WS6 - Mini Tutorial - Hyp 2 - Central tend.

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Tue, 16 Nov 2010 17:40:38 +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/Nov/16/t1289929174giqcuv2644o6h9u.htm/, Retrieved Tue, 16 Nov 2010 18:39:34 +0100

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/Nov/16/t1289929174giqcuv2644o6h9u.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:

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User-defined keywords:

Dataseries X:

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10,47 10,44 10,41 10,37 10,38 10,38 10,37 10,41 10,44 10,43 10,47 10,49 10,53 10,63 10,66 10,66 10,64 10,65 10,61 10,6 10,61 10,63 10,63 10,61 10,7 10,69 10,62 10,62 10,63 10,62 10,53 10,51 10,5 10,52 10,47 10,43 10,35 10,31 10,25 10,26 10,2 10,13 10,06 10,01 9,95 9,92 9,87 9,83 9,7 9,63 9,56 9,53 9,47 9,4 9,32 9,26 9,19 9,1 9,03 8,95 8,85 8,78 8,71 8,61 8,54 8,49 8,42 8,36 8,3 8,19 8,15 8,1 8,04 8,05 8,04 8 8,02 8 8 8,01 8,04 8,1 8,14 8,17 8,17 8,22 8,21 8,29 8,37 8,43 8,47 8,51 8,55 8,59 8,66 8,71 8,78 8,81 8,84 8,81 8,82 8,84 8,83 8,83 8,88 8,88 8,89 8,93 8,95 8,92 8,97 8,99 9,01 8,99 9,03 9,04 9,07 9,04 9,07 9,09 9,04 9,08 9,13 9,09 9,05 9,06 8,99 8,98 8,99 8,94 8,87 8,83 8,8 8,79 8,71 8,6 8,5 8,38 8,26 8,23 8,17 8,1 8,02 7,9 7,82 7,72 7,63 7,53 7,56 7,49 7,53 7,47 7,39 7,37 7,34 7,39 7,32 7,24 7,18 7,31 7,39 7,48 7,51 7,61 7,69 7,86 8,05 8, etc...

