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

Title produced by software: Central Tendency

Date of computation: Sun, 18 Nov 2007 15:15:05 -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/Nov/18/t11954237857rz4bv2csfsuvhe.htm/, Retrieved Sun, 18 Nov 2007 23:09:47 +0100

User-defined keywords:

Dataseries X:

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102,7 103,2 105,6 103,9 107,2 100,7 92,1 90,3 93,4 98,5 100,8 102,3 104,7 101,1 101,4 99,5 98,4 96,3 100,7 101,2 100,3 97,8 97,4 98,6 99,7 99 98,1 97 98,5 103,8 114,4 124,5 134,2 131,8 125,6 119,9 114,9 115,5 112,5 111,4 115,3 110,8 103,7 111,1 113 111,2 117,6 121,7 127,3 129,8 137,1 141,4 137,4 130,7 117,2 110,8 111,4 108,2 108,8 110,2 109,5 109,5 116 111,2 112,1 114 119,1 114,1 115,1 115,4 110,8 116 119,2 126,5 127,8 131,3 140,3 137,3 143 134,5 139,9 159,3 170,4 175 175,8 180,9 180,3 169,6 172,3 184,8 177,7 184,6 211,4

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 121.272043010753 2.67046262912558 45.4123722564363 Geometric Mean 118.95162920743 Harmonic Mean 116.965018537247 Quadratic Mean 123.947547438943 Winsorized Mean ( 1 / 31 ) 121.005376344086 2.57686617498025 46.9583471268209 Winsorized Mean ( 2 / 31 ) 121.029032258065 2.57237344569137 47.0495574663872 Winsorized Mean ( 3 / 31 ) 121.003225806452 2.53055588174296 47.8168558455657 Winsorized Mean ( 4 / 31 ) 121.007526881720 2.5207814321932 48.003974218597 Winsorized Mean ( 5 / 31 ) 120.889247311828 2.48331009698502 48.6806893180998 Winsorized Mean ( 6 / 31 ) 120.792473118280 2.45047019968219 49.2935899134564 Winsorized Mean ( 7 / 31 ) 120.754838709677 2.43353514574671 49.6211607712881 Winsorized Mean ( 8 / 31 ) 120.548387096774 2.37527519278830 50.7513350296325 Winsorized Mean ( 9 / 31 ) 120.374193548387 2.33107044978387 51.6390199873831 Winsorized Mean ( 10 / 31 ) 120.288172043011 2.31106190489200 52.0488749299133 Winsorized Mean ( 11 / 31 ) 119.081720430108 2.03715484790081 58.4549184136963 Winsorized Mean ( 12 / 31 ) 117.030107526882 1.61717550896704 72.3669798843504 Winsorized Mean ( 13 / 31 ) 116.876344086022 1.57022493709796 74.4328671164964 Winsorized Mean ( 14 / 31 ) 116.740860215054 1.53876528081196 75.8665806090018 Winsorized Mean ( 15 / 31 ) 116.773118279570 1.5165112300467 77.0011563158513 Winsorized Mean ( 16 / 31 ) 116.411827956989 1.43857223113558 80.9217816369888 Winsorized Mean ( 17 / 31 ) 116.393548387097 1.43567614052937 81.0722871971527 Winsorized Mean ( 18 / 31 ) 116.374193548387 1.42725990451282 81.5367917086625 Winsorized Mean ( 19 / 31 ) 115.904301075269 1.33783448450999 86.6357553324101 Winsorized Mean ( 20 / 31 ) 115.861290322581 1.32552355623182 87.4079451684358 Winsorized Mean ( 21 / 31 ) 115.364516129032 1.24020957408851 93.0201786370012 Winsorized Mean ( 22 / 31 ) 115.459139784946 1.19743691187563 96.4218980055443 Winsorized Mean ( 23 / 31 ) 115.409677419355 1.16440012035818 99.1151369718626 Winsorized Mean ( 24 / 31 ) 115.306451612903 1.11616831711692 103.305612464204 Winsorized Mean ( 25 / 31 ) 114.903225806452 1.02553017293863 112.042754897401 Winsorized Mean ( 26 / 31 ) 114.791397849462 1.00317827783272 114.427714780128 Winsorized Mean ( 27 / 31 ) 114.588172043011 0.968439375194797 118.322504204212 Winsorized Mean ( 28 / 31 ) 114.558064516129 0.903591766174668 126.780775129357 Winsorized Mean ( 29 / 31 ) 114.495698924731 0.82510700848575 138.764666579255 Winsorized Mean ( 30 / 31 ) 114.108602150538 0.647602576823264 