Inschrijvingen nieuwe personenwagens

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Thu, 19 May 2011 19:08:50 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/19/t1305832136f2qe74mrzi6tb4u.htm/, Retrieved Thu, 19 May 2011 21:08:58 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

31.514 27.071 29.462 26.105 22.397 23.843 21.705 18.089 20.764 25.316 17.704 15.548 28.029 29.383 36.438 32.034 22.679 24.319 18.004 17.537 20.366 22.782 19.169 13.807 29.743 25.591 29.096 26.482 22.405 27.044 17.970 18.730 19.684 19.785 18.479 10.698 31.956 29.506 34.506 27.165 26.736 23.691 18.157 17.328 18.205 20.995 17.382 9.367 31.124 26.551 30.651 25.859 25.100 25.778 20.418 18.688 20.424 24.776 19.814 12.738 31.566 30.111 30.019 31.934 25.826 26.835 20.205 17.789 20.520 22.518 15.572 11.509 25.447 24.090 27.786 26.195 20.516 22.759 19.028 16.971 20.036 22.485 18.730 14.538 27.561 25.985 34.670 32.066 27.186 29.586 21.359 21.553 19.573 24.256 22.380 16.167 27.297 28.287

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 'Herman Ole Andreas Wold' @ www.yougetit.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 23.3428367346939 0.572233897668272 40.7924745979063 Geometric Mean 22.6059388973299 Harmonic Mean 21.7932778311447 Quadratic Mean 24.0135552404411 Winsorized Mean ( 1 / 32 ) 23.3383775510204 0.56496179656971 41.3096561444057 Winsorized Mean ( 2 / 32 ) 23.3515816326531 0.560560841254584 41.6575328030231 Winsorized Mean ( 3 / 32 ) 23.3145102040816 0.538706447029253 43.2786916374431 Winsorized Mean ( 4 / 32 ) 23.3568367346939 0.530015753806785 44.0681933828113 Winsorized Mean ( 5 / 32 ) 23.3901530612245 0.522622062678254 44.7553877487647 Winsorized Mean ( 6 / 32 ) 23.4506428571429 0.512070332581574 45.7957459455183 Winsorized Mean ( 7 / 32 ) 23.4260714285714 0.507378425085629 46.170807173399 Winsorized Mean ( 8 / 32 ) 23.4703979591837 0.499133998988133 47.0222385306629 Winsorized Mean ( 9 / 32 ) 23.5084183673469 0.482511209517248 48.7209787123227 Winsorized Mean ( 10 / 32 ) 23.4965816326531 0.469782967317849 50.0158227676986 Winsorized Mean ( 11 / 32 ) 23.4420306122449 0.459667389848061 50.9978108736264 Winsorized Mean ( 12 / 32 ) 23.4497448979592 0.4554272669009 51.4895497090686 Winsorized Mean ( 13 / 32 ) 23.4352857142857 0.447095458770388 52.4167384270419 Winsorized Mean ( 14 / 32 ) 23.425 0.442253660268674 52.9673400233004 Winsorized Mean ( 15 / 32 ) 23.4404591836735 0.436889876254862 53.6530152280282 Winsorized Mean ( 16 / 32 ) 23.4388265306122 0.435147578542747 53.8640858558971 Winsorized Mean ( 17 / 32 ) 23.4398673469388 0.431304184693856 54.3464871864775 Winsorized Mean ( 18 / 32 ) 23.3996428571429 0.422295908164142 55.410536556863 Winsorized Mean ( 19 / 32 ) 23.2521020408163 0.39999303814944 58.1312668550226 Winsorized Mean ( 20 / 32 ) 23.2553673469388 0.386014505261392 60.2448017625432 Winsorized Mean ( 21 / 32 ) 23.2480816326531 0.373761776108126 62.2002652992733 Winsorized Mean ( 22 / 32 ) 23.207 0.366318456900809 63.3519812142143 Winsorized Mean ( 23 / 32 ) 23.1450408163265 0.358825852480923 64.5021551716568 Winsorized Mean ( 24 / 32 ) 23.1908367346939 0.346437726582602 66.9408524396503 Winsorized Mean ( 25 / 32 ) 23.2214489795918 0.341371172676757 68.0240478348186 Winsorized Mean ( 26 / 32 ) 23.303693877551 0.325501987309621 71.5930924728404 Winsorized Mean ( 27 / 32 ) 23.3268367346939 0.321018512021936 72.6650827323625 Winsorized Mean ( 28 / 32 ) 23.2959795918367 0.310576340302695 75.008867607661 Winsorized Mean ( 29 / 32 ) 23.2752653061224 0.306148266545784 76.0261214892154 Winsorized Mean ( 30 / 32 ) 23.2865918367347 0.291715523285473 79.826371851821 Winsorized