opgave 5 oef 2 stap 2

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 26 Apr 2010 14:37:50 +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/Apr/26/t1272292970gfc13io38t3ey22.htm/, Retrieved Mon, 26 Apr 2010 16:42:50 +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/Apr/26/t1272292970gfc13io38t3ey22.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:

Dataseries X:

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14861 14583,3 15305,8 17903,9 16379,4 15420,3 17870,5 15912,8 13866,5 17823,2 17872 17420,4 16704,4 15991,2 16583,6 19123,5 17838,7 17209,4 18586,5 16258,1 15141,6 19202,1 17746,5 19090,1 18040,3 17515,5 17751,8 21072,4 17170 19439,5 19795,4 17574,9 16165,4 19464,6 19932,1 19961,2 17343,4 18924,2 18574,1 21350,6 18594,6 19823,1 20844,4 19640,2 17735,4 19813,6 22160 20664,3 17877,4 20906,5 21164,1 21374,4 22952,3 21343,5 23899,3 22392,9 18274,1 22786,7 22321,5 17842,2 16373,5 16087,1 16555,9 17880,2 16764,5 16049 18288,3 17570,4 15133,4 19334,2 19291,8 20176,7

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 18426.1902777778 260.363400825981 70.7710462350786 Geometric Mean 18297.0316446690 Harmonic Mean 18169.3031182171 Quadratic Mean 18556.3335356864 Winsorized Mean ( 1 / 24 ) 18422.9930555556 254.476708132031 72.3955964016835 Winsorized Mean ( 2 / 24 ) 18426.1069444444 251.749727590027 73.192162394119 Winsorized Mean ( 3 / 24 ) 18421.0486111111 245.676198144776 74.9810065045686 Winsorized Mean ( 4 / 24 ) 18417.5375 244.693012362534 75.2679339805291 Winsorized Mean ( 5 / 24 ) 18417.725 240.085299898815 76.7132556960473 Winsorized Mean ( 6 / 24 ) 18361.8 224.942203018349 81.6289684799709 Winsorized Mean ( 7 / 24 ) 18407.3680555556 216.191685343186 85.143737264157 Winsorized Mean ( 8 / 24 ) 18415.2902777778 214.639530351868 85.7963593546297 Winsorized Mean ( 9 / 24 ) 18400.0902777778 209.251866120241 87.932741623459 Winsorized Mean ( 10 / 24 ) 18392.6458333333 206.064964420376 89.2565404559119 Winsorized Mean ( 11 / 24 ) 18379.2625 199.605867766803 92.0777665788474 Winsorized Mean ( 12 / 24 ) 18384.3625 195.374124536715 94.0982463445162 Winsorized Mean ( 13 / 24 ) 18372.6805555556 186.504979046331 98.5104025077608 Winsorized Mean ( 14 / 24 ) 18279.0166666667 170.665902676730 107.104092733099 Winsorized Mean ( 15 / 24 ) 18270.8916666667 158.069709057609 115.587558018518 Winsorized Mean ( 16 / 24 ) 18270.5805555556 156.159549840578 116.999444313254 Winsorized Mean ( 17 / 24 ) 18273.3666666667 148.033120910631 123.441068824716 Winsorized Mean ( 18 / 24 ) 18286.0166666667 145.453976447795 125.716856377795 Winsorized Mean ( 19 / 24 ) 18388.2208333333 129.727290189022 141.745201079436 Winsorized Mean ( 20 / 24 ) 18356.0541666667 121.780384358986 150.730795138209 Winsorized Mean ( 21 / 24 ) 18343.9208333333 109.150169612143 168.061313129582 Winsorized Mean ( 22 / 24 ) 18359.7791666667 105.039197559826 174.789788890092 Winsorized Mean ( 23 / 24 ) 18356.5208333333 96.419468248614 190.381892441076 Winsorized Mean ( 24 / 24 ) 18360.6875 92.175288650395 199.19316520547 Trimmed Mean ( 1 / 24 ) 18413.1414285714 247.463428575562 74.4075257283889 Trimmed Mean ( 2 / 24 ) 18402.7102941176 239.118411328485 76.9606580767937 Trimmed Mean ( 3 / 24 ) 18389.9484848485 230.903458027092 79.6434520382574 Trimmed Mean ( 4 / 24 ) 18378.2859375 223.878350555733 82.090500898723 Trimmed Mean ( 5 / 24 ) 18366.8903225806 215.757386941021 85.1275155997387 Trimmed Mean ( 6 / 24 ) 18354.69 207.412047736692 88.4938469114444 Trimmed Mean ( 7 / 24 ) 18353.2189655172 201.747150160901 90.9713914217862 Trimmed Mean ( 8 / 24 ) 18343.2732142857 197.068652624776 93.0806242899108 Trimmed Mean ( 9 / 24 ) 18331.2703703704 191.607325598809 95.6710309122142 Trimmed Mean ( 10 / 24 ) 18320.6826923077 186.086700805297 98.452402095498 Trimmed Mean ( 11 / 24 ) 18310.32 179.872899616164 101.795879418595 Trimmed Mean ( 12 / 24 ) 18300.91875 173.515566157853 105.471336982822 Trimmed Mean ( 13 / 24 ) 18290.0347826087 166.340271303052 109.955542571447 Trimmed Mean ( 14 / 24 ) 18279.6318181818 159.213190068817 114.812295452913 Trimmed Mean ( 15 / 24 ) 18279.7071428571 153.832677151934 118.828505628899 Trimmed Mean ( 16 / 24 ) 18280.765 149.681889461258 122.130773908567 Trimmed Mean ( 17 / 24 ) 18281.9710526316 144.466326824530 126.548320667397 Trimmed Mean ( 18 / 24 ) 18282.9833333333 139.386708818445 131.167336457792 Trimmed Mean ( 19 / 24 ) 18282.6264705882 132.947932680726 137.517192647846 Trimmed Mean ( 20 / 24 ) 18270.121875 128.185602719824 142.528657566428 Trimmed Mean ( 21 / 24 ) 18259.81 123.617231562110 147.712497434676 Trimmed Mean ( 22 / 24 ) 18249.5107142857 120.626478699634 151.289425928846 Trimmed Mean ( 23 / 24 ) 18235.6307692308 116.960591360342 155.912607461507 Trimmed Mean ( 24 / 24 ) 18219.8625 113.893916413938 159.972218654607 Median 17892.05 Midrange 18882.9 Midmean - Weighted Average at Xnp 18240.3189189189 Midmean - Weighted Average at X(n+1)p 18282.9833333333 Midmean - Empirical Distribution Function 18240.3189189189 Midmean - Empirical Distribution Function - Averaging 18282.9833333333 Midmean - Empirical Distribution Function - Interpolation 18282.9833333333 Midmean - Closest Observation 18240.3189189189 Midmean - True Basic - Statistics Graphics Toolkit 18282.9833333333 Midmean - MS Excel (old versions) 18281.9710526316 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Apr/26/t1272292970gfc13io38t3ey22/10die1272292666.png (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/26/t1272292970gfc13io38t3ey22/10die1272292666.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/26/t1272292970gfc13io38t3ey22/20die1272292666.png (open in new window) http://www.freestatistics.org/blog/date/2010/Apr/26/t1272292970gfc13io38t3ey22/20die1272292666.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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