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

Title produced by software: Central Tendency

Date of computation: Wed, 23 Apr 2008 03:31:27 -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/23/t1208943336rk3gjtejxd8d81r.htm/, Retrieved Wed, 23 Apr 2008 11:35:45 +0200

User-defined keywords:

Dataseries X:

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3.27 3.27 3.27 3.27 3.27 3.28 3.32 3.34 3.34 3.35 3.35 3.35 3.35 3.35 3.4 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.43 3.47 3.51 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.58 3.6 3.61 3.61 3.61 3.63 3.68 3.69 3.69 3.69 3.69 3.69 3.69 3.69 3.69 3.78 3.79 3.79 3.8 3.8 3.8 3.8 3.81 3.95 3.99 4 4.06 4.16 4.19 4.2 4.2 4.2 4.2 4.2 4.23 4.38 4.43 4.44 4.44 4.44 4.44 4.44 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.46 4.46 4.46 4.48 4.58 4.67 4.68 4.68

Text written by user:

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 3.82666666666667 0.0452472899902523 84.5722841631189 Geometric Mean 3.80200613997494 Harmonic Mean 3.77822189075174 Quadratic Mean 3.8519959652973 Winsorized Mean ( 1 / 32 ) 3.82666666666667 0.0452472899902523 84.5722841631189 Winsorized Mean ( 2 / 32 ) 3.82645833333333 0.0452061504040847 84.6446401458591 Winsorized Mean ( 3 / 32 ) 3.82364583333333 0.0446791975888743 85.5800023204864 Winsorized Mean ( 4 / 32 ) 3.81947916666667 0.0439782566370564 86.8492627660994 Winsorized Mean ( 5 / 32 ) 3.81895833333333 0.0437475511010523 87.2953625338236 Winsorized Mean ( 6 / 32 ) 3.82145833333333 0.0434334990689706 87.9841232055703 Winsorized Mean ( 7 / 32 ) 3.82291666666667 0.0432591934926835 88.3723518172674 Winsorized Mean ( 8 / 32 ) 3.82208333333333 0.0431307469261704 88.6162101453015 Winsorized Mean ( 9 / 32 ) 3.82302083333333 0.0430213430792620 88.863353854152 Winsorized Mean ( 10 / 32 ) 3.82302083333333 0.0430213430792620 88.863353854152 Winsorized Mean ( 11 / 32 ) 3.82302083333333 0.0430213430792620 88.863353854152 Winsorized Mean ( 12 / 32 ) 3.82302083333333 0.0430213430792620 88.863353854152 Winsorized Mean ( 13 / 32 ) 3.82302083333333 0.0430213430792620 88.863353854152 Winsorized Mean ( 14 / 32 ) 3.8303125 0.0422078329818285 90.7488546414842 Winsorized Mean ( 15 / 32 ) 3.8334375 0.041877753411703 91.5387571609493 Winsorized Mean ( 16 / 32 ) 3.83177083333333 0.041620411551449 92.0647031228102 Winsorized Mean ( 17 / 32 ) 3.83177083333333 0.041620411551449 92.0647031228102 Winsorized Mean ( 18 / 32 ) 3.83177083333333 0.041620411551449 92.0647031228102 Winsorized Mean ( 19 / 32 ) 3.83177083333333 0.041620411551449 92.0647031228102 Winsorized Mean ( 20 / 32 ) 3.83177083333333 0.041620411551449 92.0647031228102 Winsorized Mean ( 21 / 32 ) 3.82958333333333 0.0412847186871368 92.7603107182253 Winsorized Mean ( 22 / 32 ) 3.818125 0.0395504653475851 96.538055025265 Winsorized Mean ( 23 / 32 ) 3.7821875 0.0343843737219395 109.997277559449 Winsorized Mean ( 24 / 32 ) 3.7746875 0.0333669632300779 113.126492032616 Winsorized Mean ( 25 / 32 ) 3.7746875 0.0333669632300779 113.126492032616 Winsorized Mean ( 26 / 32 ) 3.77739583333333 0.0330656725558643 114.239195557007 Winsorized Mean ( 27 / 32 ) 3.78864583333333 0.0318506726194044 118.950261383967 Winsorized Mean ( 28 / 32 ) 3.8003125 0.0306542165057816 123.973564918328 Winsorized Mean ( 29 / 32 ) 3.8003125 0.0299405306490758 126.928695571309 Winsorized Mean ( 30 / 32 ) 3.7909375 0.0286628458254132 132.259634060442 Winsorized Mean ( 31 / 32 ) 3.75864583333333 0.0243654647528888 154.261200081878 Winsorized Mean ( 32 / 32 ) 