Centurmmaten - Wijn - Veronika Kaplova

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 14 Mar 2010 12:50:31 -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/14/t1268592767ums7q6wt37pjchw.htm/, Retrieved Sun, 14 Mar 2010 19:52:49 +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/14/t1268592767ums7q6wt37pjchw.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 «

2550 2867 3458 2961 3163 2880 3331 3062 3534 3622 4464 5411 2564 2820 3508 3088 3299 2939 3320 3418 3604 3495 4163 4882 2211 3260 2992 2425 2707 3244 3965 3315 3333 3583 4021 4904 2252 2952 3573 3048 3059 2731 3563 3092 3478 3478 4308 5029 2075 3264 3308 3688 3136 2824 3644 4694 2914 3686 4358 5587 2265 3685 3754 3708 3210 3517 3905 3670 4221 4404 5086 5725 2367 3819 4067 4022 3937 4365 4290

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 3545.83544303797 87.6437242772496 40.4573798327098 Geometric Mean 3464.43762502466 Harmonic Mean 3385.20721563031 Quadratic Mean 3629.33877403431 Winsorized Mean ( 1 / 26 ) 3545.81012658228 86.7466625962273 40.8754644900482 Winsorized Mean ( 2 / 26 ) 3542.39240506329 85.2449673139718 41.5554432910515 Winsorized Mean ( 3 / 26 ) 3530.54430379747 81.9069317666556 43.1043408371788 Winsorized Mean ( 4 / 26 ) 3532.82278481013 80.217490307383 44.0405548873794 Winsorized Mean ( 5 / 26 ) 3528.58227848101 77.6967252366166 45.414813400888 Winsorized Mean ( 6 / 26 ) 3536.40506329114 75.6578645591362 46.7420681762302 Winsorized Mean ( 7 / 26 ) 3520.98734177215 71.8005109329139 49.0384719554705 Winsorized Mean ( 8 / 26 ) 3512.17721518987 64.7585928815169 54.2349217132589 Winsorized Mean ( 9 / 26 ) 3508.07594936709 63.0578030168244 55.6327017677907 Winsorized Mean ( 10 / 26 ) 3514.40506329114 60.441839874883 58.1452363224894 Winsorized Mean ( 11 / 26 ) 3513.98734177215 60.184341652081 58.3870695485235 Winsorized Mean ( 12 / 26 ) 3512.92405063291 57.8851221402399 60.6878576177494 Winsorized Mean ( 13 / 26 ) 3512.10126582278 57.0605189436192 61.55046134952 Winsorized Mean ( 14 / 26 ) 3505.89873417722 54.1045113489432 64.7986396470004 Winsorized Mean ( 15 / 26 ) 3499.63291139241 51.5997635452691 67.8226540383685 Winsorized Mean ( 16 / 26 ) 3482.82278481013 48.1115183217779 72.3906230004305 Winsorized Mean ( 17 / 26 ) 3475.07594936709 46.3502946317267 74.9741933029354 Winsorized Mean ( 18 / 26 ) 3481.91139240506 45.3239598935573 76.8227533644961 Winsorized Mean ( 19 / 26 ) 3481.91139240506 41.4516967628091 83.999248868603 Winsorized Mean ( 20 / 26 ) 3477.60759493671 40.0269116615778 86.881736576117 Winsorized Mean ( 21 / 26 ) 3469.89873417722 38.6801504554005 89.7074776939692 Winsorized Mean ( 22 / 26 ) 3453.18987341772 34.3289406879959 100.591215581121 Winsorized Mean ( 23 / 26 ) 3435.43037974684 31.6520902077992 108.537235841074 Winsorized Mean ( 24 / 26 ) 3434.82278481013 28.0316089464692 122.533914887635 Winsorized Mean ( 25 / 26 ) 3437.03797468354 26.08617682919 131.757060346135 Winsorized Mean ( 26 / 26 ) 3451.84810126582 23.9601400618685 144.066273917960 Trimmed Mean ( 1 / 26 ) 3536.63636363636 83.1027390990154 42.5573982516091 Trimmed Mean ( 2 / 26 ) 3526.97333333333 78.7812434194505 44.7692011479797 Trimmed Mean ( 3 / 26 ) 3518.6301369863 74.6195232645302 47.1542832632764 Trimmed Mean ( 4 / 26 ) 3514.21126760563 71.2579831822399 49.3167377277316 Trimmed Mean ( 5 / 26 ) 3508.88405797101 67.8866418119296 51.6874007067824 Trimmed Mean ( 6 / 26 ) 3504.23880597015 64.6825987040006 54.1759124738662 Trimmed Mean ( 7 / 26 ) 3497.72307692308 61.412416166989 56.9546566513891 Trimmed Mean ( 8 / 26 ) 3493.55555555556 58.5394986490998 59.6786039541744 Trimmed Mean ( 9 / 26 ) 3490.54098360656 56.8392882179262 61.4107089135872 Trimmed Mean ( 10 / 26 ) 3487.93220338983 55.1621268295284 63.2305606012772 Trimmed Mean ( 11 / 26 ) 3484.26315789474 53.6760187739919 64.912846322779 Trimmed Mean ( 12 / 26 ) 3480.38181818182 51.8880139063365 67.0748705946673 Trimmed Mean ( 13 / 26 ) 3476.33962264151 50.1603809753363 69.3044900187424 Trimmed Mean ( 14 / 26 ) 3472.07843137255 48.1650824881266 72.0870442239659 Trimmed Mean ( 15 / 26 ) 3468.18367346939 46.3029589556888 74.9019879439754 Trimmed Mean ( 16 / 26 ) 3464.65957446808 44.489157974043 77.8764924364161 Trimmed Mean ( 17 / 26 ) 3462.66666666667 42.9552386240901 80.611044835978 Trimmed Mean ( 18 / 26 ) 3461.32558139535 41.3557710808856 83.6963134994032 Trimmed Mean ( 19 / 26 ) 3459.12195121951 39.471357245877 87.6362555681015 Trimmed Mean ( 20 / 26 ) 3456.69230769231 37.9104733061604 91.180404944472 Trimmed Mean ( 21 / 26 ) 3456.69230769231 36.1521765840406 95.6150537618878 Trimmed Mean ( 22 / 26 ) 3452.8 34.1005630944907 101.253459962889 Trimmed Mean ( 23 / 26 ) 3452.75757575758 32.5175951876218 106.181209152635 Trimmed Mean ( 24 / 26 ) 3454.67741935484 31.0324279609951 111.324754340751 Trimmed Mean ( 25 / 26 ) 3456.93103448276 29.9779447266765 115.315811874406 Trimmed Mean ( 26 / 26 ) 3459.25925925926 28.9854857377736 119.344533003674 Median 3478 Midrange 3900 Midmean - Weighted Average at Xnp 3446.475 Midmean - Weighted Average at X(n+1)p 3459.12195121951 Midmean - Empirical Distribution Function 3459.12195121951 Midmean - Empirical Distribution Function - Averaging 3459.12195121951 Midmean - Empirical Distribution Function - Interpolation 3456.69230769231 Midmean - Closest Observation 3446.475 Midmean - True Basic - Statistics Graphics Toolkit 3459.12195121951 Midmean - MS Excel (old versions) 3459.12195121951 Number of observations 79

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/14/t1268592767ums7q6wt37pjchw/1og2l1268592630.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t1268592767ums7q6wt37pjchw/1og2l1268592630.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t1268592767ums7q6wt37pjchw/2gr321268592630.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t1268592767ums7q6wt37pjchw/2gr321268592630.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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