*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Thu, 19 May 2011 19:10:57 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/19/t1305832072spe3gu3l1zt4alf.htm/, Retrieved Thu, 19 May 2011 21:07:54 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

193.230 199.068 195.076 191.563 191.067 186.665 185.508 184.371 183.046 175.714 175.768 171.029 170.465 170.102 156.389 124.291 99.360 86.675 85.056 128.236 164.257 162.401 152.779 156.005 153.387 153.190 148.840 144.211 145.953 145.542 150.271 147.489 143.824 134.754 131.736 126.304 125.511 125.495 130.133 126.257 110.323 98.417 105.749 120.665 124.075 127.245 146.731 144.979 148.210 144.670 142.970 142.524 146.142 146.522 148.128 148.798 150.181 152.388 155.694 160.662 155.520 158.262 154.338 158.196 160.371 154.856 150.636 145.899 141.242 140.834 141.119 139.104 134.437 129.425 123.155 119.273 120.472 121.523 121.983 123.658 124.794 124.827 120.382 117.395 115.790 114.283 117.271 117.448 118.764 120.550 123.554 125.412 124.182 119.828 115.361 114.226 115.214 115.864 114.276 113.469

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 1 seconds R Server 'Herman Ole Andreas Wold' @ www.yougetit.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 140.53284 2.43666846692799 57.6741735313608 Geometric Mean 138.460058003079 Harmonic Mean 136.393877088428 Quadratic Mean 142.608825417714 Winsorized Mean ( 1 / 33 ) 140.50911 2.42360694224205 57.9752052822629 Winsorized Mean ( 2 / 33 ) 140.70703 2.36768147207838 59.4281923727206 Winsorized Mean ( 3 / 33 ) 140.68531 2.35155030486316 59.8266214884086 Winsorized Mean ( 4 / 33 ) 140.92103 2.3047932600138 61.142590289923 Winsorized Mean ( 5 / 33 ) 140.92963 2.22417403280704 63.3626811217369 Winsorized Mean ( 6 / 33 ) 141.04897 2.18466525376338 64.5631955545703 Winsorized Mean ( 7 / 33 ) 141.02237 2.1617273557825 65.2359649438553 Winsorized Mean ( 8 / 33 ) 140.92037 2.13995047708463 65.852164108014 Winsorized Mean ( 9 / 33 ) 140.26598 2.01629372424263 69.5662434066681 Winsorized Mean ( 10 / 33 ) 140.35368 2.00337195943603 70.0587224149385 Winsorized Mean ( 11 / 33 ) 139.8545 1.91286218877166 73.1126898847883 Winsorized Mean ( 12 / 33 ) 139.8383 1.89513864125978 73.7878997111492 Winsorized Mean ( 13 / 33 ) 139.80073 1.88622515874051 74.1166712532608 Winsorized Mean ( 14 / 33 ) 139.17941 1.73461372517767 80.236543721424 Winsorized Mean ( 15 / 33 ) 138.91961 1.69238615414044 82.0850546786452 Winsorized Mean ( 16 / 33 ) 138.64985 1.6530732799742 83.8739889390531 Winsorized Mean ( 17 / 33 ) 138.8241 1.61791262817998 85.804448016557 Winsorized Mean ( 18 / 33 ) 138.5361 1.5565946841121 88.9994687853006 Winsorized Mean ( 19 / 33 ) 138.62901 1.54190332601193 89.9077183772331 Winsorized Mean ( 20 / 33 ) 138.37841 1.48293807897693 93.3136804305855 Winsorized Mean ( 21 / 33 ) 138.31667 1.47077685767135 94.0432733072736 Winsorized Mean ( 22 / 33 ) 138.26541 1.46039416742933 94.676774999302 Winsorized Mean ( 23 / 33 ) 138.25184 1.45234068426652 95.1924307414285 Winsorized Mean ( 24 / 33 ) 138.2984 1.4083219733449 98.200839451172 Winsorized Mean ( 25 / 33 ) 138.2839 1.37923532331169 100.26128077112 Winsorized Mean ( 26 / 33 ) 138.34136 1.31441963246372 105.249006164566 Winsorized Mean ( 27 / 33 ) 138.3959 1.29575872952935 106.80684362456 Winsorized Mean ( 28 / 33 ) 138.30994 1.27917908001637 108.123985265793 Winsorized Mean ( 29 / 33 ) 138.31748 1.25232433421888 110.448608416025 Winsorized Mean ( 30 / 33 ) 137.82398 1.19019034798657 115.799947658082 Winsorized Mean ( 31 / 33 ) 137.74462 1.17402937815186 117.32638259601 