean ( 18 / 27 ) 13410.2792682927 147.092436096536 91.1690609263658 Winsorized Mean ( 19 / 27 ) 13389.0085365854 142.923945229087 93.6792537816155 Winsorized Mean ( 20 / 27 ) 13360.4475609756 138.507866434417 96.4598466853267 Winsorized Mean ( 21 / 27 ) 13323.6975609756 131.926928005464 100.993010012511 Winsorized Mean ( 22 / 27 ) 13350.4731707317 127.669249952622 104.570780949101 Winsorized Mean ( 23 / 27 ) 13348.3134146341 126.670862061009 105.377931415712 Winsorized Mean ( 24 / 27 ) 13317.7573170732 111.307518685128 119.648317331977 Winsorized Mean ( 25 / 27 ) 13333.4280487805 106.163199027185 125.593691325808 Winsorized Mean ( 26 / 27 ) 13341.2280487805 102.215120250441 130.521081578662 Winsorized Mean ( 27 / 27 ) 13412.3829268293 89.6301990904511 149.641338108532 Trimmed Mean ( 1 / 27 ) 13559.4775 218.694492523354 62.0019157480703 Trimmed Mean ( 2 / 27 ) 13556.7089743590 211.153402201713 64.2031283086236 Trimmed Mean ( 3 / 27 ) 13544.9118421053 204.552212199414 66.2173813544514 Trimmed Mean ( 4 / 27 ) 13528.2027027027 199.06008717956 67.9603977591939 Trimmed Mean ( 5 / 27 ) 13516.2166666667 194.997018234897 69.3149915266129 Trimmed Mean ( 6 / 27 ) 13501.2357142857 190.68711814662 70.8030822716853 Trimmed Mean ( 7 / 27 ) 13486.4235294118 186.887192246088 72.1634445214053 Trimmed Mean ( 8 / 27 ) 13471.0984848485 182.519625275441 73.8063014567295 Trimmed Mean ( 9 / 27 ) 13454.940625 177.877018356277 75.6418156169595 Trimmed Mean ( 10 / 27 ) 13442.5629032258 173.960588244792 77.2736114476103 Trimmed Mean ( 11 / 27 ) 13431.3416666667 170.141105119737 78.9423676143067 Trimmed Mean ( 12 / 27 ) 13419.2827586207 165.732533233271 80.9695145354041 Trimmed Mean ( 13 / 27 ) 13404.4196428571 161.55963834753 82.96886388185 Trimmed Mean ( 14 / 27 ) 13390.4814814815 157.060478923411 85.2568486564418 Trimmed Mean ( 15 / 27 ) 13384.4096153846 154.171734919575 86.8149380453343 Trimmed Mean ( 16 / 27 ) 13377.356 150.934270142161 88.6303421177986 Trimmed Mean ( 17 / 27 ) 13369.84375 146.999674545710 90.9515193915791 Trimmed Mean ( 18 / 27 ) 13366.0065217391 143.541070370514 93.1162522840207 Trimmed Mean ( 19 / 27 ) 13361.4227272727 139.892398730810 95.5121425359473 Trimmed Mean ( 20 / 27 ) 13358.5880952381 135.957924898303 98.2553102750752 Trimmed Mean ( 21 / 27 ) 13358.3975 131.682318794791 101.444124179019 Trimmed Mean ( 22 / 27 ) 13361.9631578947 127.423443416118 104.862675184970 Trimmed Mean ( 23 / 27 ) 13363.1527777778 122.620305258486 108.979934029751 Trimmed Mean ( 24 / 27 ) 13364.7088235294 116.140387831700 115.073740264207 Trimmed Mean ( 25 / 27 ) 13369.721875 111.476964723657 119.932596910425 Trimmed Mean ( 26 / 27 ) 13373.69 106.250798980093 125.869077017536 Trimmed Mean ( 27 / 27 ) 13377.3464285714 99.779153552506 134.069552128762 Median 13304.4 Midrange 13562.5 Midmean - Weighted Average at Xnp 13320.7902439024 Midmean - Weighted Average at X(n+1)p 13358.5880952381 Midmean - Empirical Distribution Function 13358.5880952381 Midmean - Empirical Distribution Function - Averaging 13358.5880952381 Midmean - Empirical Distribution Function - Interpolation 13358.3975 Midmean - Closest Observation 13358.5880952381 Midmean - True Basic - Statistics Graphics Toolkit 13358.5880952381 Midmean - MS Excel (old versions) 13358.5880952381 Number of observations 82

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/12/t1236884622kgt3i6te34xz5ti/16r7c1236884368.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/12/t1236884622kgt3i6te34xz5ti/16r7c1236884368.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/12/t1236884622kgt3i6te34xz5ti/27a7s1236884368.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/12/t1236884622kgt3i6te34xz5ti/27a7s1236884368.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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