*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Thu, 12 Aug 2010 10:47:08 +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/Aug/12/t1281610016g3oqchh9hiajt90.htm/, Retrieved Thu, 12 Aug 2010 12:46:56 +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/Aug/12/t1281610016g3oqchh9hiajt90.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:

» Textbox « » Textfile « » CSV «

158 157 156 154 152 151 152 154 155 155 156 158 155 151 152 156 147 159 152 148 146 148 142 141 139 143 146 150 141 153 142 139 134 152 142 139 137 132 137 134 127 140 127 120 112 128 119 117 115 104 108 104 98 111 104 98 91 94 82 81 70 64 71 73 71 80 72 68 60 71 62 69 55 58 67 69 71 85 76 79 69 95 94 99

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 117.178571428571 3.71291804225366 31.5596978158577 Geometric Mean 111.639923896170 Harmonic Mean 105.654192359429 Quadratic Mean 121.963255590714 Winsorized Mean ( 1 / 28 ) 117.202380952381 3.70427873430887 31.6397305275269 Winsorized Mean ( 2 / 28 ) 117.25 3.6952495826279 31.7299271343445 Winsorized Mean ( 3 / 28 ) 117.285714285714 3.67741753426699 31.8934994987162 Winsorized Mean ( 4 / 28 ) 117.333333333333 3.65428462724631 32.1084275862086 Winsorized Mean ( 5 / 28 ) 117.511904761905 3.62358620015818 32.429725214423 Winsorized Mean ( 6 / 28 ) 117.583333333333 3.61168056030545 32.5564045241557 Winsorized Mean ( 7 / 28 ) 117.583333333333 3.58741378635188 32.7766297215762 Winsorized Mean ( 8 / 28 ) 117.583333333333 3.58741378635188 32.7766297215762 Winsorized Mean ( 9 / 28 ) 117.583333333333 3.58741378635188 32.7766297215762 Winsorized Mean ( 10 / 28 ) 117.583333333333 3.55326683514754 33.0916136582382 Winsorized Mean ( 11 / 28 ) 117.714285714286 3.53226954246782 33.3253972549458 Winsorized Mean ( 12 / 28 ) 117.571428571429 3.51475399069601 33.4508272506852 Winsorized Mean ( 13 / 28 ) 117.416666666667 3.49613376876887 33.5847179863526 Winsorized Mean ( 14 / 28 ) 117.416666666667 3.49613376876887 33.5847179863526 Winsorized Mean ( 15 / 28 ) 117.595238095238 3.4677068966316 33.9115275888702 Winsorized Mean ( 16 / 28 ) 117.785714285714 3.43767020351889 34.2632385634741 Winsorized Mean ( 17 / 28 ) 118.392857142857 3.3436308750966 35.4084710799414 Winsorized Mean ( 18 / 28 ) 118.821428571429 3.22075351695056 36.8924315214067 Winsorized Mean ( 19 / 28 ) 119.047619047619 3.18721200365695 37.3516474307407 Winsorized Mean ( 20 / 28 ) 119.047619047619 3.12357390348814 38.1126308280002 Winsorized Mean ( 21 / 28 ) 118.797619047619 3.02801888743222 39.2327866714069 Winsorized Mean ( 22 / 28 ) 119.583333333333 2.91430524847304 41.0332216901402 Winsorized Mean ( 23 / 28 ) 120.952380952381 2.65256804967342 45.5982197958211 Winsorized Mean ( 24 / 28 ) 121.523809523810 2.50372506129980 48.5372021881353 Winsorized Mean ( 25 / 28 ) 121.523809523810 2.50372506129980 48.5372021881353 Winsorized Mean ( 26 / 28 ) 120.904761904762 2.35549789899226 51.3287496271969 Winsorized Mean ( 27 / 28 ) 121.547619047619 2.19295832079860 55.4263242920893 Winsorized Mean ( 28 / 28 ) 121.547619047619 2.19295832079860 