*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: Sun, 18 Oct 2009 05:27:24 -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/18/t1255865299oga95djpc2bzn4v.htm/, Retrieved Sun, 18 Oct 2009 13:28:20 +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/18/t1255865299oga95djpc2bzn4v.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:

HSWWS3V2

Dataseries X:

» Textbox « » Textfile « » CSV «

14271 14013 15912 14290 14744 14721 13918 13263 15660 15629 15113 14526 15132 14908 16167 14122 13985 14236 13921 12394 15454 16146 15107 14593 14695 14513 17071 15179 15460 17173 15938 15003 18216 17847 18029 17281 16706 16750 18912 17763 16736 18061 16713 16769 19514 19251 19951 19052 19555 19083 22534 18854 19801 20346 18169 19087 20842 21602 22360 20334 21215 20530 23152 20134 21193 21628 20823 20493 22106 24178 24958 21620

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 17630.625 350.297752532587 50.330397133678 Geometric Mean 17389.5747994799 Harmonic Mean 17156.0991801814 Quadratic Mean 17875.9962655543 Winsorized Mean ( 1 / 24 ) 17631.8611111111 344.904055122646 51.1210606231965 Winsorized Mean ( 2 / 24 ) 17621.5555555556 334.727544292393 52.6444741582505 Winsorized Mean ( 3 / 24 ) 17595.9305555556 328.987627856466 53.485082919995 Winsorized Mean ( 4 / 24 ) 17589.8194444444 326.414646800189 53.8879600436921 Winsorized Mean ( 5 / 24 ) 17574.125 322.551258762911 54.4847509428501 Winsorized Mean ( 6 / 24 ) 17543.375 313.547243333184 55.9512972064561 Winsorized Mean ( 7 / 24 ) 17553.6805555556 311.721982881001 56.3119751559408 Winsorized Mean ( 8 / 24 ) 17555.5694444444 310.773938507390 56.4898380113911 Winsorized Mean ( 9 / 24 ) 17509.5694444444 301.79667835332 58.0177672596701 Winsorized Mean ( 10 / 24 ) 17537.4861111111 296.716387531125 59.1052157820957 Winsorized Mean ( 11 / 24 ) 17485.8472222222 287.362887396928 60.8493580386023 Winsorized Mean ( 12 / 24 ) 17493.8472222222 285.23237147178 61.3319138075217 Winsorized Mean ( 13 / 24 ) 17459.3611111111 274.079301194621 63.7018594071553 Winsorized Mean ( 14 / 24 ) 17457.2222222222 272.229737209036 64.1268011393532 Winsorized Mean ( 15 / 24 ) 17431.3888888889 266.789000369460 65.3377345570814 Winsorized Mean ( 16 / 24 ) 17465.1666666667 261.27975641276 66.8446989788059 Winsorized Mean ( 17 / 24 ) 17440.375 250.977326315607 69.4898429911096 Winsorized Mean ( 18 / 24 ) 17420.625 240.590204483775 72.4078731192683 Winsorized Mean ( 19 / 24 ) 17382.625 234.568650202588 74.1046383861924 Winsorized Mean ( 20 / 24 ) 17319.5694444444 224.08059225569 77.2916979114449 Winsorized Mean ( 21 / 24 ) 17321.3194444444 220.522795945116 78.5466163269372 Winsorized Mean ( 22 / 24 ) 17324.9861111111 198.03753881858 87.4833438875562 Winsorized Mean ( 23 / 24 ) 17274.5138888889 190.685191687901 90.5917954927644 Winsorized Mean ( 24 / 24 ) 17329.5138888889 183.043593062662 94.6742445279493 Trimmed Mean ( 1 / 24 ) 17600.7571428571 336.253508720117 52.3437129618393 Trimmed Mean ( 2 / 24 ) 17567.8235294118 325.921670044976 53.901980580142 Trimmed Mean ( 3 / 24 ) 17538.5151515152 320.037830108303 54.8013812791444 Trimmed Mean ( 4 / 24 ) 17516.984375 315.493172998127 55.5225465214868 Trimmed Mean ( 5 / 24 ) 17495.8387096774 310.818286104634 56.2896055085628 Trimmed Mean ( 6 / 24 ) 17477.05 306.228446191829 57.0719350776836 Trimmed Mean ( 7 / 24 ) 17463.3275862069 302.97420660125 57.6396511838735 Trimmed Mean ( 8 / 24 ) 17446.7321428571 299.219704377417 58.3074305856908 Trimmed Mean ( 9 / 24 ) 17428.5925925926 294.600011336741 59.1601898231801 Trimmed Mean ( 10 / 24 ) 17416.1346153846 290.754259190541 59.8998434756246 Trimmed Mean ( 11 / 24 ) 17398.66 286.77425468654 60.6702300351812 Trimmed Mean ( 12 / 24 ) 17386.7708333333 283.540150695397 61.3203131573832 Trimmed Mean ( 13 / 24 ) 17372.8043478261 279.534947854546 62.1489530420572 Trimmed Mean ( 14 / 24 ) 17361.9090909091 276.459815174126 62.8008417063212 Trimmed Mean ( 15 / 24 ) 17350.2380952381 272.449383272269 63.6824274911253 Trimmed Mean ( 16 / 24 ) 17340.5 268.006534554855 64.7017806069605 Trimmed Mean ( 17 / 24 ) 17325.7368421053 262.88221292487 65.9068434084463 Trimmed Mean ( 18 / 24 ) 17312.25 258.009054150837 67.099389426384 Trimmed Mean ( 19 / 24 ) 17299.5 253.399121008004 68.269771146734 Trimmed Mean ( 20 / 24 ) 17289.65625 247.982759096724 69.7212028488493 Trimmed Mean ( 21 / 24 ) 17286.0666666667 242.628887105879 71.2448829686273 Trimmed Mean ( 22 / 24 ) 17281.75 235.173855677411 73.4849966643632 Trimmed Mean ( 23 / 24 ) 17276.3076923077 230.692974580307 74.8887464984055 Trimmed Mean ( 24 / 24 ) 17276.5416666667 225.281345670532 76.6887361012712 Median 17122 Midrange 18676 Midmean - Weighted Average at Xnp 17249.8378378378 Midmean - Weighted Average at X(n+1)p 17312.25 Midmean - Empirical Distribution Function 17249.8378378378 Midmean - Empirical Distribution Function - Averaging 17312.25 Midmean - Empirical Distribution Function - Interpolation 17312.25 Midmean - Closest Observation 17249.8378378378 Midmean - True Basic - Statistics Graphics Toolkit 17312.25 Midmean - MS Excel (old versions) 17325.7368421053 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/18/t1255865299oga95djpc2bzn4v/1fr6e1255865239.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255865299oga95djpc2bzn4v/1fr6e1255865239.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255865299oga95djpc2bzn4v/2oskx1255865239.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255865299oga95djpc2bzn4v/2oskx1255865239.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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