Winsorized Mean ( 32 / 33 ) 137.87678 1.15237888722118 119.645354083562 Winsorized Mean ( 33 / 33 ) 137.44514 1.104180741959 124.477030595688 Trimmed Mean ( 1 / 33 ) 140.501632653061 2.34504317805011 59.9143051898462 Trimmed Mean ( 2 / 33 ) 140.49384375 2.25559691069501 62.2867690072825 Trimmed Mean ( 3 / 33 ) 140.380446808511 2.18790197047291 64.1621282411332 Trimmed Mean ( 4 / 33 ) 140.269989130435 2.11765038063749 66.23850207427 Trimmed Mean ( 5 / 33 ) 140.089144444444 2.0532480734987 68.228065693852 Trimmed Mean ( 6 / 33 ) 139.898125 2.00281394355036 69.8507844178498 Trimmed Mean ( 7 / 33 ) 139.675093023256 1.95458692909087 71.4601591489319 Trimmed Mean ( 8 / 33 ) 139.445964285714 1.90409043978534 73.2349479688763 Trimmed Mean ( 9 / 33 ) 139.221207317073 1.85026567855048 75.243900879219 Trimmed Mean ( 10 / 33 ) 139.0761 1.81325586138878 76.6996555541154 Trimmed Mean ( 11 / 33 ) 138.912307692308 1.77232582367839 78.3785384360088 Trimmed Mean ( 12 / 33 ) 138.799605263158 1.7410708756575 79.7208242374057 Trimmed Mean ( 13 / 33 ) 138.682635135135 1.70726049360668 81.2310925336068 Trimmed Mean ( 14 / 33 ) 138.563180555556 1.66880864732289 83.0311976018576 Trimmed Mean ( 15 / 33 ) 138.5003 1.64830779130784 84.0257509734319 Trimmed Mean ( 16 / 33 ) 138.459191176471 1.63007326871978 84.9404709796958 Trimmed Mean ( 17 / 33 ) 138.441136363636 1.61371368475243 85.7903961971266 Trimmed Mean ( 18 / 33 ) 138.4059375 1.59855468231732 86.5819224271777 Trimmed Mean ( 19 / 33 ) 138.394274193548 1.5884747686123 87.1239990260911 Trimmed Mean ( 20 / 33 ) 138.373683333333 1.57721229122056 87.7330744273174 Trimmed Mean ( 21 / 33 ) 138.373275862069 1.57085589891888 88.0878226687136 Trimmed Mean ( 22 / 33 ) 138.378089285714 1.56322511492107 88.5208969360125 Trimmed Mean ( 23 / 33 ) 138.387574074074 1.55370049367323 89.0696595885743 Trimmed Mean ( 24 / 33 ) 138.398923076923 1.54143492575961 89.7857708840485 Trimmed Mean ( 25 / 33 ) 138.4073 1.53138242127957 90.380624771931 Trimmed Mean ( 26 / 33 ) 138.417583333333 1.52142264192061 90.979047846033 Trimmed Mean ( 27 / 33 ) 138.423956521739 1.51721076908661 91.2358120190993 Trimmed Mean ( 28 / 33 ) 138.426318181818 1.5120796446511 91.5469754992691 Trimmed Mean ( 29 / 33 ) 138.426318181818 1.50526241612177 91.9615853682618 Trimmed Mean ( 30 / 33 ) 138.44645 1.49803981706951 92.4184046528426 Trimmed Mean ( 31 / 33 ) 138.501052631579 1.49647746179695 92.5513789330771 Trimmed Mean ( 32 / 33 ) 138.568833333333 1.49284981835372 92.8216834873209 Trimmed Mean ( 33 / 33 ) 138.632441176471 1.48771281237525 93.1849480782066 Median 141.883 Midrange 142.062 Midmean - Weighted Average at Xnp 138.076235294118 Midmean - Weighted Average at X(n+1)p 138.4073 Midmean - Empirical Distribution Function 138.076235294118 Midmean - Empirical Distribution Function - Averaging 138.4073 Midmean - Empirical Distribution Function - Interpolation 138.4073 Midmean - Closest Observation 138.076235294118 Midmean - True Basic - Statistics Graphics Toolkit 138.4073 Midmean - MS Excel (old versions) 138.398923076923 Number of observations 100

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305832072spe3gu3l1zt4alf/1bfyr1305832256.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305832072spe3gu3l1zt4alf/1bfyr1305832256.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305832072spe3gu3l1zt4alf/2eawz1305832256.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305832072spe3gu3l1zt4alf/2eawz1305832256.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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