opgave5oef2stap1

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 02 Jun 2009 02:24:01 -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/Jun/02/t1243931166riq0nar4y10ayi8.htm/, Retrieved Tue, 02 Jun 2009 10:26:08 +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/Jun/02/t1243931166riq0nar4y10ayi8.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 «

0,8832 0,8707 0,8766 0,8860 0,9170 0,9561 0,9935 0,9781 0,9806 0,9812 1,0013 1,0194 1,0622 1,0785 1,0797 1,0862 1,1556 1,1674 1,1365 1,1155 1,1267 1,1714 1,1710 1,2298 1,2638 1,2640 1,2261 1,1989 1,2000 1,2146 1,2266 1,2191 1,2224 1,2507 1,2997 1,3406 1,3123 1,3013 1,3185 1,2943 1,2697 1,2155 1,2041 1,2295 1,2234 1,2022 1,0000 1,1861 1,2126 1,1940 1,2028 1,2273 1,2767 1,2661 1,2681 1,2810 1,2722 1,2617 1,2888 1,3205 1,2993 1,3080 1,3246 1,3513 1,3518 1,3421 1,3726 1,3626 1,3910 1,4233 1,4683 1,4559 1,4728 1,4759 1,5520 1,5754 1,5554 1,5562 1,5759 1,4955 1,4342 1,3266 1,2744 1,3511 1,3244 1,2797 1,3050 1,3203