55.4263242920893 Trimmed Mean ( 1 / 28 ) 117.426829268293 3.69114072745269 31.8131542357451 Trimmed Mean ( 2 / 28 ) 117.6625 3.67405993100035 32.0251988834498 Trimmed Mean ( 3 / 28 ) 117.884615384615 3.65776994566837 32.2285483055645 Trimmed Mean ( 4 / 28 ) 118.105263157895 3.64424944489541 32.4086660212922 Trimmed Mean ( 5 / 28 ) 118.324324324324 3.63383805511154 32.5618044970065 Trimmed Mean ( 6 / 28 ) 118.513888888889 3.62772713538935 32.6689093379592 Trimmed Mean ( 7 / 28 ) 118.7 3.62064187942520 32.7842421186501 Trimmed Mean ( 8 / 28 ) 118.897058823529 3.61461887080228 32.8933874007966 Trimmed Mean ( 9 / 28 ) 119.106060606061 3.60426636524621 33.0458541451124 Trimmed Mean ( 10 / 28 ) 119.328125 3.58873172314459 33.2507788839228 Trimmed Mean ( 11 / 28 ) 119.564516129032 3.5732584681554 33.4609201082379 Trimmed Mean ( 12 / 28 ) 119.8 3.55511885265418 33.6978888653919 Trimmed Mean ( 13 / 28 ) 120.068965517241 3.53248360974183 33.9899568638102 Trimmed Mean ( 14 / 28 ) 120.375 3.50422402807826 34.3513996352609 Trimmed Mean ( 15 / 28 ) 120.703703703704 3.46577855395669 34.8272983471211 Trimmed Mean ( 16 / 28 ) 121.038461538462 3.4200590014648 35.3907524655631 Trimmed Mean ( 17 / 28 ) 121.38 3.36535651748755 36.0675011307919 Trimmed Mean ( 18 / 28 ) 121.6875 3.31196469647688 36.7417865683911 Trimmed Mean ( 19 / 28 ) 121.978260869565 3.26457921035927 37.3641602821276 Trimmed Mean ( 20 / 28 ) 122.272727272727 3.20648847276359 38.1329071697375 Trimmed Mean ( 21 / 28 ) 122.595238095238 3.13980468033811 39.0454982320864 Trimmed Mean ( 22 / 28 ) 122.975 3.06729804676564 40.0922890847445 Trimmed Mean ( 23 / 28 ) 123.315789473684 2.99409215899488 41.1863706677224 Trimmed Mean ( 24 / 28 ) 123.555555555556 2.95426633774889 41.8227544269766 Trimmed Mean ( 25 / 28 ) 123.764705882353 2.92784859037231 42.2715526647554 Trimmed Mean ( 26 / 28 ) 124 2.88139191274611 43.0347567269395 Trimmed Mean ( 27 / 28 ) 124.333333333333 2.84274973461257 43.7369958457769 Trimmed Mean ( 28 / 28 ) 124.642857142857 2.82244138274518 44.1613625370056 Median 127.5 Midrange 107 Midmean - Weighted Average at Xnp 121.627906976744 Midmean - Weighted Average at X(n+1)p 122.595238095238 Midmean - Empirical Distribution Function 121.627906976744 Midmean - Empirical Distribution Function - Averaging 122.595238095238 Midmean - Empirical Distribution Function - Interpolation 122.595238095238 Midmean - Closest Observation 121.627906976744 Midmean - True Basic - Statistics Graphics Toolkit 122.595238095238 Midmean - MS Excel (old versions) 122.272727272727 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/12/t1281610016g3oqchh9hiajt90/1c23n1281610024.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/12/t1281610016g3oqchh9hiajt90/1c23n1281610024.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/12/t1281610016g3oqchh9hiajt90/2c23n1281610024.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/12/t1281610016g3oqchh9hiajt90/2c23n1281610024.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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