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ws3 q3

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

Title produced by software: Central Tendency

Date of computation: Sun, 28 Oct 2007 01:34:43 -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/28/ch81lop1nmvvsoo1193560085.htm/, Retrieved Sun, 28 Oct 2007 09:28:05 +0100

User-defined keywords:

Dataseries X:

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100,00 100,35 100,38 100,52 100,34 99,97 99,88 100,26 100,93 100,88 100,73 100,74 100,25 100,29 100,57 101,24 101,69 101,89 102,07 102,43 102,51 102,71 103,22 103,79 103,99 103,83 103,55 103,24 103,77 104,37 104,61 104,21 104,77 104,33 104,14 104,37 104,20 103,58 103,51 103,39 103,11 103,28 102,83 102,56 102,62 102,66 102,72 102,92 103,26 103,02 103,33 103,57 103,61 103,85 104,22 104,15 104,52 105,27 105,60 105,99 106,23 106,40 106,25 106,74 106,96 106,74 106,59 106,65 106,56 106,69 106,66 106,40 105,99 105,99 106,38 106,41 106,75 106,90 107,29 107,24 107,56 107,45 107,35 107,63 107,88 108,21 108,78 108,94 108,66 108,38

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 4 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 104.191666666667 0.262444251258675 397.004949306249 Geometric Mean 104.162235110077 Harmonic Mean 104.132793304323 Quadratic Mean 104.221079702930 Winsorized Mean ( 1 / 30 ) 104.190888888889 0.261905704145178 397.818326366556 Winsorized Mean ( 2 / 30 ) 104.188888888889 0.261266407984617 398.784098164748 Winsorized Mean ( 3 / 30 ) 104.187888888889 0.258051737036155 403.748062638662 Winsorized Mean ( 4 / 30 ) 104.180777777778 0.25661939482859 405.973904845991 Winsorized Mean ( 5 / 30 ) 104.164111111111 0.253203687230414 411.38465340089 Winsorized Mean ( 6 / 30 ) 104.150777777778 0.249953764902048 416.680172105398 Winsorized Mean ( 7 / 30 ) 104.146111111111 0.248975363132184 418.2988621883 Winsorized Mean ( 8 / 30 ) 104.139 0.247029445241816 421.565129201738 Winsorized Mean ( 9 / 30 ) 104.143 0.243166555641954 428.278468332394 Winsorized Mean ( 10 / 30 ) 104.141888888889 0.241256743617013 431.6641571446 Winsorized Mean ( 11 / 30 ) 104.155333333333 0.237148436161895 439.198904361441 Winsorized Mean ( 12 / 30 ) 104.119333333333 0.231628808913317 449.509427699463 Winsorized Mean ( 13 / 30 ) 104.130888888889 0.227154445660617 458.41448793156 Winsorized Mean ( 14 / 30 ) 104.115333333333 0.222755370431735 467.397635044853 Winsorized Mean ( 15 / 30 ) 104.165333333333 0.21441784262499 485.805341841421 Winsorized Mean ( 16 / 30 ) 104.245333333333 0.202604465124512 514.526337162751 Winsorized Mean ( 17 / 30 ) 104.273666666667 0.196038191519745 531.904859243534 Winsorized Mean ( 18 / 30 ) 104.303666666667 0.190372094415345 547.89367626067 Winsorized Mean ( 19 / 30 ) 104.377555555556 0.180447377945811 578.437640622855 Winsorized Mean ( 20 / 30 ) 104.382 0.176428657425739 591.638578012395 Winsorized Mean ( 21 / 30 ) 104.386666666667 0.174062138229552 599.709205737793 Winsorized Mean ( 22 / 30 ) 104.364666666667 0.167245526598743 624.020676601171 Winsorized Mean ( 23 / 30 ) 104.372333333333 0.16570170467239 629.880866583048 Winsorized Mean ( 24 / 30 ) 104.385666666667 0.164162996403772 635.865992662085 Winsorized Mean ( 25 / 30 ) 104.382888888889 0.163079390180776 640.074069281094 Winsorized Mean ( 26 / 30 ) 104.377111111111 0.154323398976861 676.353111732339 Winsorized Mean ( 27 / 30 ) 104.398111111111 0.15049314644595 693.706747294343 Winsorized Mean ( 28 / 30 ) 104.354555555556 0.136952761761438 