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Central Tendency - Voeding

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 13:22:05 -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/whby0pbk0tsl4op1193084232.htm/, Retrieved Mon, 22 Oct 2007 22:17:14 +0200

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Dataseries X:

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89.28 89.47 89.53 90.72 90.91 91.38 91.49 90.9 90.93 90.57 91.28 90.83 91.5 91.58 92.49 94.16 95.46 95.8 95.32 95.41 95.35 95.68 95.59 94.96 96.92 96.06 96.59 96.67 97.27 96.38 96.47 96.05 96.76 96.51 96.55 95.97 97 97.46 97.9 98.42 98.54 99 98.94 99.02 100.07 98.72 98.73 98.04 99.08 99.22 99.57 100.44 100.84 100.75 100.49 99.98 99.96 99.76 100.11 99.79 100.29 101.12 102.65 102.71 103.39 102.8 102.07 102.15 101.21 101.27 101.86 101.65 101.94 102.62 102.71 103.39 104.51 104.09 104.29 104.57 105.39 105.15 106.13 105.46 106.47 106.62 106.52 108.04 107.15 107.32 107.76 107.26 107.89

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 98.9147311827957 0.517967956453865 190.966892739833 Geometric Mean 98.7893062182587 Harmonic Mean 98.6632614652913 Quadratic Mean 99.0394204290632 Winsorized Mean ( 1 / 31 ) 98.9151612903226 0.517252144096835 191.231998589463 Winsorized Mean ( 2 / 31 ) 98.9136559139785 0.516472798045321 191.517648728711 Winsorized Mean ( 3 / 31 ) 98.9330107526882 0.507556890252771 194.920042762927 Winsorized Mean ( 4 / 31 ) 98.9368817204301 0.505947215445985 195.547833252168 Winsorized Mean ( 5 / 31 ) 98.9368817204301 0.503855401853514 196.359672549852 Winsorized Mean ( 6 / 31 ) 98.9072043010753 0.497151972084148 198.947625383922 Winsorized Mean ( 7 / 31 ) 98.9004301075269 0.495756794505365 199.493846990445 Winsorized Mean ( 8 / 31 ) 98.8978494623656 0.494738465139702 199.899252697967 Winsorized Mean ( 9 / 31 ) 98.898817204301 0.483459822467888 204.56470756858 Winsorized Mean ( 10 / 31 ) 98.8375268817204 0.470237018009980 210.186614614043 Winsorized Mean ( 11 / 31 ) 98.8422580645161 0.466736732427108 211.773042911193 Winsorized Mean ( 12 / 31 ) 98.8125806451613 0.461844430780293 213.952088754683 Winsorized Mean ( 13 / 31 ) 98.742688172043 0.448130085608533 220.343804942166 Winsorized Mean ( 14 / 31 ) 98.8706451612903 0.423708162508617 233.346095047861 Winsorized Mean ( 15 / 31 ) 99.1045161290322 0.377088930652432 262.814705161362 Winsorized Mean ( 16 / 31 ) 99.2077419354839 0.353098855166872 280.963080122701 Winsorized Mean ( 17 / 31 ) 99.1455913978495 0.325899283121018 304.221569462714 Winsorized Mean ( 18 / 31 ) 99.1513978494624 0.325159923662194 304.931175812644 Winsorized Mean ( 19 / 31 ) 99.0431182795699 0.307022451697045 322.592428443315 Winsorized Mean ( 20 / 31 ) 99.0345161290323 0.303078814102781 326.761593093232 Winsorized Mean ( 21 / 31 ) 99.063870967742 0.299345633241366 330.934745548352 Winsorized Mean ( 22 / 31 ) 99.0709677419355 0.294795674301086 336.066558564053 Winsorized Mean ( 23 / 31 ) 99.0932258064516 0.2901297110122 341.548011269638 Winsorized Mean ( 24 / 31 ) 99.015806451613 0.269018193212127 368.063606662976 Winsorized Mean ( 25 / 31 ) 99.015806451613 0.26366453757117 375.53706449767 Winsorized Mean ( 26 / 31 ) 98.9822580645161 0.258776119754184 382.501515822021 Winsorized Mean ( 27 / 31 ) 99.051935483871 0.244663772019033 404.849212723514 Winsorized Mean ( 28 / 31 ) 99.015806451613 0.233631029083967 423.81273942866 Winsorized Mean ( 29 / 31 ) 98.9097849462366 0.217899572971656 453.923720901934 Winsorized Mean ( 30 / 31 ) 