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 9.05094444444445 0.075564611659224 119.777555203509 Geometric Mean 8.9945324766582 Harmonic Mean 8.93835329244322 Quadratic Mean 9.10723268738766 Winsorized Mean ( 1 / 60 ) 9.05122222222222 0.0755124703714475 119.863940057835 Winsorized Mean ( 2 / 60 ) 9.05166666666667 0.0753700780510754 120.096288881812 Winsorized Mean ( 3 / 60 ) 9.05183333333333 0.0753486197226136 120.132702717800 Winsorized Mean ( 4 / 60 ) 9.05205555555555 0.0752654189190105 120.268453767540 Winsorized Mean ( 5 / 60 ) 9.05261111111111 0.075127467260575 120.496689708874 Winsorized Mean ( 6 / 60 ) 9.05294444444444 0.0750052221323781 120.697521946762 Winsorized Mean ( 7 / 60 ) 9.05294444444445 0.0750052221323781 120.697521946762 Winsorized Mean ( 8 / 60 ) 9.05294444444444 0.0750052221323781 120.697521946762 Winsorized Mean ( 9 / 60 ) 9.05694444444444 0.0745195285259724 121.537865625221 Winsorized Mean ( 10 / 60 ) 9.05694444444444 0.0743882185504366 121.752404089415 Winsorized Mean ( 11 / 60 ) 9.05755555555556 0.074316025501371 121.878901548475 Winsorized Mean ( 12 / 60 ) 9.05888888888889 0.0741596784475357 122.153831819775 Winsorized Mean ( 13 / 60 ) 9.05961111111111 0.0739071155231115 122.581040363807 Winsorized Mean ( 14 / 60 ) 9.05961111111111 0.0739071155231115 122.581040363807 Winsorized Mean ( 15 / 60 ) 9.06211111111111 0.0736201007592992 123.092891990731 Winsorized Mean ( 16 / 60 ) 9.06566666666667 0.073014887557881 124.16189314104 Winsorized Mean ( 17 / 60 ) 9.06094444444444 0.0720401767871385 125.776266085762 Winsorized Mean ( 18 / 60 ) 9.06694444444444 0.0713839470111385 127.016574791384 Winsorized Mean ( 19 / 60 ) 9.06905555555555 0.0709243176082438 127.869479205274 Winsorized Mean ( 20 / 60 ) 9.07905555555556 0.0696453593899662 130.361242085335 Winsorized Mean ( 21 / 60 ) 9.08255555555555 0.0690450119118555 131.545426730472 Winsorized Mean ( 22 / 60 ) 9.08622222222222 0.0684263188733664 132.788412000325 Winsorized Mean ( 23 / 60 ) 9.09644444444444 0.0669295386379263 135.910759726795 Winsorized Mean ( 24 / 60 ) 9.09644444444444 0.0669295386379263 135.910759726795 Winsorized Mean ( 25 / 60 ) 9.09644444444444 0.0669295386379263 135.910759726795 Winsorized Mean ( 26 / 60 ) 9.09355555555556 0.0663032750656663 137.150925750641 Winsorized Mean ( 27 / 60 ) 9.09505555555556 0.0661667239970961 137.456639926056 Winsorized Mean ( 28 / 60 ) 9.0935 0.0659904002856266 137.800346120656 Winsorized Mean ( 29 / 60 ) 9.09672222222222 0.0656992106897872 138.460144752337 Winsorized Mean ( 30 / 60 ) 9.09338888888889 0.0653225850947189 139.207425359901 Winsorized Mean ( 31 / 60 ) 9.09338888888889 0.0653225850947189 139.207425359901 Winsorized Mean ( 32 / 60 ) 9.08983333333333 0.064564552744799 140.786746703911 Winsorized Mean ( 33 / 60 ) 9.08983333333333 0.064564552744799 140.786746703911 Winsorized Mean ( 34 / 60 ) 9.09738888888889 0.0635141671947586 143.234010468764 Winsorized Mean ( 35 / 60 ) 9.09738888888889 0.0635141671947586 143.234010468764 Winsorized Mean ( 36 / 60 ) 9.09338888888889 0.0630676660587943 144.184642577571 Winsorized Mean ( 37 / 60 ) 9.09338888888889 0.0614369703653897 148.011674970412 Winsorized Mean ( 38 / 60 ) 9.08494444444444 0.060093218359073 151.180860212204 Winsorized Mean ( 39 / 60 ) 9.08711111111111 0.0594815949860019 152.771813083520 Winsorized Mean ( 40 / 60 ) 9.076 0.0582761145283291 155.741337140588 Winsorized Mean ( 41 / 60 ) 9.06005555555556 0.0565745497976418 160.143661557395 Winsorized Mean ( 42 / 60 ) 9.04838888888889 0.054453276339353 166.167942448482 Winsorized Mean ( 43 / 60 ) 9.04122222222222 0.0528006837156626 171.233052036034 Winsorized Mean ( 44 / 60 ) 9.029 0.0510947258706211 176.710997977809 Winsorized Mean ( 45 / 60 ) 9.024 0.0501213672870293 180.042973455261 Winsorized Mean ( 46 / 60 ) 9.01377777777778 0.0486280525590873 185.361685352817 Winsorized Mean ( 47 / 60 ) 9.019 0.048166062576354 187.248023142910 Winsorized Mean ( 48 / 60 ) 9.027 0.0474669279489806 190.174514973933 Winsorized Mean ( 49 / 60 ) 9.027 0.0469612212408761 192.222428665094 Winsorized Mean ( 50 / 60 ) 9.03533333333333 0.0447102819381288 202.086252684263 Winsorized Mean ( 51 / 60 ) 9.03533333333333 0.0441903787231406 204.463813038151 Winsorized Mean ( 52 / 60 ) 9.00355555555555 0.0405603689226294 221.979133689100 Winsorized Mean ( 53 / 60 ) 9.01533333333333 0.0395593669482431 227.893771534019 Winsorized Mean ( 54 / 60 ) 8.99733333333333 0.0372949057351360 241.248319468384 Winsorized Mean ( 55 / 60 ) 9.00344444444445 0.0356853031091261 252.301190126137 Winsorized Mean ( 56 / 60 ) 8.99411111111111 0.0336969726318149 266.911547496684 Winsorized Mean ( 57 / 60 ) 8.98777777777778 0.0325442501179397 276.170990119799 Winsorized Mean ( 58 / 60 ) 8.97488888888889 0.0307849400177871 291.535045502876 Winsorized Mean ( 59 / 60 ) 8.98144444444445 0.0296602029053869 302.811294753929 Winsorized Mean ( 60 / 60 ) 8.96144444444444 0.0272578922360291 328.765128530347 Trimmed Mean ( 1 / 60 ) 9.05219101123595 0.0751131619483163 120.514045427412 Trimmed Mean ( 2 / 60 ) 9.05318181818182 0.0746832745627137 121.221007932366 Trimmed Mean ( 3 / 60 ) 9.05396551724138 0.0742980715413166 121.86003390689 Trimmed Mean ( 4 / 60 ) 9.05470930232558 0.0738903324364164 122.542543845195 Trimmed Mean ( 5 / 60 ) 9.05541176470588 0.0734742286488751 123.246095008097 Trimmed Mean ( 6 / 60 ) 9.0560119047619 0.0730575441761911 123.957245030325 Trimmed Mean ( 7 / 60 ) 9.05656626506024 0.0726319330014893 124.691246546812 Trimmed Mean ( 8 / 60 ) 9.05713414634146 0.0721715791297777 125.494471030696 Trimmed Mean ( 9 / 60 ) 9.05771604938272 0.0716737829397029 126.374187016230 Trimmed Mean ( 10 / 60 ) 9.0578125 0.0712075026011322 127.203063850409 Trimmed Mean ( 11 / 60 ) 9.05791139240506 0.0707203153790799 128.080755068077 Trimmed Mean ( 12 / 60 ) 9.05794871794872 0.0702015718795877 129.027719400432 Trimmed Mean ( 13 / 60 ) 9.05794871794872 0.0696582392977329 130.034132491252 Trimmed Mean ( 14 / 60 ) 9.05769736842105 0.0690981887839837 131.084439806916 Trimmed Mean ( 15 / 60 ) 9.05753333333333 0.0684903322210909 132.245428509458 Trimmed Mean ( 16 / 60 ) 9.05716216216216 0.067861175829523 133.466036381613 Trimmed Mean ( 17 / 60 ) 9.05650684931507 0.0672401903447488 134.688893694102 Trimmed Mean ( 18 / 60 ) 9.05618055555555 0.0666625141865114 135.851170122653 Trimmed Mean ( 19 / 60 ) 9.05542253521127 0.0660960715372286 137.003944782267 Trimmed Mean ( 20 / 60 ) 9.0545 0.0655208654777212 138.192619007433 Trimmed Mean ( 21 / 60 ) 9.05289855072464 0.0650084585386182 139.257240584266 Trimmed Mean ( 22 / 60 ) 9.0510294117647 0.0644995211523801 140.327079179110 Trimmed Mean ( 23 / 60 ) 9.04888059701493 0.0639938714353092 141.402299846203 Trimmed Mean ( 24 / 60 ) 9.0460606060606 0.0635630284730241 142.31638773945 Trimmed Mean ( 25 / 60 ) 9.04315384615385 0.0630856375875814 143.347268759855 Trimmed Mean ( 26 / 60 ) 9.04315384615385 0.0625570590304159 144.558487664149 Trimmed Mean ( 27 / 60 ) 9.03722222222222 0.0620261735730399 