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Central Tendency - Algemeen indexcijfer

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

Title produced by software: Central Tendency

Date of computation: Mon, 22 Oct 2007 13:18:25 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Oct/22/2y7mw8fxnj23ooi1193084015.htm/, Retrieved Mon, 22 Oct 2007 22:13:37 +0200

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Dataseries X:

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91.19 91.53 91.88 92.06 92.32 92.67 92.85 92.82 93.46 93.23 93.54 93.29 93.2 93.6 93.81 94.62 95.22 95.38 95.31 95.3 95.57 95.42 95.53 95.33 95.9 96.06 96.31 96.34 96.49 96.22 96.53 96.5 96.77 96.66 96.58 96.63 97.06 97.73 98.01 97.76 97.49 97.77 97.96 98.23 98.51 98.19 98.37 98.31 98.6 98.97 99.11 99.64 100.03 99.98 100.32 100.44 100.51 101 100.88 100.55 100.83 101.51 102.16 102.39 102.54 102.85 103.47 103.57 103.69 103.5 103.47 103.45 103.48 103.93 103.89 104.4 104.79 104.77 105.13 105.26 104.96 104.75 105.01 105.15 105.2 105.77 105.78 106.26 106.13 106.12 106.57 106.44 106.54

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 99.1967741935484 0.464548123833204 213.533903387725 Geometric Mean 99.0967951221295 Harmonic Mean 98.9969818871674 Quadratic Mean 99.296797867135 Winsorized Mean ( 1 / 31 ) 99.2001075268818 0.463821516958648 213.875604946818 Winsorized Mean ( 2 / 31 ) 99.2054838709677 0.462128627699816 214.670717035536 Winsorized Mean ( 3 / 31 ) 99.2054838709678 0.46016053858913 215.588855522326 Winsorized Mean ( 4 / 31 ) 99.2110752688172 0.457375444162662 216.913864823783 Winsorized Mean ( 5 / 31 ) 99.2293548387097 0.454269209180865 218.437333707119 Winsorized Mean ( 6 / 31 ) 99.2170967741935 0.449210324231423 220.870027740233 Winsorized Mean ( 7 / 31 ) 99.2186021505376 0.448741906374532 221.103936898033 Winsorized Mean ( 8 / 31 ) 99.2048387096774 0.437388244269261 226.811854249576 Winsorized Mean ( 9 / 31 ) 99.201935483871 0.436084630552196 227.483218929903 Winsorized Mean ( 10 / 31 ) 99.2030107526882 0.434325117013160 228.407261903028 Winsorized Mean ( 11 / 31 ) 99.220752688172 0.431024395875793 230.197533219823 Winsorized Mean ( 12 / 31 ) 99.2155913978495 0.42723423296462 232.227625369303 Winsorized Mean ( 13 / 31 ) 99.2169892473118 0.42499778029138 233.45295869378 Winsorized Mean ( 14 / 31 ) 99.2230107526882 0.416757637145812 238.083245293889 Winsorized Mean ( 15 / 31 ) 99.3504301075269 0.398619430120539 249.236295575166 Winsorized Mean ( 16 / 31 ) 99.4502150537634 0.385282389120501 258.122919349577 Winsorized Mean ( 17 / 31 ) 99.4008602150538 0.374107217005581 265.701530728745 Winsorized Mean ( 18 / 31 ) 99.3118279569892 0.360938142663364 275.149163300301 Winsorized Mean ( 19 / 31 ) 99.3077419354839 0.359311426861720 276.383478262444 Winsorized Mean ( 20 / 31 ) 99.2754838709677 0.352105717877679 281.947945831018 Winsorized Mean ( 21 / 31 ) 99.2574193548387 0.347345436622995 285.759963682988 Winsorized Mean ( 22 / 31 ) 99.2668817204301 0.342006392584747 290.248614858369 Winsorized Mean ( 23 / 31 ) 99.2718279569892 0.340168603048773 291.831247996617 Winsorized Mean ( 24 / 31 ) 99.3544086021505 0.329934700438830 301.133553003077 Winsorized Mean ( 25 / 31 ) 99.3974193548387 0.325087175104083 305.756200080839 Winsorized Mean ( 26 / 31 ) 99.436559139785 0.319380078825271 311.342396512419 Winsorized Mean ( 27 / 31 ) 99.288494623656 0.293089926725774 338.764609663825 Winsorized Mean ( 28 / 31 ) 99.2041935483871 0.279876430464604 354.457120178733 Winsorized Mean ( 29 / 31 ) 99.2041935483871 0.268661484116538 369.25350083064 Winsorized Mean ( 30 / 31 ) 