IKO - Opgave 5 - Oefening 2 Stap 1

*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 12:01:34 -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/t12687630937l46pbx148sa2cw.htm/, Retrieved Tue, 16 Mar 2010 19:11:35 +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/t12687630937l46pbx148sa2cw.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 «

5714837 6015267 3415340 115612 615159 9714993 2414534 6614721 8414518 9513816 7713310 9212714 411919 3611400 710617 2410172 529569 269509 508895 308560 198397 977631 717793 57435 667628 57696 577284 677273 447200 327096 207113 616966 276765 866845 6725 576898 187085 966784 586883 476728 406853 217097 827154 526998 456977 427122 867075 157185 87059 657279 87566 67453 297553 227345 97406 187524 337651 397672 797737 717980 717784 897934 297932 108061 187927 887990 998136 288286 768212 988170 508491 438167

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1425603.65277778 286767.304359739 4.97129076817422 Geometric Mean 551536.487744222 Harmonic Mean 191008.242936065 Quadratic Mean 2805541.89794872 Winsorized Mean ( 1 / 24 ) 1423513.83333333 285592.815621349 4.98441751847387 Winsorized Mean ( 2 / 24 ) 1415157.13888889 282296.574740795 5.01301562085296 Winsorized Mean ( 3 / 24 ) 1382305.51388889 269683.929145989 5.12565030577183 Winsorized Mean ( 4 / 24 ) 1344438.73611111 255611.241606273 5.25970112919368 Winsorized Mean ( 5 / 24 ) 1268183.04166667 229668.150113724 5.52180631506242 Winsorized Mean ( 6 / 24 ) 1219048.54166667 213505.464628689 5.70968309306152 Winsorized Mean ( 7 / 24 ) 1190875.97222222 204250.385417942 5.83047111409568 Winsorized Mean ( 8 / 24 ) 957999.75 134422.069411767 7.12680405972188 Winsorized Mean ( 9 / 24 ) 938688.875 127199.316534300 7.37966917256885 Winsorized Mean ( 10 / 24 ) 803840.819444444 89976.94294817 8.9338534196198 Winsorized Mean ( 11 / 24 ) 803241.472222222 89802.4772438131 8.94453579539267 Winsorized Mean ( 12 / 24 ) 567969.305555556 36211.9047384562 15.6846017810376 Winsorized Mean ( 13 / 24 ) 568060.305555556 35634.1321761185 15.9414659727917 Winsorized Mean ( 14 / 24 ) 567705.833333333 35048.5813493404 16.1976836572878 Winsorized Mean ( 15 / 24 ) 567526.041666667 34377.5856582499 16.5086067214982 Winsorized Mean ( 16 / 24 ) 554503.375 31623.4175930535 17.5345809278313 Winsorized Mean ( 17 / 24 ) 562110.875 29849.7314322301 18.8313545224418 Winsorized Mean ( 18 / 24 ) 558696.125 28803.0905392369 19.3970894977023 Winsorized Mean ( 19 / 24 ) 561675.694444444 28378.0610925261 19.7926029059249 Winsorized Mean ( 20 / 24 ) 553224.583333333 26385.7363217794 20.9668048140347 Winsorized Mean ( 21 / 24 ) 544755.166666667 25134.6457458693 21.6734770075760 Winsorized Mean ( 22 / 24 ) 538981.083333333 23423.2819303110 23.0104852486902 Winsorized Mean ( 23 / 24 ) 528855.972222222 20446.4455821745 25.8654234104770 Winsorized Mean ( 24 / 24 ) 532311.972222222 19952.0429673063 26.6795722670844 Trimmed Mean ( 1 / 24 ) 1327453.5 268800.831668514 4.93842780083739 Trimmed Mean ( 2 / 24 ) 1225742.55882353 247752.553318438 4.94744672620216 Trimmed Mean ( 3 / 24 ) 1122425.51515152 223237.866471818 5.02793514779095 Trimmed Mean ( 4 / 24 ) 1024970.515625 198517.167844886 5.16313287536861 Trimmed Mean ( 5 / 24 ) 932221.677419355 172662.637440683 5.3990932331241 Trimmed Mean ( 6 / 24 ) 851590.95 149723.025476646 5.6877754593119 Trimmed Mean ( 7 / 24 ) 775565.24137931 125159.963772455 6.19659208905903 Trimmed Mean ( 8 / 24 ) 699283.678571429 92968.2254986243 7.52174923013644 Trimmed Mean ( 9 / 24 ) 656164.333333333 78639.7837797595 8.343923416308 Trimmed Mean ( 10 / 24 ) 612699.019230769 60599.5502125566 10.1106199151923 Trimmed Mean ( 11 / 24 ) 585174.6 50601.7579544104 11.5643136455301 Trimmed Mean ( 12 / 24 ) 555438.208333333 34863.7941249289 15.9316626969230 Trimmed Mean ( 13 / 24 ) 553803.717391304 34127.9455866292 16.2272796639794 Trimmed Mean ( 14 / 24 ) 552009.181818182 33282.6466986904 16.5854953428299 Trimmed Mean ( 15 / 24 ) 550087.142857143 32291.2427285871 17.035180326775 Trimmed Mean ( 16 / 24 ) 547994.475 31120.9125246869 17.6085606283331 Trimmed Mean ( 17 / 24 ) 547223.684210526 30238.2800363907 18.0970506110785 Trimmed Mean ( 18 / 24 ) 545472.25 29442.2164003608 18.5268745593934 Trimmed Mean ( 19 / 24 ) 543916.5 28580.6449953429 19.0309385980837 Trimmed Mean ( 20 / 24 ) 541813.4375 27436.474768594 19.7479246903907 Trimmed Mean ( 21 / 24 ) 540444.1 26383.5418930343 20.4841375047786 Trimmed Mean ( 22 / 24 ) 539916.214285714 25212.8467937555 21.4143297146213 Trimmed Mean ( 23 / 24 ) 540033.923076923 24017.1360151886 22.4853589010530 Trimmed Mean ( 24 / 24 ) 541491.916666667 23229.9645353779 23.3100621329837 Median 528283.5 Midrange 4860859 Midmean - Weighted Average at Xnp 538013.783783784 Midmean - Weighted Average at X(n+1)p 545472.25 Midmean - Empirical Distribution Function 538013.783783784 Midmean - Empirical Distribution Function - Averaging 545472.25 Midmean - Empirical Distribution Function - Interpolation 545472.25 Midmean - Closest Observation 538013.783783784 Midmean - True Basic - Statistics Graphics Toolkit 545472.25 Midmean - MS Excel (old versions) 547223.684210526 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/16/t12687630937l46pbx148sa2cw/172b81268762492.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/16/t12687630937l46pbx148sa2cw/172b81268762492.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/16/t12687630937l46pbx148sa2cw/2h24w1268762492.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/16/t12687630937l46pbx148sa2cw/2h24w1268762492.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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