98.9033333333333 0.214083570067225 461.98469738839 Winsorized Mean ( 31 / 31 ) 98.8866666666667 0.208991452329137 473.161297099041 Trimmed Mean ( 1 / 31 ) 98.9203296703297 0.508702614934077 194.456106114471 Trimmed Mean ( 2 / 31 ) 98.9257303370786 0.498929955301597 198.275788586956 Trimmed Mean ( 3 / 31 ) 98.932183908046 0.488206363911166 202.644191516618 Trimmed Mean ( 4 / 31 ) 98.9318823529412 0.479702741000282 206.23580792273 Trimmed Mean ( 5 / 31 ) 98.9304819277108 0.470434487700026 210.295980661167 Trimmed Mean ( 6 / 31 ) 98.929012345679 0.460315230318884 214.915792113039 Trimmed Mean ( 7 / 31 ) 98.9332911392405 0.450292945201795 219.708730046624 Trimmed Mean ( 8 / 31 ) 98.938961038961 0.438940250552251 225.40416586194 Trimmed Mean ( 9 / 31 ) 98.9453333333333 0.425881865501882 232.330468489732 Trimmed Mean ( 10 / 31 ) 98.9519178082192 0.412940722430023 239.627414864582 Trimmed Mean ( 11 / 31 ) 98.9669014084507 0.400338970636677 247.207763089012 Trimmed Mean ( 12 / 31 ) 98.9821739130435 0.386078049654179 256.378662298218 Trimmed Mean ( 13 / 31 ) 98.9821739130435 0.3699845318911 267.530573256986 Trimmed Mean ( 14 / 31 ) 99.0303076923077 0.353274651354921 280.321011746795 Trimmed Mean ( 15 / 31 ) 99.0471428571429 0.33804651214189 292.998564693279 Trimmed Mean ( 16 / 31 ) 99.0413114754098 0.328511336349032 301.485216845551 Trimmed Mean ( 17 / 31 ) 99.0249152542373 0.321099019822177 308.393701447848 Trimmed Mean ( 18 / 31 ) 99.0133333333333 0.316641537058565 312.698498918101 Trimmed Mean ( 19 / 31 ) 99.0003636363636 0.311102845882601 318.223908738279 Trimmed Mean ( 20 / 31 ) 98.9964150943396 0.307219976967902 322.233000833415 Trimmed Mean ( 21 / 31 ) 98.9929411764706 0.302813641534564 326.910441269441 Trimmed Mean ( 22 / 31 ) 98.986530612245 0.297685595086735 332.520391466721 Trimmed Mean ( 23 / 31 ) 98.9789361702128 0.291785189897833 339.218505931948 Trimmed Mean ( 24 / 31 ) 98.9686666666667 0.284890480463258 347.391974999427 Trimmed Mean ( 25 / 31 ) 98.9644186046512 0.279997884489236 353.447022591543 Trimmed Mean ( 26 / 31 ) 98.9644186046512 0.27436056208024 360.709344864616 Trimmed Mean ( 27 / 31 ) 98.9576923076923 0.267641133210176 369.740223114292 Trimmed Mean ( 28 / 31 ) 98.948918918919 0.261503444755871 378.384762813713 Trimmed Mean ( 29 / 31 ) 98.9425714285714 0.255437125042426 387.346089226998 Trimmed Mean ( 30 / 31 ) 98.9457575757576 0.250587578557057 394.854996985529 Trimmed Mean ( 31 / 31 ) 98.95 0.244165464784740 405.257967531304 Median 99.02 Midrange 98.66 Midmean - Weighted Average at Xnp 98.8997826086956 Midmean - Weighted Average at X(n+1)p 98.9789361702127 Midmean - Empirical Distribution Function 98.9789361702127 Midmean - Empirical Distribution Function - Averaging 98.9789361702127 Midmean - Empirical Distribution Function - Interpolation 98.9789361702127 Midmean - Closest Observation 98.9102083333333 Midmean - True Basic - Statistics Graphics Toolkit 98.9789361702127 Midmean - MS Excel (old versions) 98.9789361702127 Number of observations 93

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/whby0pbk0tsl4op1193084232/12dp51193084522.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/whby0pbk0tsl4op1193084232/12dp51193084522.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/whby0pbk0tsl4op1193084232/2lxl81193084522.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/22/whby0pbk0tsl4op1193084232/2lxl81193084522.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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