99.1332258064516 0.258807554359972 383.038377885093 Winsorized Mean ( 31 / 31 ) 98.926559139785 0.230699309599809 428.811682667762 Trimmed Mean ( 1 / 31 ) 99.2037362637363 0.459328746537428 215.975457690308 Trimmed Mean ( 2 / 31 ) 99.2075280898876 0.454132322698329 218.455113479754 Trimmed Mean ( 3 / 31 ) 99.2086206896552 0.44912821112064 220.891536610705 Trimmed Mean ( 4 / 31 ) 99.2097647058823 0.444136305839145 223.376840401365 Trimmed Mean ( 5 / 31 ) 99.2093975903614 0.439233843598437 225.869201648000 Trimmed Mean ( 6 / 31 ) 99.2048148148148 0.434353326303979 228.396581324641 Trimmed Mean ( 7 / 31 ) 99.2024050632911 0.429845583227267 230.786144918560 Trimmed Mean ( 8 / 31 ) 99.1996103896104 0.424604010830818 233.628528839159 Trimmed Mean ( 9 / 31 ) 99.1988 0.420708324203425 235.789962530037 Trimmed Mean ( 10 / 31 ) 99.1983561643836 0.416251848931525 238.313310605143 Trimmed Mean ( 11 / 31 ) 99.1977464788732 0.411199658122871 241.239856403849 Trimmed Mean ( 12 / 31 ) 99.1949275362319 0.405692477530908 244.507682617000 Trimmed Mean ( 13 / 31 ) 99.1949275362319 0.399696195307014 248.175811280962 Trimmed Mean ( 14 / 31 ) 99.1898461538461 0.392815618588544 252.509934585220 Trimmed Mean ( 15 / 31 ) 99.1863492063492 0.385874453395495 257.043057226413 Trimmed Mean ( 16 / 31 ) 99.1696721311475 0.380377362758455 260.713916863979 Trimmed Mean ( 17 / 31 ) 99.142033898305 0.375603607696482 263.953891461074 Trimmed Mean ( 18 / 31 ) 99.1171929824561 0.37141205477907 266.865848071126 Trimmed Mean ( 19 / 31 ) 99.098909090909 0.368201715387039 269.142985894947 Trimmed Mean ( 20 / 31 ) 99.0796226415094 0.364155679146808 272.080399442475 Trimmed Mean ( 21 / 31 ) 99.0617647058824 0.360017614588928 275.158105302687 Trimmed Mean ( 22 / 31 ) 99.044081632653 0.355299040280767 278.762592644173 Trimmed Mean ( 23 / 31 ) 99.0240425531915 0.349895935312279 283.009982567570 Trimmed Mean ( 24 / 31 ) 99.0017777777778 0.342951580775557 288.675671224181 Trimmed Mean ( 25 / 31 ) 98.97 0.335471932502902 295.0172291959 Trimmed Mean ( 26 / 31 ) 98.97 0.326165862923794 303.434575012908 Trimmed Mean ( 27 / 31 ) 98.8848717948718 0.314533450908164 314.385867415239 Trimmed Mean ( 28 / 31 ) 98.8472972972973 0.30537198520271 323.694713618478 Trimmed Mean ( 29 / 31 ) 98.8134285714286 0.295980053511771 333.851647768213 Trimmed Mean ( 30 / 31 ) 98.7754545454546 0.285394494021225 346.101472224298 Trimmed Mean ( 31 / 31 ) 98.7396774193548 0.273052629481708 361.614087389587 Median 98.37 Midrange 98.88 Midmean - Weighted Average at Xnp 98.9271739130435 Midmean - Weighted Average at X(n+1)p 99.0240425531915 Midmean - Empirical Distribution Function 99.0240425531915 Midmean - Empirical Distribution Function - Averaging 99.0240425531915 Midmean - Empirical Distribution Function - Interpolation 99.0240425531915 Midmean - Closest Observation 98.95125 Midmean - True Basic - Statistics Graphics Toolkit 99.0240425531915 Midmean - MS Excel (old versions) 99.0240425531915 Number of observations 93

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/2y7mw8fxnj23ooi1193084015/1t7ao1193084302.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/2y7mw8fxnj23ooi1193084015/1t7ao1193084302.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/2y7mw8fxnj23ooi1193084015/2bvwl1193084302.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/2y7mw8fxnj23ooi1193084015/2bvwl1193084302.ps (open in new window)

Parameters:

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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Software written by Ed van Stee & Patrick Wessa

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