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

Title produced by software: Central Tendency

Date of computation: Thu, 16 Oct 2008 08:20:24 -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/Oct/16/t12241672987njwceofl77hcxz.htm/, Retrieved Thu, 16 Oct 2008 14:28:20 +0000

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@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/Oct/16/t12241672987njwceofl77hcxz.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}, }

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2.9 4.5 4.4 1.7 0.1 2.7 4 4 8.1 7.1 9.1 11.1 13.7 14.2 5.8 3.8 6.4 6.1 8.2 6.8 5.6 8.8 7.9 6.5 3.6 3.8 11.5 18 16.6 17.5 17.9 18.4 24 20.7 18.2 16.9 20.6 21.6 22.8 17.5 21.7 25 22.7 25.4 17 17.1 20.2 23.9 20.9 18.9 18.6 21.2 17.6 14.4 13.8 7 7.8 10.7 11.6 7.1 8.3 6.9 5.5 4.6 4.5 4.1 3.4 7.9 12.3 18.2 16.7 21.3 23 28.7 28.7 34.4 39.2 39.4 34.6 34.6

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 14.275 1.04305190593806 13.6858002163967 Geometric Mean 10.7546924177666 Harmonic Mean 4.17001164811969 Quadratic Mean 17.0212881416184 Winsorized Mean ( 1 / 26 ) 14.2925 1.03903676029316 13.7555287225521 Winsorized Mean ( 2 / 26 ) 14.2025 1.00300651682071 14.1599279384730 Winsorized Mean ( 3 / 26 ) 14.21 1.00192630922335 14.1826797731412 Winsorized Mean ( 4 / 26 ) 14.225 0.995849773887557 14.2842830043221 Winsorized Mean ( 5 / 26 ) 13.88125 0.9113578229693 15.2313939159192 Winsorized Mean ( 6 / 26 ) 13.89625 0.909232608256942 15.2834927760015 Winsorized Mean ( 7 / 26 ) 13.6075 0.854103599606488 15.9319080334861 Winsorized Mean ( 8 / 26 ) 13.5875 0.84429465543131 16.0933151863419 Winsorized Mean ( 9 / 26 ) 13.475 0.82558667287595 16.3217266493166 Winsorized Mean ( 10 / 26 ) 13.475 0.821763887059993 16.3976541342176 Winsorized Mean ( 11 / 26 ) 13.3925 0.796445376244832 16.8153402599239 Winsorized Mean ( 12 / 26 ) 13.3775 0.789750351116483 16.9388971857854 Winsorized Mean ( 13 / 26 ) 13.36125 0.787303308267443 16.9709054435489 Winsorized Mean ( 14 / 26 ) 13.20375 0.759256056085516 17.3903782448234 Winsorized Mean ( 15 / 26 ) 13.35375 0.733035875074044 18.2170483793186 Winsorized Mean ( 16 / 26 ) 13.31375 0.721853152581884 18.4438482430673 Winsorized Mean ( 17 / 26 ) 13.335 0.713165301199829 18.6983297947407 Winsorized Mean ( 18 / 26 ) 13.335 0.694838793798309 19.1915018548472 Winsorized Mean ( 19 / 26 ) 13.35875 0.678997058563566 19.6742383954663 Winsorized Mean ( 20 / 26 ) 13.35875 0.672346386742595 19.8688507343973 Winsorized Mean ( 21 / 26 ) 13.3325 0.648034455151338 20.5737517411577 Winsorized Mean ( 22 / 26 ) 13.0025 0.598151093798764 21.7378186461604 Winsorized Mean ( 23 / 26 ) 12.945 0.583770210123682 22.1748211462475 Winsorized Mean ( 24 / 26 ) 12.915 0.572591543728483 22.5553453267975 Winsorized Mean ( 25 / 26 ) 12.8525 0.565058457264894 22.7454342727851 Winsorized Mean ( 26 / 26 ) 13.08 0.536209150578911 24.3934665901885 Trimmed Mean ( 1 / 26 ) 14.1346153846154 1.00300551826693 14.0922608372467 Trimmed Mean ( 2 / 26 ) 13.9684210526316 0.96036946568425 14.5448408677584 Trimmed Mean ( 3 / 26 ) 13.8418918918919 0.933095088863007 14.8343851094088 Trimmed Mean ( 4 / 26 ) 13.7055555555556 0.901157508323523 15.2088346698157 Trimmed Mean ( 5 / 26 ) 13.5571428571429 0.865172875958494 15.6698657966171 Trimmed Mean ( 6 / 26 ) 13.4808823529412 0.849330308287985 15.8723669947855 Trimmed Mean ( 7 / 26 ) 13.3969696969697 0.830749288818024 16.1263691432474 Trimmed Mean ( 8 / 26 ) 13.359375 0.822014556019259 16.2519932307464 Trimmed Mean ( 9 / 26 ) 13.3225806451613 0.813241223076421 16.3820773801445 Trimmed Mean ( 10 / 26 ) 13.3 0.806106636621061 16.4990578116926 Trimmed Mean ( 11 / 26 ) 13.2758620689655 0.797623171935921 16.6442783209815 Trimmed Mean ( 12 / 26 ) 13.2607142857143 0.791581839676341 16.752170932997 Trimmed Mean ( 13 / 26 ) 13.2462962962963 0.784674630959062 16.8812597905786 Trimmed Mean ( 14 / 26 ) 13.2326923076923 0.775835661729278 17.0560506050955 Trimmed Mean ( 15 / 26 ) 13.236 0.769329206888331 17.2045983455314 Trimmed Mean ( 16 / 26 ) 13.2229166666667 0.7649991863861 17.2848767710885 Trimmed Mean ( 17 / 26 ) 13.2130434782609 0.760406760559035 17.3762835413863 Trimmed Mean ( 18 / 26 ) 13.2 0.75488542737071 17.4860972558127 Trimmed Mean ( 19 / 26 ) 13.1857142857143 0.749932799378633 17.5825277900093 Trimmed Mean ( 20 / 26 ) 13.1675 0.745038180918026 17.6735908806381 Trimmed Mean ( 21 / 26 ) 13.1473684210526 0.738214531668667 17.8096852026662 Trimmed Mean ( 22 / 26 ) 13.1277777777778 0.732560318889365 17.9204052407327 Trimmed Mean ( 23 / 26 ) 13.1411764705882 0.733743820218415 17.9097610207831 Trimmed Mean ( 24 / 26 ) 13.1625 0.735433134391761 17.8976162270497 Trimmed Mean ( 25 / 26 ) 13.19 0.736820600757844 17.9012367276833 Trimmed Mean ( 26 / 26 ) 13.2285714285714 0.736516488729766 17.9609983360808 Median 13.75 Midrange 19.75 Midmean - Weighted Average at Xnp 13.0024390243902 Midmean - Weighted Average at X(n+1)p 13.1675 Midmean - Empirical Distribution Function 13.0024390243902 Midmean - Empirical Distribution Function - Averaging 13.1675 Midmean - Empirical Distribution Function - Interpolation 13.1675 Midmean - Closest Observation 13.0024390243902 Midmean - True Basic - Statistics Graphics Toolkit 13.1675 Midmean - MS Excel (old versions) 13.1857142857143 Number of observations 80

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/16/t12241672987njwceofl77hcxz/1zupq1224166822.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/16/t12241672987njwceofl77hcxz/1zupq1224166822.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/16/t12241672987njwceofl77hcxz/2ipx81224166822.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/16/t12241672987njwceofl77hcxz/2ipx81224166822.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')

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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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