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

Title produced by software: Central Tendency

Date of computation: Mon, 21 Apr 2008 14:59:27 -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/Apr/21/t1208811681boqkvgjwvmuz1wu.htm/, Retrieved Mon, 21 Apr 2008 23:01:23 +0200

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Dataseries X:

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110.84 110.84 111.01 112.66 114.04 114.16 114.2 114.2 114.23 114.23 114.23 114.23 114.23 114.23 115.97 116.96 117.08 117.08 117.08 117.63 119.12 119.47 119.5 119.52 119.49 119.49 119.5 119.5 119.56 122.35 122.92 122.92 123.04 123.04 123.04 123.06 123.33 128.21 129.57 129.79 131.66 135.01 136.01 136.31 136.37 136.4 136.4 136.4 137.34 142.18 143.79 144.08 144.08 144.09 144.09 144.11 144.11 144.15 144.15 144.16 144.2 144.38 144.38 144.28 144.46 144.53 144.53 145.34 147.98 150.42

Text written by user:

Output produced by software:

Summary of compuational 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 128.499142857143 1.51143761851175 85.01782758568 Geometric Mean 127.891263669177 Harmonic Mean 127.291883485393 Quadratic Mean 129.111023265140 Winsorized Mean ( 1 / 23 ) 128.464285714286 1.50449689728188 85.3868731443567 Winsorized Mean ( 2 / 23 ) 128.393714285714 1.49036488885189 86.149180812105 Winsorized Mean ( 3 / 23 ) 128.429714285714 1.47329035524794 87.1720321987044 Winsorized Mean ( 4 / 23 ) 128.508571428571 1.46151511454733 87.9283218828526 Winsorized Mean ( 5 / 23 ) 128.512142857143 1.45949635223549 88.0523905800125 Winsorized Mean ( 6 / 23 ) 128.508714285714 1.45792431537989 88.144983199782 Winsorized Mean ( 7 / 23 ) 128.508714285714 1.45792431537989 88.144983199782 Winsorized Mean ( 8 / 23 ) 128.500714285714 1.4556376207267 88.2779563100071 Winsorized Mean ( 9 / 23 ) 128.490428571429 1.45402437797583 88.3688269039217 Winsorized Mean ( 10 / 23 ) 128.484714285714 1.45313032166292 88.4192645148856 Winsorized Mean ( 11 / 23 ) 128.483142857143 1.45288469450333 88.4331312341789 Winsorized Mean ( 12 / 23 ) 128.483142857143 1.45288469450333 88.4331312341789 Winsorized Mean ( 13 / 23 ) 128.475714285714 1.45172450562246 88.498688138234 Winsorized Mean ( 14 / 23 ) 128.823714285714 1.40386205210583 91.763798367849 Winsorized Mean ( 15 / 23 ) 129.031571428571 1.37561268315862 93.7993470169927 Winsorized Mean ( 16 / 23 ) 129.059 1.3721332947159 94.0571885377373 Winsorized Mean ( 17 / 23 ) 129.056571428571 1.37174777643027 94.0818521057993 Winsorized Mean ( 18 / 23 ) 129.056571428571 1.37174777643027 94.0818521057994 Winsorized Mean ( 19 / 23 ) 129.127142857143 1.34053699173326 96.3249381803232 Winsorized Mean ( 20 / 23 ) 129.092857142857 1.21637757947658 106.128935061765 Winsorized Mean ( 21 / 23 ) 127.745857142857 0.987173485456057 129.405680992172 Winsorized Mean ( 22 / 23 ) 127.456714285714 0.945337227097823 134.826716469217 Winsorized Mean ( 23 / 23 ) 127.456714285714 0.945337227097823 134.826716469217 Trimmed Mean ( 1 / 23 ) 128.436470588235 1.49928476897093 85.6651606461598 Trimmed Mean ( 2 / 23 ) 128.406969696970 1.49198197320795 86.06469247137 Trimmed Mean ( 3 / 23 ) 128.41421875 1.49072848597030 86.1419231996606 Trimmed Mean ( 4 / 23 ) 128.408387096774 1.49494852210413 85.8948553733745 Trimmed Mean ( 5 / 23 ) 128.379166666667 1.50196427492301 85.4741812505808 Trimmed Mean ( 6 / 23 ) 128.347068965517 1.50869997700212 85.0713004056316 Trimmed Mean ( 7 / 23 ) 128.313392857143 1.51483772387058 84.7043817533719 Trimmed Mean ( 8 / 23 ) 128.277222222222 1.51977234991764 84.4055507584236 Trimmed Mean ( 9 / 23 ) 128.239615384615 1.52368151250480 84.1643180232599 Trimmed Mean ( 10 / 23 ) 128.2006 1.52607514218397 84.0067415137445 Trimmed Mean ( 11 / 23 ) 128.159166666667 1.52634308468802 83.9648490253172 Trimmed Mean ( 12 / 23 ) 128.114347826087 1.52373091732845 84.0793780378948 Trimmed Mean ( 13 / 23 ) 128.065454545455 1.51734375724406 84.4010817812696 Trimmed Mean ( 14 / 23 ) 128.012857142857 1.50628741458736 84.9856779676575 Trimmed Mean ( 15 / 23 ) 127.9115 1.49839433505781 85.3657124878713 Trimmed Mean ( 16 / 23 ) 127.773947368421 1.48967315476692 85.7731422222028 Trimmed Mean ( 17 / 23 ) 127.617777777778 1.47428735063415 86.5623500892715 Trimmed Mean ( 18 / 23 ) 127.443529411765 1.44894004422416 87.9563857178125 Trimmed Mean ( 19 / 23 ) 127.2475 1.40926971479283 90.2932197182044 Trimmed Mean ( 20 / 23 ) 127.016666666667 1.35714527410265 93.5910613921937 Trimmed Mean ( 21 / 23 ) 126.757142857143 1.31547252028505 96.3586398822501 Trimmed Mean ( 22 / 23 ) 126.630384615385 1.32590560990990 95.504826036591 Trimmed Mean ( 23 / 23 ) 126.520833333333 1.34325892329966 94.1894605267467 Median 123.05 Midrange 130.63 Midmean - Weighted Average at Xnp 127.332972972973 Midmean - Weighted Average at X(n+1)p 127.332972972973 Midmean - Empirical Distribution Function 127.332972972973 Midmean - Empirical Distribution Function - Averaging 127.332972972973 Midmean - Empirical Distribution Function - Interpolation 127.332972972973 Midmean - Closest Observation 127.332972972973 Midmean - True Basic - Statistics Graphics Toolkit 127.332972972973 Midmean - MS Excel (old versions) 127.332972972973 Number of observations 70

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208811681boqkvgjwvmuz1wu/14rk91208811565.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208811681boqkvgjwvmuz1wu/14rk91208811565.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208811681boqkvgjwvmuz1wu/2oag11208811565.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208811681boqkvgjwvmuz1wu/2oag11208811565.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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