*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 28 Jul 2009 05:03:28 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jul/28/t1248779047j1ua4d9onju3twy.htm/, Retrieved Tue, 28 Jul 2009 13:04:09 +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/2009/Jul/28/t1248779047j1ua4d9onju3twy.htm/}, year = {2009}, } @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 = {2009}, 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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6430 5124 4836 4629 4597 4490 4517 4560 4135 4559 4739 4886 5605 4616 4997 4607 4882 4555 4462 4476 4277 4369 4492 5183 6039 4923 4953 4892 4614 4363 4675 4556 4217 4664 4601 5428 5607 4869 5174 5031 4671 4491 4504 4615 4582 4800 4775 5791 5818 4714 4915 4598 4407 4383 4412 4274 4236 4637 4534 5271 5467 5204 5752 4724 4623 4451 4138 4140 4169 4603 4434 5185

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 4777.04166666667 55.6494816094791 85.8416202362784 Geometric Mean 4755.59859075243 Harmonic Mean 4735.58504480271 Quadratic Mean 4800.00046730322 Winsorized Mean ( 1 / 24 ) 4771.65277777778 53.5980561908206 89.0266012780327 Winsorized Mean ( 2 / 24 ) 4765.56944444444 51.6835646544887 92.2066710433557 Winsorized Mean ( 3 / 24 ) 4765.65277777778 51.1611922249245 93.1497600139206 Winsorized Mean ( 4 / 24 ) 4766.15277777778 50.1304115391115 95.075077810986 Winsorized Mean ( 5 / 24 ) 4757.40277777778 47.2530921549181 100.679184383971 Winsorized Mean ( 6 / 24 ) 4760.40277777778 46.7325225283544 101.864879536290 Winsorized Mean ( 7 / 24 ) 4747.27777777778 43.4096034382482 109.360081681717 Winsorized Mean ( 8 / 24 ) 4752.5 41.0307911402674 115.827647187040 Winsorized Mean ( 9 / 24 ) 4733.625 36.6102555685347 129.297786275723 Winsorized Mean ( 10 / 24 ) 4726.26388888889 34.4656277543382 137.129778182961 Winsorized Mean ( 11 / 24 ) 4727.02777777778 33.3971453301907 141.539875071436 Winsorized Mean ( 12 / 24 ) 4727.52777777778 33.2207957819708 142.306277333171 Winsorized Mean ( 13 / 24 ) 4729.875 32.3855812884567 146.048791215796 Winsorized Mean ( 14 / 24 ) 4723.45833333333 30.1115163754207 156.86550867923 Winsorized Mean ( 15 / 24 ) 4706.375 26.3084169093061 178.892368029001 Winsorized Mean ( 16 / 24 ) 4701.93055555556 24.608517985225 191.069228889712 Winsorized Mean ( 17 / 24 ) 4694.84722222222 22.4627378786640 209.006010201525 Winsorized Mean ( 18 / 24 ) 4687.59722222222 21.2373469622411 220.724237851203 Winsorized Mean ( 19 / 24 ) 4685.75 20.8748201945158 224.468999317706 Winsorized Mean ( 20 / 24 ) 4682.69444444444 19.4630246015065 240.594385524334 Winsorized Mean ( 21 / 24 ) 4684.73611111111 18.7133365389294 250.34210769231 Winsorized Mean ( 22 / 24 ) 4688.70833333333 17.8831347697783 262.186042530812 Winsorized Mean ( 23 / 24 ) 4691.26388888889 16.4503211085901 285.177648382753 Winsorized Mean ( 24 / 24 ) 4680.59722222222 14.7572117024496 317.173549895287 Trimmed Mean ( 1 / 24 ) 4762.6 51.2212850425277 92.9808769156366 Trimmed Mean ( 2 / 24 ) 4753.01470588235 48.3405822593455 98.3234889555654 Trimmed Mean ( 3 / 24 ) 4746.16666666667 46.1411616537425 102.861880727741 Trimmed Mean ( 4 / 24 ) 4738.859375 43.7151894799009 108.403038654992 Trimmed Mean ( 5 / 24 ) 4730.93548387097 41.1448401304978 114.982473351847 Trimmed Mean ( 6 / 24 ) 4724.58333333333 39.0120529808132 121.10573457021 Trimmed Mean ( 7 / 24 ) 4717.17241379310 36.5078958545736 129.209649128605 Trimmed Mean ( 8 / 24 ) 4711.64285714286 34.4182584111888 136.893703360981 Trimmed Mean ( 9 / 24 ) 4704.83333333333 32.4376276187793 145.042460830568 Trimmed Mean ( 10 / 24 ) 4700.40384615385 31.1726963575762 150.785924715539 Trimmed Mean ( 11 / 24 ) 4696.68 30.115416622842 155.956002828055 Trimmed Mean ( 12 / 24 ) 4692.54166666667 29.0115371757961 161.747433037832 Trimmed Mean ( 13 / 24 ) 4687.97826086957 27.6153267170831 169.760014389746 Trimmed Mean ( 14 / 24 ) 4682.70454545455 25.9761758539066 180.269204050307 Trimmed Mean ( 15 / 24 ) 4677.71428571429 24.4233681657577 191.526175012691 Trimmed Mean ( 16 / 24 ) 4674.275 23.4159431633827 199.619334885879 Trimmed Mean ( 17 / 24 ) 4671 22.4952342036634 207.643981730109 Trimmed Mean ( 18 / 24 ) 4668.19444444444 21.8020975925626 214.116757556250 Trimmed Mean ( 19 / 24 ) 4665.91176470588 21.1609723689398 220.496094572409 Trimmed Mean ( 20 / 24 ) 4663.5625 20.3286970162633 229.407841352010 Trimmed Mean ( 21 / 24 ) 4661.26666666667 19.5391698157348 238.560118501707 Trimmed Mean ( 22 / 24 ) 4658.39285714286 18.5662932969294 250.905917656342 Trimmed Mean ( 23 / 24 ) 4654.57692307692 17.3092392471076 268.907076540335 Trimmed Mean ( 24 / 24 ) 4649.79166666667 15.8287917781045 293.75531195619 Median 4619.5 Midrange 5282.5 Midmean - Weighted Average at Xnp 4663.37837837838 Midmean - Weighted Average at X(n+1)p 4668.19444444444 Midmean - Empirical Distribution Function 4663.37837837838 Midmean - Empirical Distribution Function - Averaging 4668.19444444444 Midmean - Empirical Distribution Function - Interpolation 4668.19444444444 Midmean - Closest Observation 4663.37837837838 Midmean - True Basic - Statistics Graphics Toolkit 4668.19444444444 Midmean - MS Excel (old versions) 4671 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/28/t1248779047j1ua4d9onju3twy/1fyly1248779004.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/28/t1248779047j1ua4d9onju3twy/1fyly1248779004.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/28/t1248779047j1ua4d9onju3twy/2eg6s1248779004.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jul/28/t1248779047j1ua4d9onju3twy/2eg6s1248779004.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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