Tijdreeks 2 - Stap 9

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 28 Jul 2010 19:16:26 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jul/28/t1280344613vjgym85q5hdsdlx.htm/, Retrieved Wed, 28 Jul 2010 21:16:56 +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/2010/Jul/28/t1280344613vjgym85q5hdsdlx.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:

Patrick Fieremans

Dataseries X:

» Textbox « » Textfile « » CSV «

259 258 257 255 253 252 253 255 256 256 257 259 267 263 266 257 249 249 251 252 252 252 256 257 259 260 261 253 243 233 241 239 233 228 228 227 225 230 222 207 190 184 192 187 173 167 163 156 153 157 152 128 115 114 136 132 126 124 123 119 105 107 108 92 74 73 100 97 99 102 99 103 92 99 97 87 69 66 95 91 93 99 91 91

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 180.357142857143 7.67850571693987 23.4885731033903 Geometric Mean 165.034136285773 Harmonic Mean 149.346915139109 Quadratic Mean 193.448528899378 Winsorized Mean ( 1 / 28 ) 180.380952380952 7.67056770644507 23.5159846421002 Winsorized Mean ( 2 / 28 ) 180.404761904762 7.64472375030513 23.5985979084674 Winsorized Mean ( 3 / 28 ) 180.369047619048 7.62950495687297 23.6409896367606 Winsorized Mean ( 4 / 28 ) 180.940476190476 7.52487462685449 24.045646627087 Winsorized Mean ( 5 / 28 ) 181.119047619048 7.48219160864484 24.2066839627289 Winsorized Mean ( 6 / 28 ) 181.119047619048 7.48219160864484 24.2066839627289 Winsorized Mean ( 7 / 28 ) 181.119047619048 7.48219160864484 24.2066839627289 Winsorized Mean ( 8 / 28 ) 181.119047619048 7.45653699740447 24.2899683434942 Winsorized Mean ( 9 / 28 ) 181.011904761905 7.44329286903698 24.3187938385292 Winsorized Mean ( 10 / 28 ) 181.130952380952 7.42620570679459 24.3907803705501 Winsorized Mean ( 11 / 28 ) 181.392857142857 7.38903410286912 24.5489267768332 Winsorized Mean ( 12 / 28 ) 181.678571428571 7.349077412607 24.7212760498223 Winsorized Mean ( 13 / 28 ) 181.523809523810 7.33004952145216 24.7643360379164 Winsorized Mean ( 14 / 28 ) 181.857142857143 7.28405198545264 24.966480637472 Winsorized Mean ( 15 / 28 ) 181.857142857143 7.28405198545264 24.966480637472 Winsorized Mean ( 16 / 28 ) 181.666666666667 7.26078309293051 25.0202580550226 Winsorized Mean ( 17 / 28 ) 181.666666666667 7.26078309293051 25.0202580550226 Winsorized Mean ( 18 / 28 ) 181.452380952381 7.17963518814536 25.2732034702802 Winsorized Mean ( 19 / 28 ) 181.904761904762 7.11812509253225 25.5551510461092 Winsorized Mean ( 20 / 28 ) 182.142857142857 7.08600438027008 25.7045927956249 Winsorized Mean ( 21 / 28 ) 182.392857142857 6.98894746357671 26.0973284022248 Winsorized Mean ( 22 / 28 ) 182.916666666667 6.9193826794559 26.4354025699082 Winsorized Mean ( 23 / 28 ) 183.190476190476 6.883267233762 26.6138840712065 Winsorized Mean ( 24 / 28 ) 184.904761904762 6.6604737238381 27.7615030959405 Winsorized Mean ( 25 / 28 ) 184.904761904762 6.58630463853815 28.0741283697746 Winsorized Mean ( 26 / 28 ) 185.523809523810 6.35436334361818 29.1962859993102 Winsorized Mean ( 27 / 28 ) 186.809523809524 6.19346434787218 30.1623636331585 Winsorized Mean ( 28 / 28 ) 