Centrummaten(eigengeg)-JensVanEyseren-MAR202a

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Thu, 07 May 2009 17:49:09 -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/May/08/t1241740192i0p6j1eapq3ho2w.htm/, Retrieved Fri, 08 May 2009 01:49:55 +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/May/08/t1241740192i0p6j1eapq3ho2w.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:

» Textbox « » Textfile « » CSV «

166,7 159,7 191 239,4 321,9 362,7 413,6 407,1 383,2 347,7 333,8 312,3 295,4 283,3 287,6 265,7 250,2 234,7 244 231,2 223,8 223,5 210,5 201,6 190,7 207,5 198,8 196,6 204,2 227,4 229,7 217,9 221,4 216,3 197 193,8 196,8 180,5 174,8 181,6 190 190,6 179 174,1 161,1 168,6 169,4 152,2 148,3 137,7 145 153,4 141,7 142,7 135,9 131,8 134,6 127,5 126,5 118,7 117,1 110,7 107,1 105,4 99 104 101,1 99,3 95,8 94,1 104,8 110,9

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 195.884722222222 9.12485163120793 21.4671679210954 Geometric Mean 182.25799236839 Harmonic Mean 170.046623143457 Quadratic Mean 210.434055057108 Winsorized Mean ( 1 / 24 ) 195.818055555556 9.09122268539549 21.5392431064444 Winsorized Mean ( 2 / 24 ) 195.243055555556 8.86969657415858 22.0123714405729 Winsorized Mean ( 3 / 24 ) 194.401388888889 8.62275429316955 22.5451615898278 Winsorized Mean ( 4 / 24 ) 193.668055555556 8.38476868829058 23.0976026596912 Winsorized Mean ( 5 / 24 ) 192.904166666667 8.11048256127591 23.7845486022868 Winsorized Mean ( 6 / 24 ) 191.979166666667 7.86333629310426 24.4144672834382 Winsorized Mean ( 7 / 24 ) 191.104166666667 7.64126646560351 25.0094886138188 Winsorized Mean ( 8 / 24 ) 189.415277777778 7.20649557558432 26.2839650411385 Winsorized Mean ( 9 / 24 ) 188.890277777778 6.93580167773281 27.2340944211546 Winsorized Mean ( 10 / 24 ) 188.320833333333 6.81287270520016 27.6419128144859 Winsorized Mean ( 11 / 24 ) 186.579166666667 6.15320728152189 30.3222625421648 Winsorized Mean ( 12 / 24 ) 184.2625 5.66363991158708 32.5342894104236 Winsorized Mean ( 13 / 24 ) 184.551388888889 5.25812806718825 35.0983061900918 Winsorized Mean ( 14 / 24 ) 183.851388888889 5.08781761458163 36.1356091778866 Winsorized Mean ( 15 / 24 ) 183.768055555556 4.80111441581633 38.2761250075957 Winsorized Mean ( 16 / 24 ) 183.6125 4.59200329683778 39.9852718151231 Winsorized Mean ( 17 / 24 ) 183.565277777778 4.49455554825814 40.8416974285518 Winsorized Mean ( 18 / 24 ) 183.440277777778 4.34504136087428 42.2183041638221 Winsorized Mean ( 19 / 24 ) 183.545833333333 4.05591394634315 45.2538776121767 Winsorized Mean ( 20 / 24 ) 183.740277777778 4.00402851702013 45.8888534376675 Winsorized Mean ( 21 / 24 ) 183.798611111111 3.82237128930462 48.0849706111486 Winsorized Mean ( 22 / 24 ) 183.7375 3.53203616762861 52.0202770526442 Winsorized Mean ( 23 / 24 ) 184.472222222222 3.28818082034515 56.1016052039555 Winsorized Mean ( 24 / 24 ) 182.938888888889 2.97434686321836 61.5055665333335 Trimmed Mean ( 1 / 24 ) 194.228571428571 8.72501416773358 22.2611181706567 Trimmed Mean ( 2 / 24 ) 192.545588235294 8.28186676378987 23.2490564901557 Trimmed Mean ( 3 / 24 ) 191.074242424242 7.89278632930865 24.2087184996657 Trimmed Mean ( 4 / 24 ) 189.8265625 7.54077252072116 25.1733575012877 Trimmed Mean ( 5 / 24 ) 188.711290322581 7.20624402588083 26.1871912253921 Trimmed Mean ( 6 / 24 ) 187.705 6.89123713811862 27.2382151764473 Trimmed Mean ( 7 / 24 ) 186.820689655172 6.58107552787335 28.3875620123057 Trimmed Mean ( 8 / 24 ) 186.033928571429 6.26201819920543 29.7083021245505 Trimmed Mean ( 9 / 24 ) 185.470370370370 5.9864449899133 30.9817213192260 Trimmed Mean ( 10 / 24 ) 184.944230769231 5.71216083445259 32.3772800047487 Trimmed Mean ( 11 / 24 ) 184.458 5.39702494766462 34.1777186114024 Trimmed Mean ( 12 / 24 ) 184.16875 5.16663477133543 35.6457845678915 Trimmed Mean ( 13 / 24 ) 184.156521739130 4.99156936797472 36.8935114716938 Trimmed Mean ( 14 / 24 ) 184.106818181818 4.85900615140155 37.8898096535058 Trimmed Mean ( 15 / 24 ) 184.138095238095 4.7227609500851 38.989501519186 Trimmed Mean ( 16 / 24 ) 184.1825 4.60715982299457 39.9774496818486 Trimmed Mean ( 17 / 24 ) 184.25 4.49776260167793 40.9648121337626 Trimmed Mean ( 18 / 24 ) 184.330555555556 4.36795113686483 42.2006908456082 Trimmed Mean ( 19 / 24 ) 184.435294117647 4.22303521455879 43.6736339497743 Trimmed Mean ( 20 / 24 ) 184.540625 4.09483560310197 45.0666749259005 Trimmed Mean ( 21 / 24 ) 184.636666666667 3.91941669168578 47.1082003243836 Trimmed Mean ( 22 / 24 ) 184.739285714286 3.71645255019126 49.7085011094191 Trimmed Mean ( 23 / 24 ) 184.865384615385 3.51130456715358 52.6486327459895 Trimmed Mean ( 24 / 24 ) 184.916666666667 3.28556166567258 56.2815997637995 Median 190.3 Midrange 253.85 Midmean - Weighted Average at Xnp 183.021621621622 Midmean - Weighted Average at X(n+1)p 184.330555555556 Midmean - Empirical Distribution Function 183.021621621622 Midmean - Empirical Distribution Function - Averaging 184.330555555556 Midmean - Empirical Distribution Function - Interpolation 184.330555555556 Midmean - Closest Observation 183.021621621622 Midmean - True Basic - Statistics Graphics Toolkit 184.330555555556 Midmean - MS Excel (old versions) 184.25 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/08/t1241740192i0p6j1eapq3ho2w/1lzrl1241740148.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/08/t1241740192i0p6j1eapq3ho2w/1lzrl1241740148.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/08/t1241740192i0p6j1eapq3ho2w/2xhz51241740148.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/May/08/t1241740192i0p6j1eapq3ho2w/2xhz51241740148.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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