Nietje Vant Santfoort - jogging

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

Title produced by software: Central Tendency

Date of computation: Sun, 20 Apr 2008 12:49:12 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/20/t1208717637mtmbpxonlnb5fea.htm/, Retrieved Sun, 20 Apr 2008 20:53:57 +0200

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Dataseries X:

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71,42 71,47 71,64 71,55 71,62 71,65 71,65 71,65 71,6 71,7 71,73 71,83 71,83 71,87 71,91 71,99 72,1 72,12 72,12 72,12 72,25 72,59 72,72 72,76 72,76 72,91 73 73,16 73,16 73,11 73,11 73,33 73,51 73,66 73,65 73,65 73,65 73,65 73,71 73,73 73,85 73,77 73,77 73,78 73,88 74,3 74,53 74,71 74,71 74,78 74,9 74,65 74,65 74,53 74,53 74,53 74,65 74,85 74,96 74,96 74,96 75,19 74,98 75,54 75,61 75,59 75,58 75,44 75,37 75,22 75,33 75,33

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 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 73.5148611111111 0.158867519075477 462.743180852373 Geometric Mean 73.5026607561408 Harmonic Mean 73.4904495270504 Quadratic Mean 73.5270478482427 Winsorized Mean ( 1 / 24 ) 73.5152777777778 0.158688626846363 463.267464334119 Winsorized Mean ( 2 / 24 ) 73.5172222222222 0.15824129054622 464.589374672402 Winsorized Mean ( 3 / 24 ) 73.5176388888889 0.157576706245423 466.551437966894 Winsorized Mean ( 4 / 24 ) 73.5131944444445 0.156402587640152 470.02543598308 Winsorized Mean ( 5 / 24 ) 73.5097222222222 0.155334710070445 473.234360748383 Winsorized Mean ( 6 / 24 ) 73.5072222222222 0.15463575028728 475.3572319833 Winsorized Mean ( 7 / 24 ) 73.5072222222222 0.15463575028728 475.3572319833 Winsorized Mean ( 8 / 24 ) 73.495 0.152648244988161 481.466393574982 Winsorized Mean ( 9 / 24 ) 73.4975 0.15099782227492 486.745430448552 Winsorized Mean ( 10 / 24 ) 73.4725 0.14586994845507 503.684965807954 Winsorized Mean ( 11 / 24 ) 73.4847222222222 0.142893879802682 514.260808956234 Winsorized Mean ( 12 / 24 ) 73.4847222222222 0.142893879802682 514.260808956234 Winsorized Mean ( 13 / 24 ) 73.4919444444444 0.141722805624749 518.561173838421 Winsorized Mean ( 14 / 24 ) 73.4880555555556 0.138786045648334 529.506084075374 Winsorized Mean ( 15 / 24 ) 73.4943055555556 0.134654956143332 545.797255893984 Winsorized Mean ( 16 / 24 ) 73.5031944444444 0.12866304611731 571.284425968176 Winsorized Mean ( 17 / 24 ) 73.4913888888889 0.125653270346652 584.874461970954 Winsorized Mean ( 18 / 24 ) 73.4913888888889 0.125653270346652 584.874461970954 Winsorized Mean ( 19 / 24 ) 73.4755555555556 0.123511463941277 594.888548892021 Winsorized Mean ( 20 / 24 ) 73.5116666666667 0.117999761279300 622.981486315618 Winsorized Mean ( 21 / 24 ) 73.6108333333333 0.103614404576202 710.430500801628 Winsorized Mean ( 22 / 24 ) 73.6138888888889 0.0930319908032456 791.275003934675 Winsorized Mean ( 23 / 24 ) 73.6266666666667 0.0913132324270442 806.30884166204 Winsorized Mean ( 24 / 24 ) 73.6266666666667 0.0913132324270442 806.30884166204 Trimmed Mean ( 1 / 24 ) 73.5148571428571 0.157781690370051 465.927681281903 Trimmed Mean ( 2 / 24 ) 73.5144117647059 0.156618315834471 469.385789095081 Trimmed Mean ( 3 / 24 ) 73.5128787878788 0.155422390882019 472.987697401221 Trimmed Mean ( 4 / 24 ) 73.51109375 0.154191779998874 476.751054761394 Trimmed Mean ( 5 / 24 ) 73.5104838709677 0.153027170922961 480.375370122836 Trimmed Mean ( 6 / 24 ) 73.5106666666667 0.151832286798628 484.157014404731 Trimmed Mean ( 7 / 24 ) 73.5113793103448 0.150453729630010 488.597919713396 Trimmed Mean ( 8 / 24 ) 73.5121428571429 0.148655820187760 494.51237606636 Trimmed Mean ( 9 / 24 ) 73.515 0.146802336241376 500.775409180989 Trimmed Mean ( 10 / 24 ) 73.5176923076923 0.144766055459557 507.837918732483 Trimmed Mean ( 11 / 24 ) 73.5242 0.143202750515142 513.427289179237 Trimmed Mean ( 12 / 24 ) 73.5295833333333 0.141717228669951 518.847172100565 Trimmed Mean ( 13 / 24 ) 73.5354347826087 0.139655790286527 526.547697247199 Trimmed Mean ( 14 / 24 ) 73.5409090909091 0.137110709030504 536.361525740107 Trimmed Mean ( 15 / 24 ) 73.547380952381 0.134301677991170 547.628161110665 Trimmed Mean ( 16 / 24 ) 73.55375 0.131402048680513 559.761059577058 Trimmed Mean ( 17 / 24 ) 73.5597368421053 0.128779414235671 571.207263821592 Trimmed Mean ( 18 / 24 ) 73.5677777777778 0.125732842946521 585.111861417698 Trimmed Mean ( 19 / 24 ) 73.5767647058824 0.121324920318284 606.443956549576 Trimmed Mean ( 20 / 24 ) 73.58875 0.115514932354108 637.049674014572 Trimmed Mean ( 21 / 24 ) 73.598 0.108891383191386 675.884517608202 Trimmed Mean ( 22 / 24 ) 73.5964285714286 0.104102633379968 706.960296602742 Trimmed Mean ( 23 / 24 ) 73.5942307692308 0.100408662018194 732.947031560834 Trimmed Mean ( 24 / 24 ) 73.59 0.0949942790039393 774.678230853758 Median 73.65 Midrange 73.515 Midmean - Weighted Average at Xnp 73.5597368421053 Midmean - Weighted Average at X(n+1)p 73.5597368421053 Midmean - Empirical Distribution Function 73.5597368421053 Midmean - Empirical Distribution Function - Averaging 73.5597368421053 Midmean - Empirical Distribution Function - Interpolation 73.5597368421053 Midmean - Closest Observation 73.5597368421053 Midmean - True Basic - Statistics Graphics Toolkit 73.5597368421053 Midmean - MS Excel (old versions) 73.5597368421053 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208717637mtmbpxonlnb5fea/1r4x41208717347.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208717637mtmbpxonlnb5fea/1r4x41208717347.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208717637mtmbpxonlnb5fea/2wvho1208717347.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208717637mtmbpxonlnb5fea/2wvho1208717347.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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