tijdreeks B-Stap9

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Thu, 19 Aug 2010 19:47:31 +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/19/t1282247225a9xv0kpo501ixi5.htm/, Retrieved Thu, 19 Aug 2010 21:47:05 +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/19/t1282247225a9xv0kpo501ixi5.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:

gilian keirsebelik

Dataseries X:

» Textbox « » Textfile « » CSV «

51 50 49 47 45 44 45 47 48 48 49 51 45 42 40 37 28 33 32 38 38 34 38 48 41 41 43 37 22 30 32 41 44 37 53 67 62 63 68 62 50 64 71 76 73 68 78 89 74 74 73 65 55 69 80 81 80 86 90 100 90 89 83 63 48 62 69 73 76 77 75 77 78 73 74 55 36 41 52 53 49 47 44 55

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 3 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 57.202380952381 1.9506813439546 29.3243082114144 Geometric Mean 54.3892280672506 Harmonic Mean 51.5660613722159 Quadratic Mean 59.8994196648889 Winsorized Mean ( 1 / 28 ) 57.1547619047619 1.90821322074271 29.9519787849055 Winsorized Mean ( 2 / 28 ) 57.202380952381 1.89972215877045 30.1109194775113 Winsorized Mean ( 3 / 28 ) 57.2380952380952 1.88043486929306 30.4387544459935 Winsorized Mean ( 4 / 28 ) 57.2380952380952 1.88043486929306 30.4387544459935 Winsorized Mean ( 5 / 28 ) 57.1190476190476 1.83580166298355 31.1139535227446 Winsorized Mean ( 6 / 28 ) 56.9761904761905 1.78546565490382 31.911109754312 Winsorized Mean ( 7 / 28 ) 56.9761904761905 1.73180038825519 32.8999755760506 Winsorized Mean ( 8 / 28 ) 56.9761904761905 1.70239750201585 33.4682061085754 Winsorized Mean ( 9 / 28 ) 56.9761904761905 1.70239750201585 33.4682061085754 Winsorized Mean ( 10 / 28 ) 56.7380952380952 1.6646676808167 34.0837368875083 Winsorized Mean ( 11 / 28 ) 56.8690476190476 1.64627047356961 34.5441703122687 Winsorized Mean ( 12 / 28 ) 56.7261904761905 1.62448201643127 34.9195558352865 Winsorized Mean ( 13 / 28 ) 56.7261904761905 1.62448201643127 34.9195558352865 Winsorized Mean ( 14 / 28 ) 56.8928571428571 1.55461095456835 36.5962023975662 Winsorized Mean ( 15 / 28 ) 57.0714285714286 1.53163108456261 37.2618636084463 Winsorized Mean ( 16 / 28 ) 56.8809523809524 1.503620106834 37.8293374253421 Winsorized Mean ( 17 / 28 ) 56.6785714285714 1.47460436600009 38.4364597958662 Winsorized Mean ( 18 / 28 ) 56.6785714285714 1.47460436600009 38.4364597958662 Winsorized Mean ( 19 / 28 ) 56.9047619047619 1.44606803101411 39.3513726078679 Winsorized Mean ( 20 / 28 ) 56.9047619047619 1.38320586901632 41.1397631975277 Winsorized Mean ( 21 / 28 ) 57.1547619047619 1.35342302562557 42.229783905401 Winsorized Mean ( 22 / 28 ) 57.1547619047619 1.35342302562557 42.229783905401 Winsorized Mean ( 23 / 28 ) 57.1547619047619 1.35342302562557 42.229783905401 Winsorized Mean ( 24 / 28 ) 56.8690476190476 1.24065985648394 45.8377429734979 Winsorized Mean ( 25 / 28 ) 56.2738095238095 1.16044375828537 48.4933536175484 Winsorized Mean ( 26 / 28 ) 56.2738095238095 1.16044375828537 48.4933536175484 Winsorized Mean ( 27 / 28 ) 56.5952380952381 1.04476937307713 54.1700776780523 Winsorized Mean ( 28 / 