Centrummaten witte wijn verkoop

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 16 Mar 2010 15:52:42 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/16/t1268776427bq7agtfe3kbqyen.htm/, Retrieved Tue, 16 Mar 2010 22:53:50 +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/2010/Mar/16/t1268776427bq7agtfe3kbqyen.htm/}, year = {2010}, } @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 = {2010}, 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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

1954 2302 3054 2414 2226 2725 2589 3470 2400 3180 4009 3924 2072 2434 2956 2828 2687 2629 3150 4119 3030 3055 3821 4001 2529 2472 3134 2789 2758 2993 3282 3437 2804 3076 3782 3889 2271 2452 3084 2522 2769 3438 2839 3746 2632 2851 3871 3618 2389 2344 2678 2492 2858 2246 2800 3869 3007 3023 3907 4209 2353 2570 2903 2910 3782 2759 2931 3641 2794 3070 3576 4106 2452 2206 2488 2416 2534 2521 3093 3903 2907 3025 3812 4209

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 3010.11904761905 63.6661216377696 47.2797615150051 Geometric Mean 2956.14350124694 Harmonic Mean 2904.42622431556 Quadratic Mean 3065.49291460995 Winsorized Mean ( 1 / 28 ) 3011.52380952381 63.4003083896174 47.5001444948332 Winsorized Mean ( 2 / 28 ) 3012.57142857143 62.3939014208405 48.2831071622199 Winsorized Mean ( 3 / 28 ) 3012.82142857143 62.1850646110089 48.449277128162 Winsorized Mean ( 4 / 28 ) 3009.15476190476 61.0959726150459 49.2529152594865 Winsorized Mean ( 5 / 28 ) 3010.16666666667 60.7812633275774 49.5245821141218 Winsorized Mean ( 6 / 28 ) 3006.88095238095 59.4088115185584 50.6133833605079 Winsorized Mean ( 7 / 28 ) 3008.96428571429 58.6571459468798 51.2974887738183 Winsorized Mean ( 8 / 28 ) 3009.44047619048 58.4704331458514 51.4694404381029 Winsorized Mean ( 9 / 28 ) 3011.79761904762 57.6831135528042 52.2128129628538 Winsorized Mean ( 10 / 28 ) 3010.96428571429 57.122892067649 52.710291386306 Winsorized Mean ( 11 / 28 ) 3012.53571428571 56.8409408341693 52.9993992019703 Winsorized Mean ( 12 / 28 ) 3005.96428571429 55.5761494679253 54.0873074959812 Winsorized Mean ( 13 / 28 ) 3007.35714285714 54.9771183896594 54.7019784038517 Winsorized Mean ( 14 / 28 ) 3005.35714285714 53.7261645581981 55.9384271624607 Winsorized Mean ( 15 / 28 ) 3005.35714285714 53.7261645581981 55.9384271624607 Winsorized Mean ( 16 / 28 ) 3002.30952380952 52.0687874614736 57.6604463092399 Winsorized Mean ( 17 / 28 ) 2984.29761904762 48.0892200660807 62.0575175672804 Winsorized Mean ( 18 / 28 ) 2980.22619047619 47.175622950847 63.1730119087422 Winsorized Mean ( 19 / 28 ) 2977.28571428571 44.8259801274407 66.4187532725724 Winsorized Mean ( 20 / 28 ) 2952.28571428571 40.8331848842077 72.3011374855435 Winsorized Mean ( 21 / 28 ) 2946.03571428571 39.3975298771544 74.7771680984 Winsorized Mean ( 22 / 28 ) 2947.08333333333 39.1914523752429 75.1970941295096 Winsorized Mean ( 23 / 28 ) 2914.5 31.7423221321800 91.8174791328612 Winsorized Mean ( 24 / 28 ) 2890.78571428571 27.10572504658 106.648529390674 Winsorized Mean ( 25 / 28 ) 2893.76190476190 24.3881914834753 118.654222750491 Winsorized Mean ( 26 / 28 ) 2889.73809523810 23.6447648552999 122.214710652551 Winsorized Mean ( 27 / 28 ) 