Mean ( 31 / 32 ) 23.3182244897959 0.283097583252315 82.3681510167226 Winsorized Mean ( 32 / 32 ) 23.2770816326531 0.266464896098573 87.3551524927403 Trimmed Mean ( 1 / 32 ) 23.3428367346939 0.548716588419516 42.5407892295163 Trimmed Mean ( 2 / 32 ) 23.3520104166667 0.530223572963828 44.0418185976423 Trimmed Mean ( 3 / 32 ) 23.3740217391304 0.511805916087864 45.669698228181 Trimmed Mean ( 4 / 32 ) 23.3740217391304 0.500223243440214 46.7271804052506 Trimmed Mean ( 5 / 32 ) 23.4064204545455 0.489934616935657 47.7745798019808 Trimmed Mean ( 6 / 32 ) 23.4101279069767 0.480248695490419 48.7458438238356 Trimmed Mean ( 7 / 32 ) 23.40225 0.471733268686569 49.6090726548885 Trimmed Mean ( 8 / 32 ) 23.40225 0.462950432247852 50.5502282098983 Trimmed Mean ( 9 / 32 ) 23.387125 0.454472808496806 51.4598993883797 Trimmed Mean ( 10 / 32 ) 23.3701923076923 0.447793925393826 52.1896144239534 Trimmed Mean ( 11 / 32 ) 23.3538947368421 0.442239333305437 52.8082713997592 Trimmed Mean ( 12 / 32 ) 23.3432837837838 0.4373887437827 53.3696491178589 Trimmed Mean ( 13 / 32 ) 23.3312083333333 0.432258085408721 53.9751808488962 Trimmed Mean ( 14 / 32 ) 23.32 0.427418654738208 54.5600893678433 Trimmed Mean ( 15 / 32 ) 23.3091911764706 0.422302452508625 55.1954909046959 Trimmed Mean ( 16 / 32 ) 23.3091911764706 0.416891478122697 55.9118917024501 Trimmed Mean ( 17 / 32 ) 23.282546875 0.410538018033455 56.7122796240097 Trimmed Mean ( 18 / 32 ) 23.2679193548387 0.403369422108199 57.683894910104 Trimmed Mean ( 19 / 32 ) 23.2559666666667 0.396047159469097 58.7201955894378 Trimmed Mean ( 20 / 32 ) 23.2563103448276 0.390617927803389 59.5372323938323 Trimmed Mean ( 21 / 32 ) 23.2563928571429 0.385969869356431 60.2544258076951 Trimmed Mean ( 22 / 32 ) 23.2571111111111 0.381914911684609 60.8960540674494 Trimmed Mean ( 23 / 32 ) 23.2614038461538 0.377750997594609 61.5786695317144 Trimmed Mean ( 24 / 32 ) 23.27132 0.373403939989926 62.3221061904913 Trimmed Mean ( 25 / 32 ) 23.2781666666667 0.369655770404549 62.9725504925601 Trimmed Mean ( 26 / 32 ) 23.283 0.365332353484352 63.7310103469861 Trimmed Mean ( 27 / 32 ) 23.283 0.362167698333683 64.2878978636803 Trimmed Mean ( 28 / 32 ) 23.2772857142857 0.358297902717029 64.9662907255956 Trimmed Mean ( 29 / 32 ) 23.27565 0.354650751914237 65.6297776738639 Trimmed Mean ( 30 / 32 ) 23.2756842105263 0.350020645815098 66.4980322984203 Trimmed Mean ( 31 / 32 ) 23.2746944444444 0.34621770107665 67.2256050804623 Trimmed Mean ( 32 / 32 ) 23.2746944444444 0.342114698330053 68.031845922008 Median 22.7705 Midrange 22.9025 Midmean - Weighted Average at Xnp 23.1914285714286 Midmean - Weighted Average at X(n+1)p 23.27132 Midmean - Empirical Distribution Function 23.27132 Midmean - Empirical Distribution Function - Averaging 23.27132 Midmean - Empirical Distribution Function - Interpolation 23.2781666666667 Midmean - Closest Observation 23.27132 Midmean - True Basic - Statistics Graphics Toolkit 23.27132 Midmean - MS Excel (old versions) 23.27132 Number of observations 98

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305832136f2qe74mrzi6tb4u/1ur081305832129.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305832136f2qe74mrzi6tb4u/1ur081305832129.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305832136f2qe74mrzi6tb4u/2ak841305832129.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305832136f2qe74mrzi6tb4u/2ak841305832129.ps (open in new window)

Parameters (Session):

par1 = grey ;

Parameters (R input):

par1 = grey ;

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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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