761.974816815552 Winsorized Mean ( 29 / 30 ) 104.383555555556 0.133814143484656 780.063697583096 Winsorized Mean ( 30 / 30 ) 104.420222222222 0.129950242833282 803.540031519503 Trimmed Mean ( 1 / 30 ) 104.186704545455 0.258240708186072 403.448028303827 Trimmed Mean ( 2 / 30 ) 104.182325581395 0.254019596733104 410.134993210224 Trimmed Mean ( 3 / 30 ) 104.178809523810 0.249538380743718 417.486116617882 Trimmed Mean ( 4 / 30 ) 104.175487804878 0.245727058310146 423.947971058979 Trimmed Mean ( 5 / 30 ) 104.174 0.241778523509388 430.865398993782 Trimmed Mean ( 6 / 30 ) 104.176282051282 0.238147970479074 437.443501373176 Trimmed Mean ( 7 / 30 ) 104.181315789474 0.234700207588937 443.891025320016 Trimmed Mean ( 8 / 30 ) 104.187432432432 0.230850291574400 451.320341516026 Trimmed Mean ( 9 / 30 ) 104.195 0.226707397610787 459.601235328381 Trimmed Mean ( 10 / 30 ) 104.202428571429 0.222573916883318 468.169990583648 Trimmed Mean ( 11 / 30 ) 104.210441176471 0.218011448844312 478.004443018449 Trimmed Mean ( 12 / 30 ) 104.217272727273 0.213335869607725 488.512658086538 Trimmed Mean ( 13 / 30 ) 104.217272727273 0.208704966152762 499.352145990579 Trimmed Mean ( 14 / 30 ) 104.239677419355 0.203919677022579 511.180082968712 Trimmed Mean ( 15 / 30 ) 104.253 0.198867883350350 524.232461489696 Trimmed Mean ( 16 / 30 ) 104.262068965517 0.194240537701145 536.7678147902 Trimmed Mean ( 17 / 30 ) 104.26375 0.190673373147046 546.81861593539 Trimmed Mean ( 18 / 30 ) 104.262777777778 0.187349831160761 556.513860363782 Trimmed Mean ( 19 / 30 ) 104.258846153846 0.184116997904886 566.264100220153 Trimmed Mean ( 20 / 30 ) 104.2476 0.181638474751921 573.929065096919 Trimmed Mean ( 21 / 30 ) 104.235 0.179041478612722 582.183529803543 Trimmed Mean ( 22 / 30 ) 104.220869565217 0.17596876811354 592.269132088094 Trimmed Mean ( 23 / 30 ) 104.2075 0.173166360088745 601.776811307898 Trimmed Mean ( 24 / 30 ) 104.192142857143 0.169584631489506 614.396139213773 Trimmed Mean ( 25 / 30 ) 104.174 0.164936584550175 631.600322536749 Trimmed Mean ( 26 / 30 ) 104.174 0.158771345639419 656.1259500602 Trimmed Mean ( 27 / 30 ) 104.132777777778 0.152441823985993 683.0984768809 Trimmed Mean ( 28 / 30 ) 104.106764705882 0.144378760509697 721.067034641084 Trimmed Mean ( 29 / 30 ) 104.081875 0.137081060828632 759.272465290554 Trimmed Mean ( 30 / 30 ) 104.050666666667 0.126972649180234 819.473070290674 Median 103.92 Midrange 104.41 Midmean - Weighted Average at Xnp 104.172222222222 Midmean - Weighted Average at X(n+1)p 104.220869565217 Midmean - Empirical Distribution Function 104.220869565217 Midmean - Empirical Distribution Function - Averaging 104.220869565217 Midmean - Empirical Distribution Function - Interpolation 104.2075 Midmean - Closest Observation 104.220869565217 Midmean - True Basic - Statistics Graphics Toolkit 104.220869565217 Midmean - MS Excel (old versions) 104.220869565217 Number of observations 90

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/28/ch81lop1nmvvsoo1193560085/1fckq1193560476.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/28/ch81lop1nmvvsoo1193560085/1fckq1193560476.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/28/ch81lop1nmvvsoo1193560085/2ld601193560476.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Oct/28/ch81lop1nmvvsoo1193560085/2ld601193560476.ps (open in new window)

Parameters:

par1 = 0 ; par2 = 0 ;

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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