2891.34523809524 20.1085514704493 143.786848214514 Winsorized Mean ( 28 / 28 ) 2891.34523809524 19.3650314910497 149.307541246787 Trimmed Mean ( 1 / 28 ) 3008.37804878049 62.2125177300656 48.3564748469683 Trimmed Mean ( 2 / 28 ) 3005.075 60.8328400000226 49.398893755394 Trimmed Mean ( 3 / 28 ) 3001.03846153846 59.8413220966273 50.1499358034338 Trimmed Mean ( 4 / 28 ) 2996.69736842105 58.7655646265104 50.9941049229565 Trimmed Mean ( 5 / 28 ) 2993.16216216216 57.87663227828 51.7162461659926 Trimmed Mean ( 6 / 28 ) 2989.19444444444 56.9104038680353 52.5245691697398 Trimmed Mean ( 7 / 28 ) 2985.65714285714 56.116083786282 53.2050161274264 Trimmed Mean ( 8 / 28 ) 2981.54411764706 55.3304282676743 53.8861565145153 Trimmed Mean ( 9 / 28 ) 2977.10606060606 54.41476356291 54.7113662850738 Trimmed Mean ( 10 / 28 ) 2972.046875 53.4603418399712 55.5934880457098 Trimmed Mean ( 11 / 28 ) 2966.77419354839 52.4049108359349 56.6125224950106 Trimmed Mean ( 12 / 28 ) 2960.95 51.1583474254147 57.878140108354 Trimmed Mean ( 13 / 28 ) 2955.51724137931 49.8832165586819 59.2487302398089 Trimmed Mean ( 14 / 28 ) 2949.53571428571 48.4127610383291 60.9247572546114 Trimmed Mean ( 15 / 28 ) 2943.33333333333 46.8291346775392 62.8526098891393 Trimmed Mean ( 16 / 28 ) 2936.65384615385 44.8274039204132 65.5102368044242 Trimmed Mean ( 17 / 28 ) 2929.76 42.6464493342216 68.6988024967654 Trimmed Mean ( 18 / 28 ) 2924.14583333333 40.7886351417011 71.690210353319 Trimmed Mean ( 19 / 28 ) 2918.45652173913 38.5965344308179 75.6144706973704 Trimmed Mean ( 20 / 28 ) 2912.54545454545 36.290690577115 80.2559942571639 Trimmed Mean ( 21 / 28 ) 2908.57142857143 34.3163384331396 84.7576274560399 Trimmed Mean ( 22 / 28 ) 2904.825 32.0547985827315 90.6205974903514 Trimmed Mean ( 23 / 28 ) 2900.57894736842 28.9885107858319 100.059605296664 Trimmed Mean ( 24 / 28 ) 2899.16666666667 27.1192691993122 106.904306504697 Trimmed Mean ( 25 / 28 ) 2900.02941176471 25.8815512961254 112.050061396391 Trimmed Mean ( 26 / 28 ) 2900.6875 24.9115547382295 116.439440672427 Trimmed Mean ( 27 / 28 ) 2901.86666666667 23.7068171646180 122.406422022677 Trimmed Mean ( 28 / 28 ) 2903.03571428571 23.0672172921972 125.851145264397 Median 2905 Midrange 3081.5 Midmean - Weighted Average at Xnp 2899.58139534884 Midmean - Weighted Average at X(n+1)p 2908.57142857143 Midmean - Empirical Distribution Function 2899.58139534884 Midmean - Empirical Distribution Function - Averaging 2908.57142857143 Midmean - Empirical Distribution Function - Interpolation 2908.57142857143 Midmean - Closest Observation 2899.58139534884 Midmean - True Basic - Statistics Graphics Toolkit 2908.57142857143 Midmean - MS Excel (old versions) 2912.54545454545 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/16/t1268776427bq7agtfe3kbqyen/1vpxq1268776359.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/16/t1268776427bq7agtfe3kbqyen/1vpxq1268776359.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/16/t1268776427bq7agtfe3kbqyen/2qua41268776359.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/16/t1268776427bq7agtfe3kbqyen/2qua41268776359.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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