*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 04 Apr 2011 18:10:49 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Apr/04/t1301940439acomcqyca0be8d3.htm/, Retrieved Mon, 04 Apr 2011 20:07:21 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KEYWORD: KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

2851 2672 2755 2721 2946 3036 2282 2212 2922 4301 5764 7132 2541 2475 3031 3266 3776 3230 3028 1759 3595 4474 6838 8357 3113 3006 4047 3523 3937 3986 3260 1573 3528 5211 7614 9254 5375 3088 3718 4514 4520 4539 3663 1643 4734 5428 8314 10651 3633 4292 4154 4121 4647 4753 3965 1723 5048 6923 9858 11331 4016 3957 4510 4276 4968 4677 3523 1821 5222 6872 10803 13916 2639 2899 3370 3740 2927 3986 4217 1738 5221 6424 9842 13076 3934 3162 4286 4676 5010 4874 4633 1659 5951 6981 9851 12670

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 2 seconds R Server 'Herman Ole Andreas Wold' @ www.yougetit.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 4801.85416666667 269.483683952264 17.818719472149 Geometric Mean 4242.94163274655 Harmonic Mean 3794.8244127108 Quadratic Mean 5473.28436589951 Winsorized Mean ( 1 / 32 ) 4793.83333333333 266.402321829265 17.994713035593 Winsorized Mean ( 2 / 32 ) 4785.70833333333 263.645194491036 18.1520787533112 Winsorized Mean ( 3 / 32 ) 4745.86458333333 251.010183890258 18.9070599040246 Winsorized Mean ( 4 / 32 ) 4724.48958333333 245.01825119756 19.2821945313941 Winsorized Mean ( 5 / 32 ) 4717.66666666667 242.826087803862 19.4281706275204 Winsorized Mean ( 6 / 32 ) 4671.97916666667 230.057498047145 20.3078761019528 Winsorized Mean ( 7 / 32 ) 4699.97916666667 226.425794832671 20.7572603207155 Winsorized Mean ( 8 / 32 ) 4705.0625 225.578954363797 20.8577192551927 Winsorized Mean ( 9 / 32 ) 4668.03125 210.629619764592 22.1622735454642 Winsorized Mean ( 10 / 32 ) 4581.46875 189.29999916192 24.2021593781476 Winsorized Mean ( 11 / 32 ) 4587.77083333333 187.013055693492 24.5318211411535 Winsorized Mean ( 12 / 32 ) 4504.39583333333 168.859522924452 26.6754030529188 Winsorized Mean ( 13 / 32 ) 4445.76041666667 155.829981255432 28.5295575398889 Winsorized Mean ( 14 / 32 ) 4428.69791666667 151.298785897275 29.2712059148548 Winsorized Mean ( 15 / 32 ) 4434.63541666667 147.973490039062 29.9691209249442 Winsorized Mean ( 16 / 32 ) 4434.13541666667 145.577307806539 30.4589738845788 Winsorized Mean ( 17 / 32 ) 4432.1875 144.066694101144 30.7648310225564 Winsorized Mean ( 18 / 32 ) 4355.5 130.653082056556 33.3363739411415 Winsorized Mean ( 19 / 32 ) 4265.64583333333 115.162218710123 37.040323476838 Winsorized Mean ( 20 / 32 ) 4239.1875 107.749652289605 39.3429343846614 Winsorized Mean ( 21 / 32 ) 4170.5 96.6281997722615 43.1602783641759 Winsorized Mean ( 22 / 32 ) 4159.04166666667 94.8912199419737 43.8295731597711 Winsorized Mean ( 23 / 32 ) 4123.58333333333 89.9076837292967 45.8646376181711 Winsorized Mean ( 24 / 32 ) 4136.33333333333 88.234705780059 46.8787570238393 Winsorized Mean ( 25 / 32 ) 4140.23958333333 87.0863804698043 47.5417575170539 Winsorized Mean ( 26 / 32 ) 4109.36458333333 79.8401351163242 51.4699101817167 Winsorized Mean ( 27 / 32 ) 4117.80208333333 76.1513650506484 54.0739103047539 Winsorized Mean ( 28 / 32 ) 4114.30208333333 73.5761154391302 55.9189902698398 Winsorized Mean ( 29 / 32 ) 4087.71875 69.9376330927429 58.4480567790928 Winsorized Mean ( 30 / 32 ) 4082.40625 61.5350769639336 66.342750369724 Winsorized Mean ( 31 / 32 ) 4125.67708333333 54.9548828002996 