Opgave5, oef2, stap1

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

Title produced by software: Central Tendency

Date of computation: Sun, 20 Apr 2008 12:27:49 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/20/t1208716120ons2oh356g1t5np.htm/, Retrieved Sun, 20 Apr 2008 20:28:42 +0200

User-defined keywords:

Dataseries X:

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3,35 3,35 3,35 3,4 3,42 3,42 3,42 3,42 3,42 3,42 3,42 3,42 3,42 3,42 3,42 3,43 3,47 3,51 3,52 3,52 3,52 3,52 3,52 3,52 3,52 3,52 3,52 3,58 3,6 3,61 3,61 3,61 3,63 3,68 3,69 3,69 3,69 3,69 3,69 3,69 3,69 3,69 3,78 3,79 3,79 3,8 3,8 3,8 3,8 3,81 3,95 3,99 4 4,06 4,16 4,19 4,2 4,2 4,2 4,2 4,2 4,23 4,38 4,43 4,44 4,44 4,44 4,44 4,44 4,45 4,45 4,45 4,45 4,45 4,45 4,45 4,45 4,46 4,46 4,46 4,48 4,58 4,67 4,68 4,68

Text written by user:

Output produced by software:

Summary of compuational 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 3.89447058823529 0.046211820756782 84.2743377010036 Geometric Mean 3.87193625501677 Harmonic Mean 3.8500168431397 Quadratic Mean 3.91743358365562 Winsorized Mean ( 1 / 28 ) 3.89447058823529 0.046211820756782 84.2743377010036 Winsorized Mean ( 2 / 28 ) 3.89423529411765 0.0461644777375244 84.355666628765 Winsorized Mean ( 3 / 28 ) 3.89282352941176 0.045321636661882 85.8932690020403 Winsorized Mean ( 4 / 28 ) 3.88905882352941 0.0444034922824127 87.584525982651 Winsorized Mean ( 5 / 28 ) 3.88788235294118 0.0442196877828096 87.9219765647597 Winsorized Mean ( 6 / 28 ) 3.88788235294118 0.0442196877828096 87.9219765647597 Winsorized Mean ( 7 / 28 ) 3.88788235294118 0.0442196877828096 87.9219765647597 Winsorized Mean ( 8 / 28 ) 3.88694117647059 0.0440756363937373 88.187976272145 Winsorized Mean ( 9 / 28 ) 3.88694117647059 0.0440756363937373 88.187976272145 Winsorized Mean ( 10 / 28 ) 3.88694117647059 0.0440756363937373 88.1879762721449 Winsorized Mean ( 11 / 28 ) 3.88694117647059 0.0440756363937373 88.1879762721449 Winsorized Mean ( 12 / 28 ) 3.88694117647059 0.0440756363937373 88.1879762721449 Winsorized Mean ( 13 / 28 ) 3.88694117647059 0.0440756363937373 88.187976272145 Winsorized Mean ( 14 / 28 ) 3.88694117647059 0.0440756363937373 88.187976272145 Winsorized Mean ( 15 / 28 ) 3.88870588235294 0.0438544793234503 88.6729461241952 Winsorized Mean ( 16 / 28 ) 3.89435294117647 0.0426527398901303 91.3036993920667 Winsorized Mean ( 17 / 28 ) 3.90235294117647 0.0417309801889444 93.512132317714 Winsorized Mean ( 18 / 28 ) 3.90447058823529 0.0414956735223603 94.0934381058145 Winsorized Mean ( 19 / 28 ) 3.90447058823529 0.0414956735223603 94.0934381058145 Winsorized Mean ( 20 / 28 ) 3.90447058823529 0.0414956735223603 94.0934381058145 Winsorized Mean ( 21 / 28 ) 3.902 0.0411170359371600 94.8998367966872 Winsorized Mean ( 22 / 28 ) 3.88905882352941 0.0391615999569477 99.3079656552554 Winsorized Mean ( 23 / 28 ) 3.84847058823529 0.0333475484601373 115.404902787251 Winsorized Mean ( 24 / 28 ) 3.84 0.0322068767992997 119.229195178699 Winsorized Mean ( 25 / 28 ) 3.84 0.0322068767992997 119.229195178699 Winsorized Mean ( 26 / 28 ) 3.84 0.0322068767992997 119.229195178699 Winsorized Mean ( 27 / 28 ) 3.85905882352941 0.0300226914786962 128.538070154961 Winsorized Mean ( 28 / 28 ) 