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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: Thu, 24 Apr 2008 09:19:22 -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/24/t1209050404myjlt6w5dfcm192.htm/, Retrieved Thu, 24 Apr 2008 17:20:06 +0200

User-defined keywords:

Dataseries X:

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217,8 218,79 218,99 219,53 219,55 219,74 219,74 219,74 219,8 219,97 220,07 220,07 220,1 225,8 233,17 233,83 233,63 233,63 233,65 233,8 233,84 233,74 233,88 233,88 233,81 234,68 236,14 236,91 236,87 236,78 236,78 236,9 236,94 236,97 236,96 236,94 236,99 237,24 237,62 237,54 237,41 237,4 237,41 237,28 237,17 237,18 237,18 237,18 236,77 239,23 240,23 240,33 240,33 240,34 240,34 240,27 240,29 240,29 240,29 240,29 240,31 239,95 242,33 242,11 241,53 241,53 241,53 241,41 241,41 241,66 241,8 241,99

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 234.410833333333 0.895629270349123 261.727526214008 Geometric Mean 234.286089144862 Harmonic Mean 234.158048486626 Quadratic Mean 234.532282556392 Winsorized Mean ( 1 / 24 ) 234.421527777778 0.891760046440362 262.875118383603 Winsorized Mean ( 2 / 24 ) 234.42375 0.889993833336147 263.399296960588 Winsorized Mean ( 3 / 24 ) 234.438333333333 0.883634017386336 265.311575517168 Winsorized Mean ( 4 / 24 ) 234.431666666667 0.88246507066227 265.655462703732 Winsorized Mean ( 5 / 24 ) 234.435833333333 0.878309096021079 266.917232663735 Winsorized Mean ( 6 / 24 ) 234.435833333333 0.878309096021079 266.917232663735 Winsorized Mean ( 7 / 24 ) 234.435833333333 0.878309096021079 266.917232663735 Winsorized Mean ( 8 / 24 ) 234.429166666667 0.875231486258544 267.848186848040 Winsorized Mean ( 9 / 24 ) 234.450416666667 0.870240069891587 269.408896209381 Winsorized Mean ( 10 / 24 ) 234.315694444444 0.85118838555228 275.280652816254 Winsorized Mean ( 11 / 24 ) 234.315694444444 0.85118838555228 275.280652816254 Winsorized Mean ( 12 / 24 ) 234.319027777778 0.849843863035104 275.720091618875 Winsorized Mean ( 13 / 24 ) 235.348194444444 0.614590475454287 382.934984910858 Winsorized Mean ( 14 / 24 ) 236.777361111111 0.334252780812736 708.378133864397 Winsorized Mean ( 15 / 24 ) 236.869027777778 0.319493079494936 741.39016767508 Winsorized Mean ( 16 / 24 ) 236.869027777778 0.319493079494936 741.39016767508 Winsorized Mean ( 17 / 24 ) 236.87375 0.318819678474571 742.9709205321 Winsorized Mean ( 18 / 24 ) 236.89625 0.315632945676957 750.543481739252 Winsorized Mean ( 19 / 24 ) 236.906805555556 0.312610282661745 757.83433461751 Winsorized Mean ( 20 / 24 ) 236.898472222222 0.310540045255748 762.859656399942 Winsorized Mean ( 21 / 24 ) 236.822638888889 0.297500015981874 796.042440896266 Winsorized Mean ( 22 / 24 ) 236.605694444444 0.265398527095062 891.510955370507 Winsorized Mean ( 23 / 24 ) 236.104166666667 0.198867465361589 1187.24380701173 Winsorized Mean ( 24 / 24 ) 236.0775 0.196034807958032 1204.26317376525 Trimmed Mean ( 1 / 24 ) 234.535 0.882412436491312 265.788411746064 Trimmed Mean ( 2 / 24 ) 234.655147058824 0.870779738291145 269.477040794863 Trimmed Mean ( 3 / 24 ) 234.781363636364 0.85748754498661 273.801485524819 Trimmed Mean ( 4 / 24 ) 234.91 0.843898473121327 278.362868854518 Trimmed Mean ( 5 / 24 ) 235.048870967742 0.827342118924907 284.101178449826 Trimmed Mean ( 6 / 24 ) 235.196 0.807992322500863 291.086924281695 Trimmed Mean ( 7 / 24 ) 235.353275862069 0.783729831868495 300.298988620813 Trimmed Mean ( 8 / 24 ) 235.521785714286 0.753161307429741 312.710947032096 Trimmed Mean ( 9 / 24 ) 235.703888888889 0.715091312122251 329.613693934227 Trimmed Mean ( 10 / 24 ) 235.896730769231 0.667453611018984 353.427904014323 Trimmed Mean ( 11 / 24 ) 236.1244 0.608990878923687 387.730601839751 Trimmed Mean ( 12 / 24 ) 236.371041666667 0.528528436769205 447.224832615551 Trimmed Mean ( 13 / 24 ) 236.638695652174 0.40912344246978 578.404146737823 Trimmed Mean ( 14 / 24 ) 236.801136363636 0.336485255640002 703.748923301961 Trimmed Mean ( 15 / 24 ) 236.804047619048 0.331048217225528 715.315882392213 Trimmed Mean ( 16 / 24 ) 236.79625 0.3266870782804 724.841188229534 Trimmed Mean ( 17 / 24 ) 236.787631578947 0.320312666020057 739.239052020878 Trimmed Mean ( 18 / 24 ) 236.7775 0.311347398224157 760.492945662998 Trimmed Mean ( 19 / 24 ) 236.763529411765 0.2993906117221 790.818149072533 Trimmed Mean ( 20 / 24 ) 236.7465625 0.283062033472076 836.376958068293 Trimmed Mean ( 21 / 24 ) 236.728333333333 0.259786421266257 911.24213567232 Trimmed Mean ( 22 / 24 ) 236.716785714286 0.229826857748841 1029.97877634029 Trimmed Mean ( 23 / 24 ) 236.730769230769 0.197425680721339 1199.08802322889 Trimmed Mean ( 24 / 24 ) 236.8125 0.171613453832245 1379.91803504805 Median 236.965 Midrange 230.065 Midmean - Weighted Average at Xnp 236.96275 Midmean - Weighted Average at X(n+1)p 237.047692307692 Midmean - Empirical Distribution Function 236.96275 Midmean - Empirical Distribution Function - Averaging 237.047692307692 Midmean - Empirical Distribution Function - Interpolation 237.047692307692 Midmean - Closest Observation 236.96275 Midmean - True Basic - Statistics Graphics Toolkit 237.047692307692 Midmean - MS Excel (old versions) 236.96275 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/24/t1209050404myjlt6w5dfcm192/13dv51209050359.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/24/t1209050404myjlt6w5dfcm192/13dv51209050359.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/24/t1209050404myjlt6w5dfcm192/2n18b1209050359.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/24/t1209050404myjlt6w5dfcm192/2n18b1209050359.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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