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*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 16 Aug 2010 14:58:44 +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/16/t1281970705jxmn1jbpn7w2mcd.htm/, Retrieved Mon, 16 Aug 2010 16:58:25 +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/16/t1281970705jxmn1jbpn7w2mcd.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 «

93 92 91 89 87 86 87 89 90 90 91 93 93 87 89 92 98 92 92 87 92 98 101 102 102 90 87 92 105 90 88 83 98 109 118 118 115 107 101 111 128 115 111 105 120 132 135 142 139 127 113 130 143 139 137 134 139 157 152 153 147 132 117 123 139 134 134 128 118 144 140 151 144 135 122 124 146 146 147 148 132 161 159 173

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 116.785714285714 2.60048052780516 44.9092823564739 Geometric Mean 114.406926895109 Harmonic Mean 112.093548924541 Quadratic Mean 119.164552095791 Winsorized Mean ( 1 / 28 ) 116.678571428571 2.56158571500099 45.549352787723 Winsorized Mean ( 2 / 28 ) 116.654761904762 2.54846843230120 45.7744582692066 Winsorized Mean ( 3 / 28 ) 116.583333333333 2.5344560915993 45.9993502036828 Winsorized Mean ( 4 / 28 ) 116.392857142857 2.49934115570594 46.5694156546555 Winsorized Mean ( 5 / 28 ) 116.333333333333 2.4889505292479 46.7399138577842 Winsorized Mean ( 6 / 28 ) 116.261904761905 2.47674896610134 46.9413357401792 Winsorized Mean ( 7 / 28 ) 116.095238095238 2.42403928409532 47.8932989481505 Winsorized Mean ( 8 / 28 ) 116.095238095238 2.39594818663280 48.4548199927459 Winsorized Mean ( 9 / 28 ) 116.095238095238 2.39594818663280 48.4548199927459 Winsorized Mean ( 10 / 28 ) 115.976190476190 2.37764112834362 48.7778366102648 Winsorized Mean ( 11 / 28 ) 116.107142857143 2.3599630636582 49.1987118972803 Winsorized Mean ( 12 / 28 ) 115.821428571429 2.31722334150704 49.9828508097551 Winsorized Mean ( 13 / 28 ) 115.821428571429 2.31722334150704 49.9828508097551 Winsorized Mean ( 14 / 28 ) 115.654761904762 2.29303955940663 50.4373164563676 Winsorized Mean ( 15 / 28 ) 115.654761904762 2.24371973952647 51.5459929630829 Winsorized Mean ( 16 / 28 ) 115.273809523810 2.19086084764012 52.6157604431959 Winsorized Mean ( 17 / 28 ) 115.273809523810 2.13677141498200 53.9476561299753 Winsorized Mean ( 18 / 28 ) 115.273809523810 2.13677141498200 53.9476561299753 Winsorized Mean ( 19 / 28 ) 115.273809523810 2.13677141498200 53.9476561299753 Winsorized Mean ( 20 / 28 ) 115.273809523810 2.13677141498200 53.9476561299753 Winsorized Mean ( 21 / 28 ) 114.773809523810 2.07098298107007 55.4199675095864 Winsorized Mean ( 22 / 28 ) 114.25 2.00443248070555 56.9986772314649 Winsorized Mean ( 23 / 28 ) 114.523809523810 1.9680812267272 58.1905909006895 Winsorized Mean ( 24 / 28 ) 114.238095238095 1.93257095041193 59.1119799320925 Winsorized Mean ( 25 / 28 ) 114.238095238095 1.93257095041193 59.1119799320925 Winsorized Mean ( 26 / 28 ) 115.785714285714 1.73412572596103 66.76892716158 Winsorized Mean ( 27 / 28 ) 115.142857142857 1.65395116697832 69.6168420457158 Winsorized Mean ( 28 / 28 ) 115.142857142857 1.65395116697832 69.6168420457158 Trimmed Mean ( 1 / 28 ) 116.512195121951 2.53967280197939 45.8768527312429 Trimmed Mean ( 2 / 28 ) 116.3375 2.51350427060597 46.2849820310641 Trimmed Mean ( 3 / 28 ) 116.166666666667 2.49023511967664 46.6488749390663 Trimmed Mean ( 4 / 28 ) 116.013157894737 2.46821857920957 47.0027893282812 Trimmed Mean ( 5 / 28 ) 115.905405405405 2.45335371175745 47.2436586905266 Trimmed Mean ( 6 / 28 ) 115.805555555556 2.4376127146917 47.5077746590283 Trimmed Mean ( 7 / 28 ) 115.714285714286 2.42084998309248 47.7990319608603 Trimmed Mean ( 8 / 28 ) 115.647058823529 2.4115398511854 47.9556905380116 Trimmed Mean ( 9 / 28 ) 115.575757575758 2.4044500901299 48.067438808644 Trimmed Mean ( 10 / 28 ) 115.5 2.39398220412158 48.2459726731262 Trimmed Mean ( 11 / 28 ) 115.435483870968 2.38291345965038 48.4430029984826 Trimmed Mean ( 12 / 28 ) 115.35 2.37058540053779 48.6588671194176 Trimmed Mean ( 13 / 28 ) 115.293103448276 2.36108404315823 48.830580081367 Trimmed Mean ( 14 / 28 ) 115.232142857143 2.34700570103012 49.0975129743257 Trimmed Mean ( 15 / 28 ) 115.185185185185 2.33154679645572 49.4029051273098 Trimmed Mean ( 16 / 28 ) 115.134615384615 2.31836865431505 49.6619099685986 Trimmed Mean ( 17 / 28 ) 115.12 2.30821779469683 49.8739764785152 Trimmed Mean ( 18 / 28 ) 115.104166666667 2.30137169691301 50.0154611360973 Trimmed Mean ( 19 / 28 ) 115.086956521739 2.28877244632775 50.2832672188063 Trimmed Mean ( 20 / 28 ) 115.068181818182 2.26877828167690 50.7181255865745 Trimmed Mean ( 21 / 28 ) 115.047619047619 2.23916993003087 51.3795837933716 Trimmed Mean ( 22 / 28 ) 115.075 2.21022898802074 52.0647410850627 Trimmed Mean ( 23 / 28 ) 115.157894736842 2.18149671165744 52.7884796348597 Trimmed Mean ( 24 / 28 ) 115.222222222222 2.14665154945546 53.6753262314279 Trimmed Mean ( 25 / 28 ) 115.323529411765 2.10242224628337 54.852696510243 Trimmed Mean ( 26 / 28 ) 115.4375 2.03593597204285 56.6999658069652 Trimmed Mean ( 27 / 28 ) 115.4 1.99516657328966 57.8397821740401 Trimmed Mean ( 28 / 28 ) 115.428571428571 1.95344531575954 59.0897377558227 Median 116 Midrange 128 Midmean - Weighted Average at Xnp 113.043478260870 Midmean - Weighted Average at X(n+1)p 113.043478260870 Midmean - Empirical Distribution Function 113.043478260870 Midmean - Empirical Distribution Function - Averaging 113.043478260870 Midmean - Empirical Distribution Function - Interpolation 113.043478260870 Midmean - Closest Observation 113.043478260870 Midmean - True Basic - Statistics Graphics Toolkit 113.043478260870 Midmean - MS Excel (old versions) 115.12 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281970705jxmn1jbpn7w2mcd/1hbir1281970720.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t1281970705jxmn1jbpn7w2mcd/1hbir1281970720.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t1281970705jxmn1jbpn7w2mcd/2slhc1281970720.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t1281970705jxmn1jbpn7w2mcd/2slhc1281970720.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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