*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 05:34:36 -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/t1255865713mihtgfh8uiwj2h5.htm/, Retrieved Sun, 18 Oct 2009 13:35:16 +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/t1255865713mihtgfh8uiwj2h5.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:

HSWWS3V2C

Dataseries X:

» Textbox « » Textfile « » CSV «

4915 4676 5763 4502 4974 4810 4489 4488 5471 5100 5199 4736 5507 5179 5578 4511 4597 4726 4231 3960 5610 5545 5165 4364 5314 4878 5843 5180 5371 5551 5405 5038 6649 6526 6343 5534 6111 5999 6713 6073 5758 6308 5874 6251 7331 7284 7588 6693 7393 6987 8209 6184 5936 6783 5435 6623 7453 7641 8272 7191 7802 6951 7764 6426 6504 6745 6832 6639 7742 8506 9054 7604

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 6060.93055555556 137.664568363763 44.0268009960284 Geometric Mean 5951.91306929319 Harmonic Mean 5845.46712296855 Quadratic Mean 6170.93494289516 Winsorized Mean ( 1 / 24 ) 6057.08333333333 134.758964021671 44.9475356040825 Winsorized Mean ( 2 / 24 ) 6054.27777777778 132.475579026582 45.7010856058456 Winsorized Mean ( 3 / 24 ) 6056.81944444444 130.962022661730 46.2486705790197 Winsorized Mean ( 4 / 24 ) 6034.26388888889 126.096205839722 47.8544445386319 Winsorized Mean ( 5 / 24 ) 6032.52777777778 125.423631086126 48.0972184072341 Winsorized Mean ( 6 / 24 ) 6031.44444444444 124.939905568548 48.2747639114815 Winsorized Mean ( 7 / 24 ) 6029.98611111111 121.666749458226 49.5614959548295 Winsorized Mean ( 8 / 24 ) 6034.65277777778 119.471809915660 50.5111020083975 Winsorized Mean ( 9 / 24 ) 6038.90277777778 118.112225087293 51.1285158950704 Winsorized Mean ( 10 / 24 ) 6021.54166666667 114.510038337633 52.5852733444396 Winsorized Mean ( 11 / 24 ) 6023.68055555556 111.143992286038 54.1970864250865 Winsorized Mean ( 12 / 24 ) 6024.68055555556 107.6420156419 55.9695999710584 Winsorized Mean ( 13 / 24 ) 6022.875 105.203608642111 57.2496996798756 Winsorized Mean ( 14 / 24 ) 6016.26388888889 100.498643302172 59.8641304121847 Winsorized Mean ( 15 / 24 ) 5987.09722222222 91.7839436721383 65.2303331354855 Winsorized Mean ( 16 / 24 ) 5992.875 88.5789413392775 67.6557532681038 Winsorized Mean ( 17 / 24 ) 5980.125 82.2237774874849 72.7298742861847 Winsorized Mean ( 18 / 24 ) 5971.375 79.9655819876357 74.6743142683973 Winsorized Mean ( 19 / 24 ) 5961.61111111111 78.5071355158222 75.9371880268083 Winsorized Mean ( 20 / 24 ) 5958 76.5261367688432 77.855752969693 Winsorized Mean ( 21 / 24 ) 5985.70833333333 71.1351961662242 84.1455236778473 Winsorized Mean ( 22 / 24 ) 5989.68055555556 66.9693797149188 89.439092627899 Winsorized Mean ( 23 / 24 ) 5997.34722222222 65.1237991629689 92.0914826730881 Winsorized Mean ( 24 / 24 ) 6002.01388888889 63.1107978586847 95.102804789893 Trimmed Mean ( 1 / 24 ) 6048.18571428571 131.480260573357 46.0007128667901 Trimmed Mean ( 2 / 24 ) 6038.76470588235 127.572255890798 47.3360344983752 Trimmed Mean ( 3 / 24 ) 6030.30303030303 124.363687595695 48.4892587771078 Trimmed Mean ( 4 / 24 ) 6020.359375 121.190763158723 49.6767180772279 Trimmed Mean ( 5 / 24 ) 6016.32258064516 119.157184303880 50.4906407095193 Trimmed Mean ( 6 / 24 ) 6012.43333333333 116.868295581997 51.446231019215 Trimmed Mean ( 7 / 24 ) 6008.5 114.183789743949 52.6213047707887 Trimmed Mean ( 8 / 24 ) 6004.55357142857 111.723745919860 53.7446495549447 Trimmed Mean ( 9 / 24 ) 5999.53703703704 109.187520094325 54.9470949780171 Trimmed Mean ( 10 / 24 ) 5993.48076923077 106.311923629811 56.3763740189735 Trimmed Mean ( 11 / 24 ) 5989.44 103.531973410958 57.8511140343632 Trimmed Mean ( 12 / 24 ) 5984.77083333333 100.748802148623 59.4028981555998 Trimmed Mean ( 13 / 24 ) 5979.5652173913 97.9514897790048 61.0461896075518 Trimmed Mean ( 14 / 24 ) 5974.11363636364 94.8584302669812 62.9792588760889 Trimmed Mean ( 15 / 24 ) 5968.95238095238 91.8966744950716 64.9528659633107 Trimmed Mean ( 16 / 24 ) 5966.775 90.0107008417646 66.2896182809349 Trimmed Mean ( 17 / 24 ) 5963.68421052632 88.123491726755 67.6741705721097 Trimmed Mean ( 18 / 24 ) 5961.75 86.9530102530297 68.5628937129554 Trimmed Mean ( 19 / 24 ) 5960.61764705882 85.6944372062923 69.556646164906 Trimmed Mean ( 20 / 24 ) 5960.5 84.091611909562 70.8810292090766 Trimmed Mean ( 21 / 24 ) 5960.8 82.1317052756988 72.5761139378618 Trimmed Mean ( 22 / 24 ) 5957.75 80.6222431955574 73.8971004012984 Trimmed Mean ( 23 / 24 ) 5953.73076923077 79.338002489685 75.0426098767087 Trimmed Mean ( 24 / 24 ) 5948.04166666667 77.5527048268865 76.6967661533394 Median 5905 Midrange 6507 Midmean - Weighted Average at Xnp 5940.21621621622 Midmean - Weighted Average at X(n+1)p 5961.75 Midmean - Empirical Distribution Function 5940.21621621622 Midmean - Empirical Distribution Function - Averaging 5961.75 Midmean - Empirical Distribution Function - Interpolation 5961.75 Midmean - Closest Observation 5940.21621621622 Midmean - True Basic - Statistics Graphics Toolkit 5961.75 Midmean - MS Excel (old versions) 5963.68421052632 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/18/t1255865713mihtgfh8uiwj2h5/1mqdd1255865673.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255865713mihtgfh8uiwj2h5/1mqdd1255865673.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255865713mihtgfh8uiwj2h5/29bwp1255865673.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255865713mihtgfh8uiwj2h5/29bwp1255865673.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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