145.700140789441 Trimmed Mean ( 28 / 60 ) 9.0341129032258 0.0614485526887943 147.019132394851 Trimmed Mean ( 29 / 60 ) 9.03098360655738 0.0608236616276352 148.478131123467 Trimmed Mean ( 30 / 60 ) 9.02758333333333 0.0601536310242102 150.075451466928 Trimmed Mean ( 31 / 60 ) 9.0242372881356 0.0594434819811709 151.812057224274 Trimmed Mean ( 32 / 60 ) 9.02077586206897 0.0586539608157143 153.796533714261 Trimmed Mean ( 33 / 60 ) 9.01736842105263 0.0578439743016645 155.891232058603 Trimmed Mean ( 34 / 60 ) 9.01383928571429 0.056941180439589 158.300885512505 Trimmed Mean ( 35 / 60 ) 9.00981818181818 0.0560234940914215 160.822139495898 Trimmed Mean ( 36 / 60 ) 9.00564814814815 0.0549965027913829 163.749469349153 Trimmed Mean ( 37 / 60 ) 9.00150943396226 0.0538901402288706 167.034440729473 Trimmed Mean ( 38 / 60 ) 8.99721153846154 0.0528031375538039 170.391608439817 Trimmed Mean ( 39 / 60 ) 8.99313725490196 0.0517156593621377 173.895825090960 Trimmed Mean ( 40 / 60 ) 8.9888 0.0505461645179409 177.833473335242 Trimmed Mean ( 41 / 60 ) 8.98479591836735 0.0493537511631925 182.048896114468 Trimmed Mean ( 42 / 60 ) 8.98135416666667 0.0481888235458133 186.378365475722 Trimmed Mean ( 43 / 60 ) 8.97829787234043 0.0470929410790076 190.650608490932 Trimmed Mean ( 44 / 60 ) 8.9754347826087 0.0460219761594354 195.024975709752 Trimmed Mean ( 45 / 60 ) 8.973 0.0449872918662945 199.456327059393 Trimmed Mean ( 46 / 60 ) 8.97068181818182 0.0439104708792284 204.29482168057 Trimmed Mean ( 47 / 60 ) 8.96872093023256 0.0428447381505062 209.330744389824 Trimmed Mean ( 48 / 60 ) 8.96642857142857 0.0416659126232893 215.198180164587 Trimmed Mean ( 49 / 60 ) 8.96642857142857 0.0403781851728593 222.061207878542 Trimmed Mean ( 50 / 60 ) 8.96075 0.038942823634891 230.100161303444 Trimmed Mean ( 51 / 60 ) 8.9573076923077 0.0375470281545805 238.562361192225 Trimmed Mean ( 52 / 60 ) 8.9573076923077 0.0359750606135637 248.986590697515 Trimmed Mean ( 53 / 60 ) 8.95135135135135 0.0346625581940016 258.242663488709 Trimmed Mean ( 54 / 60 ) 8.94833333333333 0.033236361293771 269.233242900461 Trimmed Mean ( 55 / 60 ) 8.946 0.0318942351534700 280.489560478665 Trimmed Mean ( 56 / 60 ) 8.94323529411765 0.0305254259917616 292.976592579946 Trimmed Mean ( 57 / 60 ) 8.94075757575758 0.0292049350860908 306.13858751618 Trimmed Mean ( 58 / 60 ) 8.9384375 0.0278051421513993 321.467067182397 Trimmed Mean ( 59 / 60 ) 8.9366129032258 0.0264214545416127 338.233191861221 Trimmed Mean ( 60 / 60 ) 8.93433333333333 0.0249183601072210 358.544193714589 Median 8.945 Midrange 8.94 Midmean - Weighted Average at Xnp 8.96472527472528 Midmean - Weighted Average at X(n+1)p 8.973 Midmean - Empirical Distribution Function 8.96472527472528 Midmean - Empirical Distribution Function - Averaging 8.973 Midmean - Empirical Distribution Function - Interpolation 8.973 Midmean - Closest Observation 8.96472527472528 Midmean - True Basic - Statistics Graphics Toolkit 8.973 Midmean - MS Excel (old versions) 8.9754347826087 Number of observations 180

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289929174giqcuv2644o6h9u/1lyib1289929234.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289929174giqcuv2644o6h9u/1lyib1289929234.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289929174giqcuv2644o6h9u/2lyib1289929234.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289929174giqcuv2644o6h9u/2lyib1289929234.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')

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