3.73864583333333 0.0217993339426591 171.50275522947 Trimmed Mean ( 1 / 32 ) 3.82351063829787 0.0449109308018255 85.1354129169476 Trimmed Mean ( 2 / 32 ) 3.82021739130435 0.0445173667805691 85.814091613608 Trimmed Mean ( 3 / 32 ) 3.81688888888889 0.0440827290711245 86.5846777029298 Trimmed Mean ( 4 / 32 ) 3.81443181818182 0.043794326091032 87.0987673209777 Trimmed Mean ( 5 / 32 ) 3.81302325581395 0.0436755447408678 87.3033932017809 Trimmed Mean ( 6 / 32 ) 3.81166666666667 0.0435800492461055 87.4635695141462 Trimmed Mean ( 7 / 32 ) 3.80975609756098 0.0435184620302851 87.5434452373274 Trimmed Mean ( 8 / 32 ) 3.8075 0.0434564746599792 87.6164030743726 Trimmed Mean ( 9 / 32 ) 3.80525641025641 0.0433821253877983 87.7148451404985 Trimmed Mean ( 10 / 32 ) 3.80276315789474 0.0432859114409128 87.8522140647466 Trimmed Mean ( 11 / 32 ) 3.80013513513514 0.0431444081796589 88.0794359099997 Trimmed Mean ( 12 / 32 ) 3.79736111111111 0.0429497254302819 88.4140951558625 Trimmed Mean ( 13 / 32 ) 3.79442857142857 0.0426923297469824 88.8784611642509 Trimmed Mean ( 14 / 32 ) 3.79132352941176 0.0423606036076621 89.5011686926481 Trimmed Mean ( 15 / 32 ) 3.78727272727273 0.042054768073245 90.055727347648 Trimmed Mean ( 16 / 32 ) 3.78265625 0.0417019149642022 90.7070155710383 Trimmed Mean ( 17 / 32 ) 3.77790322580645 0.0412868985310188 91.5036818027908 Trimmed Mean ( 18 / 32 ) 3.77283333333333 0.0407514802799778 92.5815039702256 Trimmed Mean ( 19 / 32 ) 3.76741379310345 0.0400676683710059 94.0262796981133 Trimmed Mean ( 20 / 32 ) 3.76160714285714 0.0391987748166228 95.962365162035 Trimmed Mean ( 21 / 32 ) 3.75537037037037 0.0380955738077673 98.5776035116366 Trimmed Mean ( 22 / 32 ) 3.74884615384615 0.0367604592047861 101.980395102302 Trimmed Mean ( 23 / 32 ) 3.7428 0.035429769564994 105.639975815650 Trimmed Mean ( 24 / 32 ) 3.739375 0.0348074824968132 107.430205569804 Trimmed Mean ( 25 / 32 ) 3.73630434782609 0.0341824582744747 109.304729280285 Trimmed Mean ( 26 / 32 ) 3.73295454545455 0.0333404178357821 111.964839908161 Trimmed Mean ( 27 / 32 ) 3.72904761904762 0.032264170776414 115.578597847419 Trimmed Mean ( 28 / 32 ) 3.72375 0.0310349007425924 119.985883985429 Trimmed Mean ( 29 / 32 ) 3.71684210526316 0.0295559966239987 125.755938889409 Trimmed Mean ( 30 / 32 ) 3.70916666666667 0.0276525351172853 134.134778273841 Trimmed Mean ( 31 / 32 ) 3.70147058823529 0.0253746696471956 145.872661189281 Trimmed Mean ( 32 / 32 ) 3.6959375 0.0237589515176437 155.559789633619 Median 3.69 Midrange 3.975 Midmean - Weighted Average at Xnp 3.68894736842105 Midmean - Weighted Average at X(n+1)p 3.68894736842105 Midmean - Empirical Distribution Function 3.68894736842105 Midmean - Empirical Distribution Function - Averaging 3.68894736842105 Midmean - Empirical Distribution Function - Interpolation 3.68894736842105 Midmean - Closest Observation 3.68894736842105 Midmean - True Basic - Statistics Graphics Toolkit 3.68894736842105 Midmean - MS Excel (old versions) 3.69827586206896 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/23/t1208943336rk3gjtejxd8d81r/12t2i1208943084.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/23/t1208943336rk3gjtejxd8d81r/12t2i1208943084.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/23/t1208943336rk3gjtejxd8d81r/2qwbj1208943084.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/23/t1208943336rk3gjtejxd8d81r/2qwbj1208943084.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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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