185.142857142857 5.91307619817296 31.3107511112512 Trimmed Mean ( 1 / 28 ) 180.695121951220 7.66734785521753 23.5668350208291 Trimmed Mean ( 2 / 28 ) 181.025 7.65876214921366 23.6363261416319 Trimmed Mean ( 3 / 28 ) 181.358974358974 7.65898153291523 23.6792546867447 Trimmed Mean ( 4 / 28 ) 181.723684210526 7.65979704472577 23.7243471529907 Trimmed Mean ( 5 / 28 ) 181.945945945946 7.6885142484325 23.6646431373969 Trimmed Mean ( 6 / 28 ) 182.138888888889 7.72571933626487 23.5756543774404 Trimmed Mean ( 7 / 28 ) 182.342857142857 7.76067716289109 23.4957405540277 Trimmed Mean ( 8 / 28 ) 182.558823529412 7.7928453249461 23.4264656767937 Trimmed Mean ( 9 / 28 ) 182.787878787879 7.82654365722328 23.3548660549769 Trimmed Mean ( 10 / 28 ) 183.046875 7.85895094551669 23.2915151486501 Trimmed Mean ( 11 / 28 ) 183.306451612903 7.8901631220718 23.2322765419292 Trimmed Mean ( 12 / 28 ) 183.55 7.9229133844297 23.1669830394356 Trimmed Mean ( 13 / 28 ) 183.775862068966 7.95719959979204 23.0955450801773 Trimmed Mean ( 14 / 28 ) 184.035714285714 7.98895196081952 23.0362774977602 Trimmed Mean ( 15 / 28 ) 184.277777777778 8.02169562782081 22.9724220822673 Trimmed Mean ( 16 / 28 ) 184.538461538462 8.04734583051353 22.931593276225 Trimmed Mean ( 17 / 28 ) 184.84 8.06748879826951 22.9117144903441 Trimmed Mean ( 18 / 28 ) 185.166666666667 8.07655817549623 22.9264326020025 Trimmed Mean ( 19 / 28 ) 185.543478260870 8.0846790466106 22.9500116443901 Trimmed Mean ( 20 / 28 ) 185.909090909091 8.08790356795527 22.9860667040682 Trimmed Mean ( 21 / 28 ) 186.285714285714 8.07854054406183 23.0593277671478 Trimmed Mean ( 22 / 28 ) 186.675 8.06427604171156 23.1483891467064 Trimmed Mean ( 23 / 28 ) 187.052631578947 8.03751404994213 23.2724484730816 Trimmed Mean ( 24 / 28 ) 187.444444444444 7.98594444270528 23.4717941990774 Trimmed Mean ( 25 / 28 ) 187.705882352941 7.94326241831924 23.6308298111922 Trimmed Mean ( 26 / 28 ) 188 7.87362379167961 23.8771885695971 Trimmed Mean ( 27 / 28 ) 188.266666666667 7.80611804466235 24.1178349583631 Trimmed Mean ( 28 / 28 ) 188.428571428571 7.72072531536472 24.4055530707182 Median 188.5 Midrange 166.5 Midmean - Weighted Average at Xnp 184.348837209302 Midmean - Weighted Average at X(n+1)p 186.285714285714 Midmean - Empirical Distribution Function 184.348837209302 Midmean - Empirical Distribution Function - Averaging 186.285714285714 Midmean - Empirical Distribution Function - Interpolation 186.285714285714 Midmean - Closest Observation 184.348837209302 Midmean - True Basic - Statistics Graphics Toolkit 186.285714285714 Midmean - MS Excel (old versions) 188.826086956522 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/28/t1280344613vjgym85q5hdsdlx/1g3e71280344584.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/28/t1280344613vjgym85q5hdsdlx/1g3e71280344584.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/28/t1280344613vjgym85q5hdsdlx/28dvs1280344584.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/28/t1280344613vjgym85q5hdsdlx/28dvs1280344584.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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