central tendensy

*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: Thu, 15 Oct 2009 16:21:41 -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/Oct/16/t12556453447q1a9f0w3wj61e0.htm/, Retrieved Fri, 16 Oct 2009 00:22:27 +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/Oct/16/t12556453447q1a9f0w3wj61e0.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?

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Dataseries X:

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-346091 -347267 -345867 -339554 -336425 -339056 -352054 -350456 -369289 -366864 -360592 -358237 -355622 -359025 -357244 -351422 -350314 -349576 -364289 -363039 -379608 -371003 -366159 -365336 -374131 -370759 -367189 -359434 -361633 -361485 -379519 -385173 -389336 -378830 -367820 -362678 -365995 -363168 -353567 -353311 -343736 -330609 -353062 -362203 -359141 -353594 -343402 -342961 -347221 -343379 -330708 -330631 -318356 -319466 -341849 -346521 -343615 -336812 -335039 -338104 -341810 -343412 -344759 -347629 -337592 -340905 -363038 -369695 -366397

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -353827 1792.98517934963 -197.339612214945 Geometric Mean NaN Harmonic Mean -353207.645753870 Quadratic Mean 354135.781935445 Winsorized Mean ( 1 / 23 ) -353782.753623188 1771.70236736284 -199.685206804679 Winsorized Mean ( 2 / 23 ) -353944.434782609 1652.19702995112 -214.22652889836 Winsorized Mean ( 3 / 23 ) -353941.521739130 1651.11568038986 -214.365065962887 Winsorized Mean ( 4 / 23 ) -353906.043478261 1641.17833430542 -215.641430355612 Winsorized Mean ( 5 / 23 ) -353879.376811594 1507.72391593848 -234.710992556832 Winsorized Mean ( 6 / 23 ) -353727.898550725 1434.94423005549 -246.509858112776 Winsorized Mean ( 7 / 23 ) -353742.405797101 1423.66316622915 -248.473384848509 Winsorized Mean ( 8 / 23 ) -353709.478260870 1386.72088554662 -255.068977432645 Winsorized Mean ( 9 / 23 ) -353723.304347826 1366.47539051508 -258.858159322205 Winsorized Mean ( 10 / 23 ) -353648.376811594 1308.75991559464 -270.216387740538 Winsorized Mean ( 11 / 23 ) -353627.173913043 1279.98363643042 -276.274761526819 Winsorized Mean ( 12 / 23 ) -353805.608695652 1234.11116100725 -286.688606241016 Winsorized Mean ( 13 / 23 ) -353888.130434783 1194.70313739154 -296.214280651714 Winsorized Mean ( 14 / 23 ) -353847.753623188 1186.12306330977 -298.322968812198 Winsorized Mean ( 15 / 23 ) -354053.84057971 1145.46154168883 -309.092734844424 Winsorized Mean ( 16 / 23 ) -353997.956521739 1108.52168814706 -319.34238211745 Winsorized Mean ( 17 / 23 ) -353745.666666667 1069.61063970682 -330.723773244841 Winsorized Mean ( 18 / 23 ) -353455.84057971 1027.70414586766 -343.927619637358 Winsorized Mean ( 19 / 23 ) -353476.217391304 1014.76317015573 -348.333707595102 Winsorized Mean ( 20 / 23 ) -353511 1009.72031675772 -350.107840887214 Winsorized Mean ( 21 / 23 ) -353712.782608696 950.782328493902 -372.022882639183 Winsorized Mean ( 22 / 23 ) -353914.608695652 881.60865044496 -401.441851230732 Winsorized Mean ( 23 / 23 ) -353799.275362319 845.509399891197 -418.445111796329 Trimmed Mean ( 1 / 23 ) -353826.432835821 1685.64999940654 -209.905041355199 Trimmed Mean ( 2 / 23 ) -353872.8 1581.24181651881 -223.794233306498 Trimmed Mean ( 3 / 23 ) -353833.571428571 1534.52776721820 -230.581406858477 Trimmed Mean ( 4 / 23 ) -353792.868852459 1478.40108570210 -239.307771263196 Trimmed Mean ( 5 / 23 ) -353759.779661017 1413.77105073937 -250.224235017408 Trimmed Mean ( 6 / 23 ) -353730.824561403 1379.47445318652 -256.424338808380 Trimmed Mean ( 7 / 23 ) -353731.436363636 1357.90440988047 -260.498039324266 Trimmed Mean ( 8 / 23 ) -353729.396226415 1333.41973308166 -265.279857085145 Trimmed Mean ( 9 / 23 ) -353732.764705882 1311.31933520891 -269.753335597335 Trimmed Mean ( 10 / 23 ) -353734.244897959 1287.46888659672 -274.751684161483 Trimmed Mean ( 11 / 23 ) -353734.244897959 1269.57425613459 -278.624305107568 Trimmed Mean ( 12 / 23 ) -353763.533333333 1251.78888464356 -282.6063864867 Trimmed Mean ( 13 / 23 ) -353757.906976744 1237.48348034835 -285.868791458261 Trimmed Mean ( 14 / 23 ) -353741.048780488 1225.52503479779 -288.6444901053 Trimmed Mean ( 15 / 23 ) -353727.564102564 1209.36003575422 -292.491527456471 Trimmed Mean ( 16 / 23 ) -353687 1194.65521619653 -296.057804130338 Trimmed Mean ( 17 / 23 ) -353648.685714286 1180.73698732160 -299.515209154671 Trimmed Mean ( 18 / 23 ) -353636.757575758 1168.07714388757 -302.751200489028 Trimmed Mean ( 19 / 23 ) -353659.129032258 1157.21443700313 -305.612441154934 Trimmed Mean ( 20 / 23 ) -353682.034482759 1140.6739878288 -310.064083389830 Trimmed Mean ( 21 / 23 ) -353703.888888889 1113.27957715216 -317.713444266792 Trimmed Mean ( 22 / 23 ) -353703.888888889 1087.43354819195 -325.26483064366 Trimmed Mean ( 23 / 23 ) -353673.826086957 1066.77690777276 -331.534947475911 Median -353311 Midrange -353846 Midmean - Weighted Average at Xnp -353950.058823529 Midmean - Weighted Average at X(n+1)p -353648.685714286 Midmean - Empirical Distribution Function -353648.685714286 Midmean - Empirical Distribution Function - Averaging -353648.685714286 Midmean - Empirical Distribution Function - Interpolation -353648.685714286 Midmean - Closest Observation -353973.333333333 Midmean - True Basic - Statistics Graphics Toolkit -353648.685714286 Midmean - MS Excel (old versions) -353648.685714286 Number of observations 69

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/16/t12556453447q1a9f0w3wj61e0/1bkkj1255645299.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/16/t12556453447q1a9f0w3wj61e0/1bkkj1255645299.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/16/t12556453447q1a9f0w3wj61e0/2x84o1255645299.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/16/t12556453447q1a9f0w3wj61e0/2x84o1255645299.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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