Centrummaten prijzen Roze zalm

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

Title produced by software: Central Tendency

Date of computation: Mon, 21 Apr 2008 11:22:27 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/21/t1208798600gakzjhd0xd1w2ap.htm/, Retrieved Mon, 21 Apr 2008 19:23:20 +0200

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Dataseries X:

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11.98 11.79 11.66 11.96 11.83 12.36 12.53 12.55 12.53 12.24 12.34 12.05 12.22 12.23 11.92 12.13 12.1 12.15 12.23 12.08 12.02 11.93 12.16 11.87 11.93 11.79 11.43 11.63 11.93 11.89 11.83 11.59 12.04 11.81 11.9 11.72 11.91 11.94 11.91 11.84 12.01 11.89 11.8 11.7 11.5 11.76 11.61 11.27 11.64 11.39 11.54 11.62 11.59 11.44 11.31 11.56 11.4 11.51 11.5 11.24 11.8 11.87 11.86 12.11 11.92 12.61 13.34 13.31 13.47 13.24 13.18 13.3

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 11.9894444444444 0.0590813505394759 202.931116756269 Geometric Mean 11.9794592783188 Harmonic Mean 11.9698081265545 Quadratic Mean 11.9997754608622 Winsorized Mean ( 1 / 24 ) 11.9880555555556 0.0583948833190362 205.292910511691 Winsorized Mean ( 2 / 24 ) 11.9883333333333 0.0579372873413637 206.919134178627 Winsorized Mean ( 3 / 24 ) 11.99125 0.0572819187183013 209.337436110862 Winsorized Mean ( 4 / 24 ) 11.9884722222222 0.0561400759426589 213.545707249616 Winsorized Mean ( 5 / 24 ) 11.9863888888889 0.0545400835912082 219.772103371347 Winsorized Mean ( 6 / 24 ) 11.9397222222222 0.0414156628486726 288.290018823274 Winsorized Mean ( 7 / 24 ) 11.9397222222222 0.0391517913127579 304.959794223555 Winsorized Mean ( 8 / 24 ) 11.9375 0.0386680376557983 308.717502198097 Winsorized Mean ( 9 / 24 ) 11.93875 0.0384703295523777 310.336566879296 Winsorized Mean ( 10 / 24 ) 11.9193055555556 0.0330056228842194 361.129544422396 Winsorized Mean ( 11 / 24 ) 11.9193055555556 0.0319454778018886 373.114017247565 Winsorized Mean ( 12 / 24 ) 11.9076388888889 0.0282146735480936 422.037096002249 Winsorized Mean ( 13 / 24 ) 11.9058333333333 0.0279172359972778 426.468914562111 Winsorized Mean ( 14 / 24 ) 11.9097222222222 0.0273067059571049 436.146426483325 Winsorized Mean ( 15 / 24 ) 11.9097222222222 0.0266431617523533 447.008592032824 Winsorized Mean ( 16 / 24 ) 11.8986111111111 0.024187343878462 491.9354175845 Winsorized Mean ( 17 / 24 ) 11.8986111111111 0.0234615070781932 507.154594607034 Winsorized Mean ( 18 / 24 ) 11.8986111111111 0.0219414728282553 542.288624115906 Winsorized Mean ( 19 / 24 ) 11.9038888888889 0.0195734597580415 608.164782110037 Winsorized Mean ( 20 / 24 ) 11.9066666666667 0.0183557268272123 648.662228346909 Winsorized Mean ( 21 / 24 ) 11.9125 0.0158604906708226 751.080168151078 Winsorized Mean ( 22 / 24 ) 11.9125 0.0132918221178012 896.22776278702 Winsorized Mean ( 23 / 24 ) 11.9093055555556 0.0128298824530604 928.247441013365 Winsorized Mean ( 24 / 24 ) 11.9059722222222 0.0114477443128417 1040.02779035400 Trimmed Mean ( 1 / 24 ) 11.979 0.0558811034480108 214.365845712848 Trimmed Mean ( 2 / 24 ) 11.9694117647059 0.0528415069982861 226.515336988669 Trimmed Mean ( 3 / 24 ) 11.9590909090909 0.0494311356221129 241.934375137865 Trimmed Mean ( 4 / 24 ) 11.94703125 0.0455105951423764 262.510987004776 Trimmed Mean ( 5 / 24 ) 11.935 0.0410438557672811 290.786520342327 Trimmed Mean ( 6 / 24 ) 11.9226666666667 0.0358786928780374 332.304933939356 Trimmed Mean ( 7 / 24 ) 11.9191379310345 0.034129290919304 349.234853991439 Trimmed Mean ( 8 / 24 ) 11.9153571428571 0.0326153938295519 365.329243152078 Trimmed Mean ( 9 / 24 ) 11.9116666666667 0.0308586076932045 386.007910178325 Trimmed Mean ( 10 / 24 ) 11.9075 0.0286760064935181 415.242617645926 Trimmed Mean ( 11 / 24 ) 11.9058 0.0274108424845769 434.346372487419 Trimmed Mean ( 12 / 24 ) 11.9039583333333 0.026063784933261 456.72408530897 Trimmed Mean ( 13 / 24 ) 11.9034782608696 0.0252623287762330 471.194812097785 Trimmed Mean ( 14 / 24 ) 11.9031818181818 0.0242885506381240 490.073779844989 Trimmed Mean ( 15 / 24 ) 11.9023809523810 0.0231563125546297 514.001567576926 Trimmed Mean ( 16 / 24 ) 11.9015 0.0218196277201549 545.449269466981 Trimmed Mean ( 17 / 24 ) 11.9018421052632 0.0206950879719694 575.104687710615 Trimmed Mean ( 18 / 24 ) 11.9022222222222 0.0193551236443345 614.939095246035 Trimmed Mean ( 19 / 24 ) 11.9026470588235 0.0179487725364923 663.145462154798 Trimmed Mean ( 20 / 24 ) 11.9025 0.0167223532068364 711.771833352617 Trimmed Mean ( 21 / 24 ) 11.902 0.0153533103248464 775.207414438754 Trimmed Mean ( 22 / 24 ) 11.9007142857143 0.0142346972640107 836.035643399498 Trimmed Mean ( 23 / 24 ) 11.8992307692308 0.0135069563493218 880.970550395555 Trimmed Mean ( 24 / 24 ) 11.8979166666667 0.0125394907592938 948.83571391034 Median 11.905 Midrange 12.355 Midmean - Weighted Average at Xnp 11.8951351351351 Midmean - Weighted Average at X(n+1)p 11.9022222222222 Midmean - Empirical Distribution Function 11.8951351351351 Midmean - Empirical Distribution Function - Averaging 11.9022222222222 Midmean - Empirical Distribution Function - Interpolation 11.9022222222222 Midmean - Closest Observation 11.8951351351351 Midmean - True Basic - Statistics Graphics Toolkit 11.9022222222222 Midmean - MS Excel (old versions) 11.9018421052632 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208798600gakzjhd0xd1w2ap/1lvdg1208798541.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208798600gakzjhd0xd1w2ap/1lvdg1208798541.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208798600gakzjhd0xd1w2ap/23zov1208798541.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208798600gakzjhd0xd1w2ap/23zov1208798541.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

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Software written by Ed van Stee & Patrick Wessa

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