3.86564705882353 0.0293025591653104 131.921824200251 Trimmed Mean ( 1 / 28 ) 3.89156626506024 0.0458912722900358 84.7997030996503 Trimmed Mean ( 2 / 28 ) 3.88851851851852 0.0455044127256185 85.4536579114958 Trimmed Mean ( 3 / 28 ) 3.88544303797468 0.0450690254512285 86.2109397546064 Trimmed Mean ( 4 / 28 ) 3.88272727272727 0.0449000699372545 86.4748602430504 Trimmed Mean ( 5 / 28 ) 3.88093333333333 0.0449757385382059 86.2894853863615 Trimmed Mean ( 6 / 28 ) 3.87931506849315 0.0450744896613537 86.064536673373 Trimmed Mean ( 7 / 28 ) 3.87760563380282 0.045147406586405 85.8876716734923 Trimmed Mean ( 8 / 28 ) 3.87579710144928 0.0451894778533383 85.7676894171717 Trimmed Mean ( 9 / 28 ) 3.87402985074627 0.0452237313281104 85.6636490836887 Trimmed Mean ( 10 / 28 ) 3.87215384615385 0.0452176851823978 85.6336150454067 Trimmed Mean ( 11 / 28 ) 3.87015873015873 0.0451631236181227 85.6928932303909 Trimmed Mean ( 12 / 28 ) 3.86803278688525 0.0450499538594593 85.8609711111405 Trimmed Mean ( 13 / 28 ) 3.86576271186441 0.0448656696187065 86.163045034607 Trimmed Mean ( 14 / 28 ) 3.86333333333333 0.0445946188840860 86.6322760460232 Trimmed Mean ( 15 / 28 ) 3.86072727272727 0.0442169845221565 87.3132194438251 Trimmed Mean ( 16 / 28 ) 3.8577358490566 0.0437432487093864 88.190428531862 Trimmed Mean ( 17 / 28 ) 3.85392156862745 0.0433110758205693 88.9823560281351 Trimmed Mean ( 18 / 28 ) 3.84897959183673 0.0428593698805892 89.8048572006636 Trimmed Mean ( 19 / 28 ) 3.84340425531915 0.0422617680579544 90.9428173958224 Trimmed Mean ( 20 / 28 ) 3.83733333333333 0.0414343828336815 92.6122961390899 Trimmed Mean ( 21 / 28 ) 3.83069767441860 0.0403025591421178 95.0484970671596 Trimmed Mean ( 22 / 28 ) 3.82365853658537 0.0388536279147982 98.41187919363 Trimmed Mean ( 23 / 28 ) 3.81717948717949 0.0373948344848179 102.077721155023 Trimmed Mean ( 24 / 28 ) 3.81405405405405 0.0368962091435975 103.372518277149 Trimmed Mean ( 25 / 28 ) 3.81142857142857 0.0364106893002334 104.678835931956 Trimmed Mean ( 26 / 28 ) 3.80848484848485 0.0356411013908983 106.856542021943 Trimmed Mean ( 27 / 28 ) 3.80516129032258 0.0344632294860939 110.412208811075 Trimmed Mean ( 28 / 28 ) 3.79931034482759 0.0332364681693929 114.311494394171 Median 3.78 Midrange 4.015 Midmean - Weighted Average at Xnp 3.79666666666666 Midmean - Weighted Average at X(n+1)p 3.81043478260869 Midmean - Empirical Distribution Function 3.81043478260869 Midmean - Empirical Distribution Function - Averaging 3.81043478260869 Midmean - Empirical Distribution Function - Interpolation 3.81043478260869 Midmean - Closest Observation 3.81043478260869 Midmean - True Basic - Statistics Graphics Toolkit 3.81043478260869 Midmean - MS Excel (old versions) 3.81043478260869 Number of observations 85

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208716120ons2oh356g1t5np/17vto1208716067.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208716120ons2oh356g1t5np/17vto1208716067.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208716120ons2oh356g1t5np/23ksn1208716067.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208716120ons2oh356g1t5np/23ksn1208716067.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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