176.201587569777 Winsorized Mean ( 31 / 31 ) 113.841935483871 0.533758280727847 213.283689629382 Trimmed Mean ( 1 / 31 ) 120.621978021978 2.51722360099012 47.9186584674212 Trimmed Mean ( 2 / 31 ) 120.221348314607 2.44835912193545 49.1028245152086 Trimmed Mean ( 3 / 31 ) 119.789655172414 2.37120581972876 50.5184552836989 Trimmed Mean ( 4 / 31 ) 119.347058823529 2.29984568245873 51.8935073486918 Trimmed Mean ( 5 / 31 ) 118.881927710843 2.21967674853657 53.5582164336416 Trimmed Mean ( 6 / 31 ) 118.420987654321 2.13707261704482 55.4127111590975 Trimmed Mean ( 7 / 31 ) 117.955696202532 2.04858208643607 57.579189520172 Trimmed Mean ( 8 / 31 ) 117.472727272727 1.94743520654119 60.321764173797 Trimmed Mean ( 9 / 31 ) 116.996 1.84082280858659 63.5563615652021 Trimmed Mean ( 10 / 31 ) 116.517808219178 1.72258405417271 67.6412903840197 Trimmed Mean ( 11 / 31 ) 116.023943661972 1.58186587835300 73.3462585227345 Trimmed Mean ( 12 / 31 ) 115.649275362319 1.478052887263 78.244341835747 Trimmed Mean ( 13 / 31 ) 115.649275362319 1.44422638224958 80.0769718540798 Trimmed Mean ( 14 / 31 ) 115.336923076923 1.41207289191139 81.6791567472144 Trimmed Mean ( 15 / 31 ) 115.188888888889 1.37881177855856 83.5421416324932 Trimmed Mean ( 16 / 31 ) 115.027868852459 1.34203607475464 85.7114581465249 Trimmed Mean ( 17 / 31 ) 114.891525423729 1.31139253047980 87.6103247146707 Trimmed Mean ( 18 / 31 ) 114.747368421053 1.27392665829770 90.0737634098853 Trimmed Mean ( 19 / 31 ) 114.594545454545 1.22883541862727 93.2545918822548 Trimmed Mean ( 20 / 31 ) 114.473584905660 1.1904468277949 96.160183078234 Trimmed Mean ( 21 / 31 ) 114.347058823529 1.14439247669456 99.919442981491 Trimmed Mean ( 22 / 31 ) 114.255102040816 1.10405121803519 103.487139160219 Trimmed Mean ( 23 / 31 ) 114.146808510638 1.06080559975872 107.603889474755 Trimmed Mean ( 24 / 31 ) 114.033333333333 1.01187394911070 112.695196307359 Trimmed Mean ( 25 / 31 ) 113.918604651163 0.958954163472207 118.794629598023 Trimmed Mean ( 26 / 31 ) 113.918604651163 0.911760852673972 124.943513770160 Trimmed Mean ( 27 / 31 ) 113.741025641026 0.854058485552267 133.177092160704 Trimmed Mean ( 28 / 31 ) 113.662162162162 0.785150770236056 144.764759165924 Trimmed Mean ( 29 / 31 ) 113.577142857143 0.708911886220685 160.213342539140 Trimmed Mean ( 30 / 31 ) 113.487878787879 0.626766557597549 181.06881647114 Trimmed Mean ( 31 / 31 ) 113.425806451613 0.575241281624184 197.179531572138 Median 113 Midrange 150.85 Midmean - Weighted Average at Xnp 113.786956521739 Midmean - Weighted Average at X(n+1)p 114.146808510638 Midmean - Empirical Distribution Function 114.146808510638 Midmean - Empirical Distribution Function - Averaging 114.146808510638 Midmean - Empirical Distribution Function - Interpolation 114.146808510638 Midmean - Closest Observation 113.9 Midmean - True Basic - Statistics Graphics Toolkit 114.146808510638 Midmean - MS Excel (old versions) 114.146808510638 Number of observations 93

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t11954237857rz4bv2csfsuvhe/1pxsm1195424101.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t11954237857rz4bv2csfsuvhe/1pxsm1195424101.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t11954237857rz4bv2csfsuvhe/2unlm1195424101.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/18/t11954237857rz4bv2csfsuvhe/2unlm1195424101.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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