paper - central tendency elektronische apparaten

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Sat, 27 Dec 2008 05:37:53 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/27/t1230381537488qmvqpz6xg7lq.htm/, Retrieved Sat, 27 Dec 2008 13:38:57 +0100

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/2008/Dec/27/t1230381537488qmvqpz6xg7lq.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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Dataseries X:

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0.084299365852926 -15.5692124815993 -6.9953619930182 -2.07575919037298 6.06472185178652 3.10063183929146 -7.27872604143293 11.9305592423578 -15.1800926797913 -4.96965957564265 -3.06184332688462 5.17876413221274 -2.29638814463019 -1.85853257792512 -8.74637895628288 -8.02346934029272 4.80319999595127 3.90173526693944 -11.3069080265042 4.26225040152088 -6.88628010104842 4.12797896412461 4.24824928932737 -5.91811547446539 -2.62127541719435 -5.11947651478644 -6.19169292552164 1.57682830128841 6.93381888926023 1.30435330636300 0.701451547474772 18.1487693268603 -13.6251962127511 -8.9684198944174 -3.48024416476534 0.133268755660886 0.156896176204026 -1.28412130463800 -8.4586972345603 -2.91518278408049 0.150465578819962 3.86877987666889 7.70993797103159 -4.11650976301151 -2.74475852656699 3.19286810860467 -6.2212027713738 1.25489355791219 4.23585013027417 0.153440583363572 -2.05719003274709 2.14422869581576 -1.68156215590428 5.0318450949173 2.24823311061623 -6.58372573676435 -2.85420176875137 5.0379752614482 4.43711208741108 -0.675511401722624 -2.50684702275299 2.35909448398834 -6.31849429304567 -3.81949862816358 2.17307118170725 4.13663986179168 -6.96229654560136 5.28008601863276 4.2774558989149

