Tijdreeks B - 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: Sat, 14 Aug 2010 10:38:32 +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/Aug/14/t1281782313pjppi6ctzps3p31.htm/, Retrieved Sat, 14 Aug 2010 12:38:33 +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/Aug/14/t1281782313pjppi6ctzps3p31.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:

Jacobs Jeff

Dataseries X:

» Textbox « » Textfile « » CSV «

335 334 333 331 329 328 329 331 332 332 333 335 335 333 325 322 322 315 321 324 329 332 322 324 324 323 309 306 305 300 301 302 308 311 301 301 308 302 290 286 286 275 284 289 292 293 285 280 281 280 265 260 254 238 247 246 247 237 222 216 212 209 185 186 178 158 166 162 164 147 132 124 117 120 89 81 71 52 63 62 74 67 53 42

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 249.452380952381 9.86180187344192 25.2948075973989 Geometric Mean 223.847125714072 Harmonic Mean 185.880989025274 Quadratic Mean 265.13895727838 Winsorized Mean ( 1 / 28 ) 249.571428571429 9.83230425852508 25.3828016311678 Winsorized Mean ( 2 / 28 ) 249.595238095238 9.82655258466873 25.4000816608516 Winsorized Mean ( 3 / 28 ) 249.880952380952 9.74675615399828 25.6373452287967 Winsorized Mean ( 4 / 28 ) 249.880952380952 9.7307912015065 25.6794074815074 Winsorized Mean ( 5 / 28 ) 250.119047619048 9.6760998856218 25.8491593282033 Winsorized Mean ( 6 / 28 ) 250.404761904762 9.6113983633512 26.0528959926965 Winsorized Mean ( 7 / 28 ) 250.571428571429 9.54683604751617 26.2465415059286 Winsorized Mean ( 8 / 28 ) 251.238095238095 9.39981169242329 26.7279923746351 Winsorized Mean ( 9 / 28 ) 252.095238095238 9.21488573240489 27.3573916612688 Winsorized Mean ( 10 / 28 ) 255.309523809524 8.51976164874845 29.9667448850554 Winsorized Mean ( 11 / 28 ) 255.702380952381 8.44330387409793 30.2846355840414 Winsorized Mean ( 12 / 28 ) 255.988095238095 8.3027636781522 30.8316730622719 Winsorized Mean ( 13 / 28 ) 257.22619047619 8.06839934812792 31.8806964526209 Winsorized Mean ( 14 / 28 ) 259.72619047619 7.61129605591183 34.1237797831365 Winsorized Mean ( 15 / 28 ) 261.511904761905 7.24722223177747 36.0844329590491 Winsorized Mean ( 16 / 28 ) 261.702380952381 7.05430903013799 37.0982302921966 Winsorized Mean ( 17 / 28 ) 261.904761904762 6.96375377386036 37.6097102812374 Winsorized Mean ( 18 / 28 ) 262.333333333333 6.89136532518288 38.0669607479229 Winsorized Mean ( 19 / 28 ) 265.047619047619 6.44157966522572 41.1463698071538 Winsorized Mean ( 20 / 28 ) 266.47619047619 6.14643631246784 43.3545841735401 Winsorized Mean ( 21 / 28 ) 266.47619047619 6.07892902890007 43.8360423701816 Winsorized Mean ( 22 / 28 ) 272.5 5.14821906052213 52.9309255873745 Winsorized Mean ( 23 / 28 ) 273.321428571429 5.02681166807219 54.3727210445202 Winsorized Mean ( 24 / 28 ) 274.178571428571 4.82645347042782 56.8074618575507 Winsorized Mean ( 25 / 28 ) 274.178571428571 4.36288395129053 62.8434252411114 Winsorized Mean ( 26 / 28 ) 277.583333333333 3.56909538436406 77.7741425878964 Winsorized Mean ( 27 / 28 ) 277.261904761905 3.4531998949555 80.2912988520978 Winsorized Mean ( 28 / 28 ) 279.595238095238 