Anke Winckelmans Opgave 5

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 22 Apr 2009 14:19:58 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Apr/22/t1240431641dnaorjwz14aqcgj.htm/, Retrieved Wed, 22 Apr 2009 22:20:42 +0200

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/2009/Apr/22/t1240431641dnaorjwz14aqcgj.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

» Textbox « » Textfile « » CSV «

3779,7 3795,5 3813,1 3826,9 3833,3 3844,8 3851,3 3851,8 3854,1 3858,4 3861,6 3856,3 3855,8 3860,4 3855,1 3839,5 3833 3833,6 3826,8 3818,2 3811,4 3806,8 3810,3 3818,2 3858,9 3867,8 3872,3 3873,3 3876,7 3882,6 3883,5 3882,2 3888,1 3893,7 3901,9 3914,3 3930,3 3948,3 3971,5 3990,1 3993 3998 4015,8 4041,2 4060,7 4076,7 4103 4125,3 4139,7 4146,7 4158 4155,1 4144,8 4148,2 4142,5 4142,1 4145,4 4146,3 4143,5 4149,2 4158,9 4166,1 4179,1 4194,4 4211,7 4226,3 4235,8 4243,6 4258,7 4278,2 4298 4315,1 4334,3 4356 4374 4395,5

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 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 4010.95131578947 20.2782208373366 197.796017114304 Geometric Mean 4007.15380695152 Harmonic Mean 4003.40575394724 Quadratic Mean 4014.79400787362 Winsorized Mean ( 1 / 25 ) 4010.87631578947 20.1779100050005 198.775607324817 Winsorized Mean ( 2 / 25 ) 4010.7 20.0252691245030 200.281952520303 Winsorized Mean ( 3 / 25 ) 4009.98157894737 19.8146465153472 202.374621007823 Winsorized Mean ( 4 / 25 ) 4009.02894736842 19.5913208330941 204.632907680032 Winsorized Mean ( 5 / 25 ) 4008.01578947368 19.3466702382472 207.16824859867 Winsorized Mean ( 6 / 25 ) 4006.85526315789 18.9877645178426 211.023012182013 Winsorized Mean ( 7 / 25 ) 4005.05921052632 18.6537711889751 214.705067943228 Winsorized Mean ( 8 / 25 ) 4004.375 18.2515505830110 219.399167308413 Winsorized Mean ( 9 / 25 ) 4003.46315789474 18.0902052437714 221.305568618309 Winsorized Mean ( 10 / 25 ) 4003.01578947368 17.7750622722162 225.204037441304 Winsorized Mean ( 11 / 25 ) 4000.94605263158 17.4220588588135 229.648291574194 Winsorized Mean ( 12 / 25 ) 3998.26184210526 16.9852529397839 235.39607306879 Winsorized Mean ( 13 / 25 ) 3996.65394736842 16.4607965359900 242.798332306101 Winsorized Mean ( 14 / 25 ) 3995.23552631579 15.9897661025373 249.862036798763 Winsorized Mean ( 15 / 25 ) 3995.09736842105 15.6300552775043 255.603534183980 Winsorized Mean ( 16 / 25 ) 3995.01315789474 15.5907098228181 256.243186057363 Winsorized Mean ( 17 / 25 ) 3994.87894736842 15.4378328080656 258.772004920358 Winsorized Mean ( 18 / 25 ) 3993.71842105263 15.2171723991814 262.448128751402 Winsorized Mean ( 19 / 25 ) 3993.64342105263 15.1619193266721 263.399595724481 Winsorized Mean ( 20 / 25 ) 3993.38026315790 15.0924177570548 264.595131637622 Winsorized Mean ( 21 / 25 ) 3993.85 15.0073962466933 266.125444703974 Winsorized Mean ( 22 / 25 ) 3993.73421052632 14.9547296458733 267.054925438145 Winsorized Mean ( 23 / 25 ) 3994.00657894737 14.8757149715275 268.491738823445 Winsorized Mean ( 24 / 25 ) 3993.975 14.7749497728241 270.320715901601 Winsorized Mean ( 25 / 25 ) 3995.68552631579 14.4886902903485 275.779621638919 Trimmed Mean ( 1 / 25 ) 4008.87972972973 19.9137493203705 201.312151982796 Trimmed Mean ( 2 / 25 ) 4006.77222222222 19.5960757886732 204.468091746113 Trimmed Mean ( 3 / 25 ) 4004.64 19.3088253028394 207.399463053359 Trimmed Mean ( 4 / 25 ) 4002.65 19.053891790438 210.069944976212 Trimmed Mean ( 5 / 25 ) 4000.81363636364 18.8209281775784 212.572599959754 Trimmed Mean ( 6 / 25 ) 3999.103125 18.6065403312641 214.929968376787 Trimmed Mean ( 7 / 25 ) 3997.51935483871 18.4336057353318 216.860413108253 Trimmed Mean ( 8 / 25 ) 3996.155 18.2932245530421 218.450005269052 Trimmed Mean ( 9 / 25 ) 3994.80862068966 18.1961619648473 219.541276254143 Trimmed Mean ( 10 / 25 ) 3993.50357142857 18.0929427592685 220.721616409404 Trimmed Mean ( 11 / 25 ) 3992.16481481481 18.0088469518551 221.677980022123 Trimmed Mean ( 12 / 25 ) 3990.99807692308 17.9522496962986 222.311863105710 Trimmed Mean ( 13 / 25 ) 3990.078 17.9398815298798 222.413843333041 Trimmed Mean ( 14 / 25 ) 3989.27708333333 17.9892669536093 221.758735006872 Trimmed Mean ( 15 / 25 ) 3988.57391304348 18.0967588404471 220.402667030564 Trimmed Mean ( 16 / 25 ) 3987.82272727273 18.2481995009883 218.532394226442 Trimmed Mean ( 17 / 25 ) 3987.00952380952 18.3927290870531 216.770959053381 Trimmed Mean ( 18 / 25 ) 3986.13 18.5463619350438 214.927866390233 Trimmed Mean ( 19 / 25 ) 3985.28684210526 18.7216198384344 212.870834708635 Trimmed Mean ( 20 / 25 ) 3984.35833333333 18.8869461827769 210.958314529783 Trimmed Mean ( 21 / 25 ) 3983.35 19.0382569389303 209.228713152551 Trimmed Mean ( 22 / 25 ) 3982.1625 19.1677767180890 207.752967835959 Trimmed Mean ( 23 / 25 ) 3980.83 19.2554229710257 206.738122864925 Trimmed Mean ( 24 / 25 ) 3979.275 19.2832476744198 206.359170777997 Trimmed Mean ( 25 / 25 ) 3977.48461538462 19.2239111463644 206.9029858233 Median 3959.9 Midrange 4087.6 Midmean - Weighted Average at Xnp 3981.94871794872 Midmean - Weighted Average at X(n+1)p 3985.28684210526 Midmean - Empirical Distribution Function 3981.94871794872 Midmean - Empirical Distribution Function - Averaging 3985.28684210526 Midmean - Empirical Distribution Function - Interpolation 3985.28684210526 Midmean - Closest Observation 3981.94871794872 Midmean - True Basic - Statistics Graphics Toolkit 3985.28684210526 Midmean - MS Excel (old versions) 3986.13 Number of observations 76

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240431641dnaorjwz14aqcgj/1lfdn1240431593.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240431641dnaorjwz14aqcgj/1lfdn1240431593.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240431641dnaorjwz14aqcgj/29ojl1240431593.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240431641dnaorjwz14aqcgj/29ojl1240431593.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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