75.0738946769411 Winsorized Mean ( 32 / 32 ) 4106.67708333333 52.7665611626151 77.8272639499369 Trimmed Mean ( 1 / 32 ) 4739.24468085106 254.999439121839 18.5853141370505 Trimmed Mean ( 2 / 32 ) 4682.28260869565 241.694161460732 19.3727584497584 Trimmed Mean ( 3 / 32 ) 4627.12222222222 227.849308365839 20.3078177213197 Trimmed Mean ( 4 / 32 ) 4583.94318181818 217.537526854224 21.0719651368013 Trimmed Mean ( 5 / 32 ) 4544.72093023256 207.714840999185 21.8796158636079 Trimmed Mean ( 6 / 32 ) 4505.19047619048 196.86845872071 22.8842675229242 Trimmed Mean ( 7 / 32 ) 4472.64634146341 187.806091715636 23.8152357072401 Trimmed Mean ( 8 / 32 ) 4433.675 177.941873576276 24.9164230481111 Trimmed Mean ( 9 / 32 ) 4391.92307692308 166.298193517678 26.4099265543507 Trimmed Mean ( 10 / 32 ) 4353.17105263158 155.973428222997 27.9096965568251 Trimmed Mean ( 11 / 32 ) 4323.55405405405 148.601046642579 29.0950444276025 Trimmed Mean ( 12 / 32 ) 4291.52777777778 140.180130836949 30.6143798850458 Trimmed Mean ( 13 / 32 ) 4267.2 134.017455987333 31.840628286537 Trimmed Mean ( 14 / 32 ) 4247.80882352941 129.263713637881 32.861571929066 Trimmed Mean ( 15 / 32 ) 4229.01515151515 124.414311779189 33.9913880568727 Trimmed Mean ( 16 / 32 ) 4208.453125 119.129023212112 35.3268499272989 Trimmed Mean ( 17 / 32 ) 4186.61290322581 113.10518953597 37.0152149552288 Trimmed Mean ( 18 / 32 ) 4163.5 105.927644263474 39.3051316202608 Trimmed Mean ( 19 / 32 ) 4145.84482758621 100.006481343875 41.4557613854105 Trimmed Mean ( 20 / 32 ) 4135.03571428571 95.9564463035106 43.0928392367364 Trimmed Mean ( 21 / 32 ) 4125.77777777778 92.3840904721891 44.6589640780171 Trimmed Mean ( 22 / 32 ) 4121.84615384615 90.0916090854937 45.7517208948357 Trimmed Mean ( 23 / 32 ) 4118.6 87.5146308467613 47.061845089785 Trimmed Mean ( 24 / 32 ) 4118.16666666667 85.1952353854821 48.3379927062028 Trimmed Mean ( 25 / 32 ) 4116.58695652174 82.5234943919249 49.8838177764386 Trimmed Mean ( 26 / 32 ) 4114.52272727273 79.2800885495153 51.8985637194761 Trimmed Mean ( 27 / 32 ) 4114.97619047619 76.6349514370555 53.6958152032764 Trimmed Mean ( 28 / 32 ) 4114.725 73.9408459643456 55.6488764273015 Trimmed Mean ( 29 / 32 ) 4114.76315789474 70.912939572951 58.0255618040163 Trimmed Mean ( 30 / 32 ) 4117.25 67.6898432628735 60.8252257877251 Trimmed Mean ( 31 / 32 ) 4120.52941176471 65.4770405841737 62.9309048637832 Trimmed Mean ( 32 / 32 ) 4120.03125 64.1074810121548 64.2675579347571 Median 4084 Midrange 7744.5 Midmean - Weighted Average at Xnp 4096.08163265306 Midmean - Weighted Average at X(n+1)p 4118.16666666667 Midmean - Empirical Distribution Function 4096.08163265306 Midmean - Empirical Distribution Function - Averaging 4118.16666666667 Midmean - Empirical Distribution Function - Interpolation 4118.16666666667 Midmean - Closest Observation 4096.08163265306 Midmean - True Basic - Statistics Graphics Toolkit 4118.16666666667 Midmean - MS Excel (old versions) 4118.6 Number of observations 96

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Apr/04/t1301940439acomcqyca0be8d3/1a8tk1301940647.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/04/t1301940439acomcqyca0be8d3/1a8tk1301940647.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/04/t1301940439acomcqyca0be8d3/2w6l41301940647.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/04/t1301940439acomcqyca0be8d3/2w6l41301940647.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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