3.05651111518535 91.4752891642218 Trimmed Mean ( 1 / 28 ) 250.939024390244 9.72000900183621 25.816748147336 Trimmed Mean ( 2 / 28 ) 252.375 9.58571218869819 26.3282471903921 Trimmed Mean ( 3 / 28 ) 253.871794871795 9.42897382772956 26.924647316889 Trimmed Mean ( 4 / 28 ) 255.342105263158 9.27709029988029 27.5239430693536 Trimmed Mean ( 5 / 28 ) 256.891891891892 9.10023917501165 28.2291362843838 Trimmed Mean ( 6 / 28 ) 258.472222222222 8.90450933358587 29.0271156488456 Trimmed Mean ( 7 / 28 ) 260.085714285714 8.68650563029055 29.9413510282862 Trimmed Mean ( 8 / 28 ) 261.764705882353 8.43893308376195 31.018696710137 Trimmed Mean ( 9 / 28 ) 263.439393939394 8.17444219885457 32.2272012610607 Trimmed Mean ( 10 / 28 ) 265.09375 7.89563995711185 33.5747009032778 Trimmed Mean ( 11 / 28 ) 266.41935483871 7.71270039794079 34.542941005441 Trimmed Mean ( 12 / 28 ) 267.783333333333 7.50243243668634 35.6928683587862 Trimmed Mean ( 13 / 28 ) 269.206896551724 7.26966359915934 37.0315480048974 Trimmed Mean ( 14 / 28 ) 270.589285714286 7.02979636076611 38.4917673041665 Trimmed Mean ( 15 / 28 ) 271.796296296296 6.82830154923319 39.8043780487138 Trimmed Mean ( 16 / 28 ) 272.903846153846 6.64978592151275 41.0394935077494 Trimmed Mean ( 17 / 28 ) 274.08 6.45827044516232 42.4386067953076 Trimmed Mean ( 18 / 28 ) 275.333333333333 6.2278923421977 44.2097130465447 Trimmed Mean ( 19 / 28 ) 276.652173913043 5.94257685703293 46.5542441551481 Trimmed Mean ( 20 / 28 ) 277.818181818182 5.6812134984789 48.9012042748553 Trimmed Mean ( 21 / 28 ) 278.952380952381 5.40765066291851 51.5847635767637 Trimmed Mean ( 22 / 28 ) 280.2 5.05104711154795 55.4736461197111 Trimmed Mean ( 23 / 28 ) 280.973684210526 4.84180568372532 58.0307642570123 Trimmed Mean ( 24 / 28 ) 281.75 4.58593000036568 61.437919893573 Trimmed Mean ( 25 / 28 ) 282.529411764706 4.28637007719963 65.913443467599 Trimmed Mean ( 26 / 28 ) 283.40625 3.99996456007486 70.8521902490797 Trimmed Mean ( 27 / 28 ) 284.033333333333 3.85736594461186 73.6340127983148 Trimmed Mean ( 28 / 28 ) 284.785714285714 3.67076147357988 77.5821900538743 Median 287.5 Midrange 188.5 Midmean - Weighted Average at Xnp 276.767441860465 Midmean - Weighted Average at X(n+1)p 278.952380952381 Midmean - Empirical Distribution Function 276.767441860465 Midmean - Empirical Distribution Function - Averaging 278.952380952381 Midmean - Empirical Distribution Function - Interpolation 278.952380952381 Midmean - Closest Observation 276.767441860465 Midmean - True Basic - Statistics Graphics Toolkit 278.952380952381 Midmean - MS Excel (old versions) 277.818181818182 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/14/t1281782313pjppi6ctzps3p31/1w4jd1281782308.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/14/t1281782313pjppi6ctzps3p31/1w4jd1281782308.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/14/t1281782313pjppi6ctzps3p31/2ovjg1281782308.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/14/t1281782313pjppi6ctzps3p31/2ovjg1281782308.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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