*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Tue, 20 Oct 2009 12:22:12 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/20/t1256062967cmjmq0pz5lzt6u1.htm/, Retrieved Tue, 20 Oct 2009 20:22:48 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Oct/20/t1256062967cmjmq0pz5lzt6u1.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

HSWWS3Q2

Dataseries X:

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-12197 -12436 -11349 -12610 -12138 -12302 -12623 -12624 -11641 -12012 -11913 -12376 -11605 -11933 -11534 -12601 -12515 -12386 -12881 -13152 -11502 -11567 -11947 -12748 -11798 -12234 -11269 -11932 -11741 -11561 -11707 -12074 -10463 -10586 -10769 -11578 -11001 -11113 -10399 -11039 -11354 -10804 -11238 -10861 -9781 -9828 -9524 -10419 -9719 -10125 -8903 -10928 -11176 -10329 -11677 -10489 -9659 -9471 -8840 -9921 -9310 -10161 -9348 -10686 -10608 -10367 -10280 -10473 -9370 -8606 -8058 -9508

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -11051.0694444444 137.664568363763 -80.275335736667 Geometric Mean NaN Harmonic Mean -10922.2087951604 Quadratic Mean 11111.7817984386 Winsorized Mean ( 1 / 24 ) -11054.9166666667 134.758964021671 -82.0347406714175 Winsorized Mean ( 2 / 24 ) -11057.7222222222 132.475579026582 -83.4698916092561 Winsorized Mean ( 3 / 24 ) -11055.1805555556 130.962022661730 -84.4151635020995 Winsorized Mean ( 4 / 24 ) -11077.7361111111 126.096205839722 -87.8514625982622 Winsorized Mean ( 5 / 24 ) -11079.4722222222 125.423631086126 -88.3364014123792 Winsorized Mean ( 6 / 24 ) -11080.5555555556 124.939905568548 -88.6870812422396 Winsorized Mean ( 7 / 24 ) -11082.0138888889 121.666749458226 -91.0849836807213 Winsorized Mean ( 8 / 24 ) -11077.3472222222 119.471809915660 -92.719338813417 Winsorized Mean ( 9 / 24 ) -11073.0972222222 118.112225087293 -93.7506444742572 Winsorized Mean ( 10 / 24 ) -11090.4583333333 114.510038337633 -96.851407041129 Winsorized Mean ( 11 / 24 ) -11088.3194444444 111.143992286038 -99.7653513822659 Winsorized Mean ( 12 / 24 ) -11087.3194444444 107.6420156419 -103.001782141737 Winsorized Mean ( 13 / 24 ) -11089.125 105.203608642111 -105.406317740714 Winsorized Mean ( 14 / 24 ) -11095.7361111111 100.498643302172 -110.406824873737 Winsorized Mean ( 15 / 24 ) -11124.9027777778 91.7839436721383 -121.207504631933 Winsorized Mean ( 16 / 24 ) -11119.125 88.5789413392775 -125.527860593989 Winsorized Mean ( 17 / 24 ) -11131.875 82.2237774874849 -135.385108057026 Winsorized Mean ( 18 / 24 ) -11140.625 79.9655819876357 -139.317750500741 Winsorized Mean ( 19 / 24 ) -11150.3888888889 78.5071355158222 -142.030260251206 Winsorized Mean ( 20 / 24 ) -11154 76.5261367688432 -145.754123636112 Winsorized Mean ( 21 / 24 ) -11126.2916666667 71.1351961662242 -156.410500937784 Winsorized Mean ( 22 / 24 ) -11122.3194444444 66.9693797149188 -166.080669879144 Winsorized Mean ( 23 / 24 ) -11114.6527777778 65.1237991629689 -170.669600370887 Winsorized Mean ( 24 / 24 ) -11109.9861111111 63.1107978586847 -176.039386096626 Trimmed Mean ( 1 / 24 ) -11063.8142857143 131.480260573357 -84.148101300282 Trimmed Mean ( 2 / 24 ) -11073.2352941176 127.572255890798 -86.79971375278 Trimmed Mean ( 3 / 24 ) -11081.6969696970 124.363687595695 -89.1071757676042 Trimmed Mean ( 4 / 24 ) -11091.640625 121.190763158723 -91.5221617217913 Trimmed Mean ( 5 / 24 ) -11095.6774193548 119.157184303880 -93.1179893531067 Trimmed Mean ( 6 / 24 ) -11099.5666666667 116.868295581997 -94.9750025136543 Trimmed Mean ( 7 / 24 ) -11103.5 114.183789743949 -97.2423495918202 Trimmed Mean ( 8 / 24 ) -11107.4464285714 111.723745919860 -99.4188508192236 Trimmed Mean ( 9 / 24 ) -11112.4629629630 109.187520094325 -101.774112585056 Trimmed Mean ( 10 / 24 ) -11118.5192307692 106.311923629811 -104.583934248853 Trimmed Mean ( 11 / 24 ) -11122.56 103.531973410958 -107.431159993930 Trimmed Mean ( 12 / 24 ) -11127.2291666667 100.748802148623 -110.445275073861 Trimmed Mean ( 13 / 24 ) -11132.4347826087 97.9514897790048 -113.652531551336 Trimmed Mean ( 14 / 24 ) -11137.8863636364 94.8584302669812 -117.415883145953 Trimmed Mean ( 15 / 24 ) -11143.0476190476 91.8966744950716 -121.256266130122 Trimmed Mean ( 16 / 24 ) -11145.225 90.0107008417646 -123.821111220908 Trimmed Mean ( 17 / 24 ) -11148.3157894737 88.123491726755 -126.50787628844 Trimmed Mean ( 18 / 24 ) -11150.25 86.9530102530297 -128.233053318720 Trimmed Mean ( 19 / 24 ) -11151.3823529412 85.6944372062923 -130.129594364409 Trimmed Mean ( 20 / 24 ) -11151.5 84.091611909562 -132.611324087747 Trimmed Mean ( 21 / 24 ) -11151.2 82.1317052756988 -135.77217181316 Trimmed Mean ( 22 / 24 ) -11154.25 80.6222431955574 -138.352017481630 Trimmed Mean ( 23 / 24 ) -11158.2692307692 79.338002489685 -140.642175005855 Trimmed Mean ( 24 / 24 ) -11163.9583333333 77.5527048268865 -143.953178141930 Median -11207 Midrange -10605 Midmean - Weighted Average at Xnp -11171.7837837838 Midmean - Weighted Average at X(n+1)p -11150.25 Midmean - Empirical Distribution Function -11171.7837837838 Midmean - Empirical Distribution Function - Averaging -11150.25 Midmean - Empirical Distribution Function - Interpolation -11150.25 Midmean - Closest Observation -11171.7837837838 Midmean - True Basic - Statistics Graphics Toolkit -11150.25 Midmean - MS Excel (old versions) -11148.3157894737 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256062967cmjmq0pz5lzt6u1/1zivi1256062927.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256062967cmjmq0pz5lzt6u1/1zivi1256062927.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256062967cmjmq0pz5lzt6u1/26gzr1256062927.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256062967cmjmq0pz5lzt6u1/26gzr1256062927.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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