Uitvoer per gewest - Vlaams 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 11:03:14 -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/t1228673040ji041qnjsqx2bnk.htm/, Retrieved Sun, 07 Dec 2008 18:04:03 +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/t1228673040ji041qnjsqx2bnk.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:

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Dataseries X:

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11316.9 11309.2 12710.3 12120.8 12469.5 12054.6 12112.9 9617.2 12645.8 13581.3 12162.3 10969.7 11880 11887.6 12926.9 12300 12092.8 12380.8 12196.9 9455 13168 13427.9 11980.5 11884.8 11691.7 12233.8 14341.4 13130.7 12421.1 14285.8 12864.6 11160.2 14316.2 14388.7 14013.9 13419 12769.6 13315.5 15332.9 14243 13824.4 14962.9 13202.9 12199 15508.9 14199.8 15169.6 14058 13786.2 14147.9 16541.7 13587.5 15582.4 15802.8 14130.5 12923.2 15612.2 16033.7 16036.6 14037.8 15330.6 15038.3 17401.8 14992.5 16043.7 16929.6 15921.3 14417.2 15961 17785.1 16469.7 14272

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 13673.4805555556 208.968984308977 65.4330622353901 Geometric Mean 13559.0369216852 Harmonic Mean 13443.2130938245 Quadratic Mean 13786.3882539183 Winsorized Mean ( 1 / 24 ) 13670.4097222222 206.923921886721 66.0649073223443 Winsorized Mean ( 2 / 24 ) 13694.8625 194.791731186126 70.3051531839121 Winsorized Mean ( 3 / 24 ) 13686.6375 189.658705653174 72.1645624062655 Winsorized Mean ( 4 / 24 ) 13690.9152777778 187.298667939659 73.0967039348538 Winsorized Mean ( 5 / 24 ) 13661.8666666667 181.369610007499 75.3261070920414 Winsorized Mean ( 6 / 24 ) 13692.5083333333 175.908555164124 77.838785729086 Winsorized Mean ( 7 / 24 ) 13710.5333333333 173.024265080737 79.240523442973 Winsorized Mean ( 8 / 24 ) 13702.9888888889 171.431562189385 79.9327073374669 Winsorized Mean ( 9 / 24 ) 13698.3763888889 170.463190034854 80.3597327146586 Winsorized Mean ( 10 / 24 ) 13694.8208333333 165.569169941045 82.713592380814 Winsorized Mean ( 11 / 24 ) 13677.0222222222 158.817126495597 86.1180561820666 Winsorized Mean ( 12 / 24 ) 13678.4222222222 157.056197930490 87.092533771103 Winsorized Mean ( 13 / 24 ) 13668.7805555556 154.292742315178 88.5899125937753 Winsorized Mean ( 14 / 24 ) 13636.0944444444 148.441892369922 91.8614969584387 Winsorized Mean ( 15 / 24 ) 13644.2611111111 147.129808169845 92.7362121981452 Winsorized Mean ( 16 / 24 ) 13616.1722222222 140.358238818789 97.0101387479042 Winsorized Mean ( 17 / 24 ) 13585.6666666667 135.529610711089 100.241316974100 Winsorized Mean ( 18 / 24 ) 13582.9166666667 132.557394218989 102.468193092475 Winsorized Mean ( 19 / 24 ) 13592.575 128.901687476282 105.449162583702 Winsorized Mean ( 20 / 24 ) 13463.4361111111 104.417051307243 128.939056816453 Winsorized Mean ( 21 / 24 ) 13466.8777777778 101.641376024325 132.494052171774 Winsorized Mean ( 22 / 24 ) 13467.2138888889 97.671520579634 137.882709401547 Winsorized Mean ( 23 / 24 ) 13515.4819444444 88.7050390273929 152.364308641708 Winsorized Mean ( 24 / 24 ) 13526.8486111111 84.4710845645767 160.135846258373 Trimmed Mean ( 1 / 24 ) 13675.0071428571 197.567949003326 69.2167287854315 Trimmed Mean ( 2 / 24 ) 13679.875 186.326633607388 73.418784717729 Trimmed Mean ( 3 / 24 ) 13671.7 180.818702257944 75.609988509357 Trimmed Mean ( 4 / 24 ) 13666.0984375 176.577877248517 77.3941710617931 Trimmed Mean ( 5 / 24 ) 13658.8935483871 172.316141348936 79.2664775421601 Trimmed Mean ( 6 / 24 ) 13658.18 169.016849923882 80.8095761230378 Trimmed Mean ( 7 / 24 ) 13651.0775862069 166.454115422526 82.0110548276628 Trimmed Mean ( 8 / 24 ) 13640.1571428571 163.939891876331 83.2021845735186 Trimmed Mean ( 9 / 24 ) 13629.6851851852 161.129676680770 84.5882984807838 Trimmed Mean ( 10 / 24 ) 13619.1173076923 157.771634699796 86.3217100691544 Trimmed Mean ( 11 / 24 ) 13608.216 154.594677637877 88.0251261422848 Trimmed Mean ( 12 / 24 ) 13598.8333333333 151.996042616379 89.4683381175603 Trimmed Mean ( 13 / 24 ) 13588.4521739130 148.928993706940 91.2411467753029 Trimmed Mean ( 14 / 24 ) 13578.3409090909 145.478736860848 93.33557055887 Trimmed Mean ( 15 / 24 ) 13571.2690476190 142.234946948446 95.414448690574 Trimmed Mean ( 16 / 24 ) 13562.51 138.105068177856 98.2042887994073 Trimmed Mean ( 17 / 24 ) 13556.1552631579 134.15541584389 101.048140158072 Trimmed Mean ( 18 / 24 ) 13552.6833333333 129.913507582472 104.320817638842 Trimmed Mean ( 19 / 24 ) 13549.1264705882 124.719718161149 108.636602698873 Trimmed Mean ( 20 / 24 ) 13543.98125 118.342038657695 114.447760099656 Trimmed Mean ( 21 / 24 ) 13553.6466666667 116.335302133984 116.505019697777 Trimmed Mean ( 22 / 24 ) 13564.2714285714 113.804798865856 119.188923171508 Trimmed Mean ( 23 / 24 ) 13576.4884615385 110.836153685994 122.491515719695 Trimmed Mean ( 24 / 24 ) 13584.4458333333 109.098335010869 124.515610911752 Median 13584.4 Midrange 13620.05 Midmean - Weighted Average at Xnp 13516.0972972973 Midmean - Weighted Average at X(n+1)p 13552.6833333333 Midmean - Empirical Distribution Function 13516.0972972973 Midmean - Empirical Distribution Function - Averaging 13552.6833333333 Midmean - Empirical Distribution Function - Interpolation 13552.6833333333 Midmean - Closest Observation 13516.0972972973 Midmean - True Basic - Statistics Graphics Toolkit 13552.6833333333 Midmean - MS Excel (old versions) 13556.1552631579 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228673040ji041qnjsqx2bnk/1t10f1228672992.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228673040ji041qnjsqx2bnk/1t10f1228672992.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228673040ji041qnjsqx2bnk/2z4rw1228672992.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/07/t1228673040ji041qnjsqx2bnk/2z4rw1228672992.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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