28 ) 56.5952380952381 1.04476937307713 54.1700776780523 Trimmed Mean ( 1 / 28 ) 57.109756097561 1.87930023571524 30.3888410229597 Trimmed Mean ( 2 / 28 ) 57.0625 1.84565378540224 30.9172286001428 Trimmed Mean ( 3 / 28 ) 56.9871794871795 1.8115967120933 31.4568795067699 Trimmed Mean ( 4 / 28 ) 56.8947368421053 1.78006297418352 31.9622045215572 Trimmed Mean ( 5 / 28 ) 56.7972972972973 1.74291602966421 32.5875121524011 Trimmed Mean ( 6 / 28 ) 56.7222222222222 1.71242607441528 33.123895430984 Trimmed Mean ( 7 / 28 ) 56.6714285714286 1.68929419499839 33.5474002925125 Trimmed Mean ( 8 / 28 ) 56.6176470588235 1.67379605832025 33.8258934100027 Trimmed Mean ( 9 / 28 ) 56.5606060606061 1.66075344317303 34.0571963244233 Trimmed Mean ( 10 / 28 ) 56.5 1.64419372820633 34.3633472325896 Trimmed Mean ( 11 / 28 ) 56.4677419354839 1.63073302110149 34.6272143905828 Trimmed Mean ( 12 / 28 ) 56.4166666666667 1.61670161299523 34.8961528912837 Trimmed Mean ( 13 / 28 ) 56.3793103448276 1.60248362633131 35.1824564185414 Trimmed Mean ( 14 / 28 ) 56.3392857142857 1.58386277480875 35.570812453174 Trimmed Mean ( 15 / 28 ) 56.2777777777778 1.57203386504961 35.7993418774105 Trimmed Mean ( 16 / 28 ) 56.1923076923077 1.55953701543686 36.0314036384492 Trimmed Mean ( 17 / 28 ) 56.12 1.54725299700298 36.2707327817133 Trimmed Mean ( 18 / 28 ) 56.0625 1.53516876252503 36.518786317531 Trimmed Mean ( 19 / 28 ) 56 1.51768957382993 36.8981911489861 Trimmed Mean ( 20 / 28 ) 55.9090909090909 1.49834940256087 37.3137873005689 Trimmed Mean ( 21 / 28 ) 55.8095238095238 1.48325461244535 37.6263949164561 Trimmed Mean ( 22 / 28 ) 55.675 1.46602003519384 37.9769707530897 Trimmed Mean ( 23 / 28 ) 55.5263157894737 1.43999804513522 38.5599938673941 Trimmed Mean ( 24 / 28 ) 55.3611111111111 1.4018993792311 39.4900746310874 Trimmed Mean ( 25 / 28 ) 55.2058823529412 1.37573795576474 40.128196014083 Trimmed Mean ( 26 / 28 ) 55.09375 1.357743157543 40.5774462525731 Trimmed Mean ( 27 / 28 ) 54.9666666666667 1.32741502603406 41.408802513628 Trimmed Mean ( 28 / 28 ) 54.7857142857143 1.31067770229931 41.7995317915335 Median 52.5 Midrange 61 Midmean - Weighted Average at Xnp 55.9090909090909 Midmean - Weighted Average at X(n+1)p 56.2093023255814 Midmean - Empirical Distribution Function 55.9090909090909 Midmean - Empirical Distribution Function - Averaging 56.2093023255814 Midmean - Empirical Distribution Function - Interpolation 56.2093023255814 Midmean - Closest Observation 55.9090909090909 Midmean - True Basic - Statistics Graphics Toolkit 56.2093023255814 Midmean - MS Excel (old versions) 55.9090909090909 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282247225a9xv0kpo501ixi5/1vm1d1282247247.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282247225a9xv0kpo501ixi5/1vm1d1282247247.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282247225a9xv0kpo501ixi5/26diy1282247247.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/19/t1282247225a9xv0kpo501ixi5/26diy1282247247.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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