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1.23869318181818 0.0176290019723732 70.2645097980795 Geometric Mean 1.22727699277978 Harmonic Mean 1.21529655188421 Quadratic Mean 1.24955944536465 Winsorized Mean ( 1 / 29 ) 1.23875454545455 0.0176117864872785 70.3366774488965 Winsorized Mean ( 2 / 29 ) 1.23846818181818 0.0174830187460893 70.8383489032871 Winsorized Mean ( 3 / 29 ) 1.23853636363636 0.0174550973549981 70.9555689348087 Winsorized Mean ( 4 / 29 ) 1.23979090909091 0.0171062867411956 72.4757469489404 Winsorized Mean ( 5 / 29 ) 1.23880227272727 0.0160053513596370 77.3992550923521 Winsorized Mean ( 6 / 29 ) 1.23896590909091 0.0154666407026469 80.1056889411594 Winsorized Mean ( 7 / 29 ) 1.23891818181818 0.0153849198568164 80.5280881115066 Winsorized Mean ( 8 / 29 ) 1.23856363636364 0.0153033468469284 80.9341674571163 Winsorized Mean ( 9 / 29 ) 1.23855340909091 0.0148462389951498 83.4253988161944 Winsorized Mean ( 10 / 29 ) 1.23682613636364 0.0143026177075087 86.4755083060295 Winsorized Mean ( 11 / 29 ) 1.23562613636364 0.0140589703042013 87.888807617325 Winsorized Mean ( 12 / 29 ) 1.23368977272727 0.0129407093836292 95.3340142456154 Winsorized Mean ( 13 / 29 ) 1.23729431818182 0.0114026805724391 108.509074714627 Winsorized Mean ( 14 / 29 ) 1.23829659090909 0.0107374039164674 115.325510760564 Winsorized Mean ( 15 / 29 ) 1.23666022727273 0.0104632943713137 118.190331208035 Winsorized Mean ( 16 / 29 ) 1.23775113636364 0.0102494248882057 120.762984251726 Winsorized Mean ( 17 / 29 ) 1.24337272727273 0.00931520814237783 133.477718186052 Winsorized Mean ( 18 / 29 ) 1.24382272727273 0.0087156629936688 142.711200304126 Winsorized Mean ( 19 / 29 ) 1.24561477272727 0.00835111204962824 149.1555574066 Winsorized Mean ( 20 / 29 ) 1.24677386363636 0.00730440000202248 170.688059702529 Winsorized Mean ( 21 / 29 ) 1.2491125 0.00684882851046648 182.383381054306 Winsorized Mean ( 22 / 29 ) 1.2499625 0.00671998013391864 186.006874289836 Winsorized Mean ( 23 / 29 ) 1.24904772727273 0.00657728290488164 189.903299787468 Winsorized Mean ( 24 / 29 ) 1.25300227272727 0.00604256388551539 207.36268518912 Winsorized Mean ( 25 / 29 ) 1.25473522727273 0.00569645438675573 220.266000933842 Winsorized Mean ( 26 / 29 ) 1.25435113636364 0.00528710330168328 237.24732897961 Winsorized Mean ( 27 / 29 ) 1.25336931818182 0.00508174102490342 246.64171433365 Winsorized Mean ( 28 / 29 ) 1.25311477272727 0.00488020026198797 256.77527672129 Winsorized Mean ( 29 / 29 ) 1.25209318181818 0.00470869290906146 265.910987613705 Trimmed Mean ( 1 / 29 ) 1.23905116279070 0.0170707321264476 72.583363947879 Trimmed Mean ( 2 / 29 ) 1.23936190476190 0.0164458849293515 75.3600010024376 Trimmed Mean ( 3 / 29 ) 1.23984146341463 0.0158015789551017 78.4631375723587 Trimmed Mean ( 4 / 29 ) 1.24032 0.0150612725772283 82.3516069867353 Trimmed Mean ( 5 / 29 ) 1.24046923076923 0.0143220593133808 86.6124908175939 Trimmed Mean ( 6 / 29 ) 1.24085526315789 0.0138033885230539 89.8949747799585 Trimmed Mean ( 7 / 29 ) 1.24122972972973 0.0133429711336555 93.0249880102735 Trimmed Mean ( 8 / 29 ) 1.24163333333333 0.0128200806517987 96.8506647545256 Trimmed Mean ( 9 / 29 ) 1.24211571428571 0.0122174946071200 101.666974631758 Trimmed Mean ( 10 / 29 ) 1.24262794117647 0.0116035355041734 107.090458828651 Trimmed Mean ( 11 / 29 ) 1.24340151515152 0.0109865508993488 113.174874129533 Trimmed Mean ( 12 / 29 ) 1.2443734375 0.0102883089862506 120.950239651919 Trimmed Mean ( 13 / 29 ) 1.24563709677419 0.00968260152321586 128.646944087035 Trimmed Mean ( 14 / 29 ) 1.24657833333333 0.00927835525425199 134.353373973481 Trimmed Mean ( 15 / 29 ) 1.24657833333333 0.00891909264520227 139.765151335645 Trimmed Mean ( 16 / 29 ) 1.24860892857143 0.00852591247993384 146.448715197358 Trimmed Mean ( 17 / 29 ) 1.24971481481481 0.00808110287470777 154.646566711355 Trimmed Mean ( 18 / 29 ) 1.25034615384615 0.00773299207141775 161.689827468932 Trimmed Mean ( 19 / 29 ) 1.250984 0.00741922233671647 168.613898226111 Trimmed Mean ( 20 / 29 ) 1.25150208333333 0.00709951457334635 176.279951312705 Trimmed Mean ( 21 / 29 ) 1.25195434782609 0.00691085731695298 181.157603233238 Trimmed Mean ( 22 / 29 ) 1.252225 0.00675895156577549 185.269118710769 Trimmed Mean ( 23 / 29 ) 1.25244047619048 0.00658299825036221 190.253806633104 Trimmed Mean ( 24 / 29 ) 1.252765 0.00637606155063107 196.479439549326 Trimmed Mean ( 25 / 29 ) 1.25274210526316 0.00622110805009578 201.369610554163 Trimmed Mean ( 26 / 29 ) 1.25254722222222 0.0060840129902274 205.875172231578 Trimmed Mean ( 27 / 29 ) 1.25236764705882 0.00598495249258264 209.252729843875 Trimmed Mean ( 28 / 29 ) 1.252265625 0.0058846430972966 212.802306664153 Trimmed Mean ( 29 / 29 ) 1.25217666666667 0.00577989715402542 216.643416534598 Median 1.26275 Midrange 1.2233 Midmean - Weighted Average at Xnp 1.25034 Midmean - Weighted Average at X(n+1)p 1.252225 Midmean - Empirical Distribution Function 1.25034 Midmean - Empirical Distribution Function - Averaging 1.252225 Midmean - Empirical Distribution Function - Interpolation 1.252225 Midmean - Closest Observation 1.25034 Midmean - True Basic - Statistics Graphics Toolkit 1.252225 Midmean - MS Excel (old versions) 1.25195434782609 Number of observations 88

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243931166riq0nar4y10ayi8/1iigo1243931039.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243931166riq0nar4y10ayi8/1iigo1243931039.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243931166riq0nar4y10ayi8/2ys3c1243931039.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243931166riq0nar4y10ayi8/2ys3c1243931039.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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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