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -0.942363461661107 0.733091035651206 -1.28546580960986 Geometric Mean NaN Harmonic Mean 1.79653775616133 Quadratic Mean 6.11823312888783 Winsorized Mean ( 1 / 23 ) -1.02684303097552 0.701827899444391 -1.46309804980456 Winsorized Mean ( 2 / 23 ) -1.10411041660700 0.66008683252889 -1.67267450613579 Winsorized Mean ( 3 / 23 ) -1.03705958597763 0.627377636143494 -1.65300693909407 Winsorized Mean ( 4 / 23 ) -0.951877493536289 0.588253795036159 -1.61814084595541 Winsorized Mean ( 5 / 23 ) -0.992645239552176 0.575499130813947 -1.72484229150485 Winsorized Mean ( 6 / 23 ) -0.976440036482388 0.56919590971277 -1.71547268668028 Winsorized Mean ( 7 / 23 ) -0.946569410909616 0.558552240694174 -1.69468375909335 Winsorized Mean ( 8 / 23 ) -0.860933105712063 0.542881914042571 -1.58585704080861 Winsorized Mean ( 9 / 23 ) -0.853795851436146 0.53181653071723 -1.60543308100010 Winsorized Mean ( 10 / 23 ) -0.902059976236631 0.522866430013191 -1.72522067674889 Winsorized Mean ( 11 / 23 ) -0.915393848459467 0.517013583708869 -1.77054119524822 Winsorized Mean ( 12 / 23 ) -0.865420132478589 0.507795864468153 -1.70426778363979 Winsorized Mean ( 13 / 23 ) -0.818086881611527 0.499216282053339 -1.63874238686013 Winsorized Mean ( 14 / 23 ) -0.800862344268609 0.495653950845738 -1.61576911250701 Winsorized Mean ( 15 / 23 ) -0.816014610057811 0.491412272060955 -1.6605499220349 Winsorized Mean ( 16 / 23 ) -0.754584684634233 0.481002448239875 -1.56877514323570 Winsorized Mean ( 17 / 23 ) -0.613559764889389 0.442357330727722 -1.38702293885358 Winsorized Mean ( 18 / 23 ) -0.583074143444196 0.435241762239838 -1.33965578221075 Winsorized Mean ( 19 / 23 ) -0.534269464505479 0.373521569678827 -1.43035772998296 Winsorized Mean ( 20 / 23 ) -0.474914431017154 0.357599816130893 -1.32806117227790 Winsorized Mean ( 21 / 23 ) -0.597348354640378 0.311035017015696 -1.92051801874846 Winsorized Mean ( 22 / 23 ) -0.499292293492706 0.288261792617538 -1.73207933302198 Winsorized Mean ( 23 / 23 ) -0.475459422194322 0.278407035605421 -1.70778522590276 Trimmed Mean ( 1 / 23 ) -1.00899456268474 0.662846248495786 -1.52221509131940 Trimmed Mean ( 2 / 23 ) -0.990047727114521 0.615230819945521 -1.60922973137495 Trimmed Mean ( 3 / 23 ) -0.927584825725784 0.585499544055828 -1.58426225117152 Trimmed Mean ( 4 / 23 ) -0.886307457106236 0.565245437159129 -1.56800462036586 Trimmed Mean ( 5 / 23 ) -0.867136556624568 0.555436382507464 -1.5611806931155 Trimmed Mean ( 6 / 23 ) -0.836750243915779 0.547206487917104 -1.52913070731453 Trimmed Mean ( 7 / 23 ) -0.807542378197306 0.538569285692856 -1.49942152226231 Trimmed Mean ( 8 / 23 ) -0.78168559852844 0.53035362392971 -1.47389508293817 Trimmed Mean ( 9 / 23 ) -0.768283446578269 0.523628356943778 -1.46723040566873 Trimmed Mean ( 10 / 23 ) -0.75490395466173 0.517281809632188 -1.45936690717677 Trimmed Mean ( 11 / 23 ) -0.75490395466173 0.510680821752886 -1.47823047685746 Trimmed Mean ( 12 / 23 ) -0.70791744706891 0.502942225308569 -1.40755222259293 Trimmed Mean ( 13 / 23 ) -0.686856041461802 0.494485638772429 -1.38903132387613 Trimmed Mean ( 14 / 23 ) -0.669867433637541 0.484839383542983 -1.38162751701906 Trimmed Mean ( 15 / 23 ) -0.653313131744604 0.472324096346082 -1.38318823197601 Trimmed Mean ( 16 / 23 ) -0.633085380386746 0.456013389538782 -1.38830436761310 Trimmed Mean ( 17 / 23 ) -0.61811493039911 0.436159612335962 -1.41717598997450 Trimmed Mean ( 18 / 23 ) -0.618675191397631 0.419334547417986 -1.47537376828851 Trimmed Mean ( 19 / 23 ) -0.623077471520906 0.397058628542531 -1.56923292111297 Trimmed Mean ( 20 / 23 ) -0.63419861940487 0.384186443092272 -1.65075741429156 Trimmed Mean ( 21 / 23 ) -0.654551599032189 0.369307293811772 -1.77237658177907 Trimmed Mean ( 22 / 23 ) -0.654551599032189 0.362114796686531 -1.80758037236134 Trimmed Mean ( 23 / 23 ) -0.684266664209727 0.35685319735429 -1.91750184468818 Median -0.675511401722624 Midrange 1.2897784226305 Midmean - Weighted Average at Xnp -0.751051700909066 Midmean - Weighted Average at X(n+1)p -0.618114930399109 Midmean - Empirical Distribution Function -0.618114930399109 Midmean - Empirical Distribution Function - Averaging -0.618114930399109 Midmean - Empirical Distribution Function - Interpolation -0.618114930399109 Midmean - Closest Observation -0.765337167734284 Midmean - True Basic - Statistics Graphics Toolkit -0.618114930399109 Midmean - MS Excel (old versions) -0.618114930399109 Number of observations 69

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/27/t1230381537488qmvqpz6xg7lq/1s8nh1230381468.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/27/t1230381537488qmvqpz6xg7lq/1s8nh1230381468.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/27/t1230381537488qmvqpz6xg7lq/2bwab1230381468.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/27/t1230381537488qmvqpz6xg7lq/2bwab1230381468.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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FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

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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