*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 06 Jun 2010 20:54:02 +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/Jun/06/t1275857699b7k572cti2hbuj4.htm/, Retrieved Sun, 06 Jun 2010 22:55:01 +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/Jun/06/t1275857699b7k572cti2hbuj4.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:

Dataseries X:

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133 126 120 114 116 153 162 161 149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107 99 103 131 137 135 124 118 121 121 118 113 107

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 41 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 120.693333333333 2.06034837720116 58.5790901523591 Geometric Mean 119.419256046999 Harmonic Mean 118.169790496441 Quadratic Mean 121.987758948730 Winsorized Mean ( 1 / 25 ) 120.72 2.04750430374978 58.9595830294054 Winsorized Mean ( 2 / 25 ) 120.773333333333 1.98721801406777 60.7750797740176 Winsorized Mean ( 3 / 25 ) 120.773333333333 1.98721801406777 60.7750797740176 Winsorized Mean ( 4 / 25 ) 120.666666666667 1.91686054640246 62.9501540386608 Winsorized Mean ( 5 / 25 ) 120.466666666667 1.87273787464961 64.3264966749316 Winsorized Mean ( 6 / 25 ) 120.706666666667 1.80017750209224 67.0526470452923 Winsorized Mean ( 7 / 25 ) 120.893333333333 1.77079137735141 68.2707939961593 Winsorized Mean ( 8 / 25 ) 121 1.75489020728923 68.9501824657783 Winsorized Mean ( 9 / 25 ) 120.88 1.68650820036841 71.6747181979868 Winsorized Mean ( 10 / 25 ) 120.746666666667 1.56724275396310 77.0440101645602 Winsorized Mean ( 11 / 25 ) 120.013333333333 1.42746462487000 84.0744710883906 Winsorized Mean ( 12 / 25 ) 119.693333333333 1.37139021110372 87.2788301711748 Winsorized Mean ( 13 / 25 ) 119.693333333333 1.37139021110372 87.2788301711748 Winsorized Mean ( 14 / 25 ) 119.506666666667 1.28222404379987 93.2026405560985 Winsorized Mean ( 15 / 25 ) 119.706666666667 1.25429328773284 95.4375406752268 Winsorized Mean ( 16 / 25 ) 119.493333333333 1.21956621047885 97.9801935365326 Winsorized Mean ( 17 / 25 ) 119.266666666667 1.18357122339166 100.768474519762 Winsorized Mean ( 18 / 25 ) 119.266666666667 1.11295942364431 107.161738454162 Winsorized Mean ( 19 / 25 ) 119.266666666667 1.03980825213171 114.700634873938 Winsorized Mean ( 20 / 25 ) 119 0.999639574686436 119.042906076750 Winsorized Mean ( 21 / 25 ) 119 0.999639574686436 119.042906076750 Winsorized Mean ( 22 / 25 ) 118.706666666667 0.793390110770148 149.619544099734 Winsorized Mean ( 23 / 25 ) 118.4 0.750735375217928 157.712029975449 Winsorized Mean ( 24 / 25 ) 118.4 0.66522366353169 177.985249910401 Winsorized Mean ( 25 / 25 ) 118.066666666667 0.62134214895343 190.018763197595 Trimmed Mean ( 1 / 25 ) 120.630136986301 1.97525664953966 61.0706142993695 Trimmed Mean ( 2 / 25 ) 120.535211267606 1.88959141846554 63.7890340153466 Trimmed Mean ( 3 / 25 ) 120.405797101449 1.82671270351549 65.9139211490288 Trimmed Mean ( 4 / 25 ) 120.268656716418 1.75147183560933 68.6671942255794 Trimmed Mean ( 5 / 25 ) 120.153846153846 1.68808476609286 71.177614162082 Trimmed Mean ( 6 / 25 ) 120.079365079365 1.62628523947490 73.8365953060833 Trimmed Mean ( 7 / 25 ) 119.950819672131 1.5723752923016 76.286380394944 Trimmed Mean ( 8 / 25 ) 119.779661016949 1.51402324682961 79.1134886916495 Trimmed Mean ( 9 / 25 ) 119.578947368421 1.44574983545909 82.7106767959268 Trimmed Mean ( 10 / 25 ) 119.381818181818 1.37840265458816 86.6088133133252 Trimmed Mean ( 11 / 25 ) 119.188679245283 1.32357670736195 90.0504508596562 Trimmed Mean ( 12 / 25 ) 119.078431372549 1.28851431007139 92.4152960054837 Trimmed Mean ( 13 / 25 ) 119 1.2566151489828 94.6988424390139 Trimmed Mean ( 14 / 25 ) 118.914893617021 1.21539225831297 97.8407528957617 Trimmed Mean ( 15 / 25 ) 118.844444444444 1.18234297249215 100.516049242415 Trimmed Mean ( 16 / 25 ) 118.744186046512 1.14463117866281 103.740128925399 Trimmed Mean ( 17 / 25 ) 118.658536585366 1.10299467973949 107.578521243087 Trimmed Mean ( 18 / 25 ) 118.589743589744 1.05625694942524 112.273574772004 Trimmed Mean ( 19 / 25 ) 118.513513513514 1.01091759645347 117.233604330646 Trimmed Mean ( 20 / 25 ) 118.428571428571 0.967788533646862 122.370298170721 Trimmed Mean ( 21 / 25 ) 118.363636363636 0.91888661818523 128.812014476172 Trimmed Mean ( 22 / 25 ) 118.290322580645 0.84775928363127 139.532913250992 Trimmed Mean ( 23 / 25 ) 118.241379310345 0.814969509559594 145.086874936268 Trimmed Mean ( 24 / 25 ) 118.222222222222 0.779607128272915 151.643331538185 Trimmed Mean ( 25 / 25 ) 118.2 0.754983443527075 156.559724605088 Median 117 Midrange 123 Midmean - Weighted Average at Xnp 118.236842105263 Midmean - Weighted Average at X(n+1)p 118.589743589744 Midmean - Empirical Distribution Function 118.589743589744 Midmean - Empirical Distribution Function - Averaging 118.589743589744 Midmean - Empirical Distribution Function - Interpolation 118.513513513514 Midmean - Closest Observation 118.236842105263 Midmean - True Basic - Statistics Graphics Toolkit 118.589743589744 Midmean - MS Excel (old versions) 118.589743589744 Number of observations 75

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/06/t1275857699b7k572cti2hbuj4/1xs0q1275857600.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275857699b7k572cti2hbuj4/1xs0q1275857600.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275857699b7k572cti2hbuj4/28jzt1275857600.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/06/t1275857699b7k572cti2hbuj4/28jzt1275857600.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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