*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: Mon, 08 Dec 2008 07:09:30 -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/08/t1228745440jzbxqnsvj25dksi.htm/, Retrieved Mon, 08 Dec 2008 14:10:42 +0000

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/08/t1228745440jzbxqnsvj25dksi.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

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Dataseries X:

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4.43 4.61 4.54 4.2 4.08 3.95 4.19 4.23 3.89 3.92 4.14 4.24 4.08 4.37 4.43 4.3 4.27 4.06 3.96 4.21 4.31 4.35 4.25 4.06 4 3.87 3.71 3.63 3.48 3.6 3.66 3.45 3.3 3.14 3.21 3.12 3.14 3.4 3.42 3.29 3.49 3.52 3.81 4.03 3.98 4.1 3.96 3.83 3.72 3.82 3.76 3.98 4.14 4 4.13 4.28 4.46 4.63 4.49 4.41 4.5 4.39 4.33 4.45 4.17 4.13 4.33 4.47 4.63 4.9

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 4.019 0.0492204867377375 81.6529918002339 Geometric Mean 3.99730257916325 Harmonic Mean 3.97468413139924 Quadratic Mean 4.03974309649937 Winsorized Mean ( 1 / 23 ) 4.01542857142857 0.0482877356333865 83.1562822062063 Winsorized Mean ( 2 / 23 ) 4.01542857142857 0.0482877356333865 83.1562822062063 Winsorized Mean ( 3 / 23 ) 4.01757142857143 0.0473659974109748 84.8197366923926 Winsorized Mean ( 4 / 23 ) 4.01814285714286 0.0455762700492276 88.1630474104793 Winsorized Mean ( 5 / 23 ) 4.016 0.0449510430723462 89.3416420512527 Winsorized Mean ( 6 / 23 ) 4.02371428571429 0.0429228068390078 93.7430373741909 Winsorized Mean ( 7 / 23 ) 4.02371428571429 0.0421940559964497 95.3621118115038 Winsorized Mean ( 8 / 23 ) 4.026 0.0413175352163716 97.4404687723179 Winsorized Mean ( 9 / 23 ) 4.02857142857143 0.0403526307963402 99.834170636944 Winsorized Mean ( 10 / 23 ) 4.02714285714286 0.0396449787729881 101.580149158428 Winsorized Mean ( 11 / 23 ) 4.03185714285714 0.0387305245827792 104.100246157002 Winsorized Mean ( 12 / 23 ) 4.04214285714286 0.0356703870994375 113.319287673404 Winsorized Mean ( 13 / 23 ) 4.044 0.0341294575956958 118.490016686055 Winsorized Mean ( 14 / 23 ) 4.046 0.0325025241892833 124.482639454016 Winsorized Mean ( 15 / 23 ) 4.05242857142857 0.0300781836390817 134.729830100615 Winsorized Mean ( 16 / 23 ) 4.05014285714286 0.029054452239076 139.398355330056 Winsorized Mean ( 17 / 23 ) 4.05985714285714 0.0274857334400746 147.707797272668 Winsorized Mean ( 18 / 23 ) 4.06757142857143 0.0247667677180579 164.235053797742 Winsorized Mean ( 19 / 23 ) 4.06757142857143 0.0239758640837521 169.652756387117 Winsorized Mean ( 20 / 23 ) 4.06471428571429 0.0227550840027888 178.628841151109 Winsorized Mean ( 21 / 23 ) 4.07371428571428 0.0205827838455131 197.918528236516 Winsorized Mean ( 22 / 23 ) 4.07371428571428 0.0188259670768800 216.38804896866 Winsorized Mean ( 23 / 23 ) 4.08028571428571 0.0170080621834738 239.903033647795 Trimmed Mean ( 1 / 23 ) 4.01926470588235 0.0471232651124499 85.2925767408352 Trimmed Mean ( 2 / 23 ) 4.02333333333333 0.0457261195694322 87.9876396951672 Trimmed Mean ( 3 / 23 ) 4.02765625 0.0440405556846741 91.4533476561379 Trimmed Mean ( 4 / 23 ) 4.03145161290323 0.0424393970342916 94.9931406811872 Trimmed Mean ( 5 / 23 ) 4.03533333333333 0.0411779016668817 97.9975464990447 Trimmed Mean ( 6 / 23 ) 4.04 0.0398294913946311 101.432377329945 Trimmed Mean ( 7 / 23 ) 4.04339285714286 0.0387794938328171 104.266261818022 Trimmed Mean ( 8 / 23 ) 4.04703703703704 0.0376665921129015 107.443673823915 Trimmed Mean ( 9 / 23 ) 4.05057692307692 0.0364987380322125 110.978547244620 Trimmed Mean ( 10 / 23 ) 4.054 0.0352669122839074 114.951940429723 Trimmed Mean ( 11 / 23 ) 4.05791666666667 0.0338631977861306 119.832648183293 Trimmed Mean ( 12 / 23 ) 4.06152173913044 0.0322923951073397 125.773319867726 Trimmed Mean ( 13 / 23 ) 4.06409090909091 0.0310481420187064 130.896428734522 Trimmed Mean ( 14 / 23 ) 4.06666666666667 0.0297973540334457 136.477442329345 Trimmed Mean ( 15 / 23 ) 4.06925 0.0285468294974937 142.546477897213 Trimmed Mean ( 16 / 23 ) 4.07131578947368 0.0274993108736404 148.051556934696 Trimmed Mean ( 17 / 23 ) 4.07388888888889 0.0263169864203795 154.800736825023 Trimmed Mean ( 18 / 23 ) 4.07558823529412 0.0251278058497325 162.194353922768 Trimmed Mean ( 19 / 23 ) 4.0765625 0.0242409335188004 168.168544203892 Trimmed Mean ( 20 / 23 ) 4.07766666666667 0.0231719377117670 175.974349551094 Trimmed Mean ( 21 / 23 ) 4.07928571428571 0.0219663557763279 185.706075045992 Trimmed Mean ( 22 / 23 ) 4.08 0.0209247736868563 194.984187693404 Trimmed Mean ( 23 / 23 ) 4.08083333333333 0.0199448212255665 204.606162531167 Median 4.08 Midrange 4.01 Midmean - Weighted Average at Xnp 4.06657142857143 Midmean - Weighted Average at X(n+1)p 4.08081081081081 Midmean - Empirical Distribution Function 4.08081081081081 Midmean - Empirical Distribution Function - Averaging 4.08081081081081 Midmean - Empirical Distribution Function - Interpolation 4.07558823529412 Midmean - Closest Observation 4.08081081081081 Midmean - True Basic - Statistics Graphics Toolkit 4.08081081081081 Midmean - MS Excel (old versions) 4.08081081081081 Number of observations 70

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/08/t1228745440jzbxqnsvj25dksi/14v0l1228745368.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/08/t1228745440jzbxqnsvj25dksi/14v0l1228745368.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/08/t1228745440jzbxqnsvj25dksi/2g2pm1228745368.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/08/t1228745440jzbxqnsvj25dksi/2g2pm1228745368.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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