KDGP1W52

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sat, 15 Jan 2011 17:54:35 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/15/t1295113933c093rf1w33zp3wz.htm/, Retrieved Sat, 15 Jan 2011 18:52:15 +0100

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/2011/Jan/15/t1295113933c093rf1w33zp3wz.htm/}, year = {2011}, } @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 = {2011}, 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:

Dataseries X:

» Textbox « » Textfile « » CSV «

10574 10653 10805 10872 10625 10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745 19394 20148 20108 18584 18441 18391 19178 18073 18483 19644 19195 19650 20830 23595 22937 21814 21928 21777 21383 21467 22052 22680 24320 24977 25204 27390 26434 27525 30695 32436 30160 30236

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 'Gwilym Jenkins' @ www.wessa.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 17840.5205479452 639.807908562447 27.8841825947888 Geometric Mean 17054.9137158249 Harmonic Mean 16312.9882831012 Quadratic Mean 18648.2619278985 Winsorized Mean ( 1 / 24 ) 17817.4383561644 632.531752707739 28.1684489037769 Winsorized Mean ( 2 / 24 ) 17807.4109589041 628.61724017135 28.3279073829571 Winsorized Mean ( 3 / 24 ) 17805.0273972603 627.643016736722 28.3680801386642 Winsorized Mean ( 4 / 24 ) 17663.4383561644 590.618741093749 29.9066675795861 Winsorized Mean ( 5 / 24 ) 17655.6301369863 588.245914478484 30.0140293411797 Winsorized Mean ( 6 / 24 ) 17577.6301369863 570.642957457692 30.8032017345794 Winsorized Mean ( 7 / 24 ) 17464.3835616438 545.484958584477 32.0162513865892 Winsorized Mean ( 8 / 24 ) 17450.7945205479 538.681078559815 32.395410225292 Winsorized Mean ( 9 / 24 ) 17378.0547945205 521.911654835349 33.2969280021212 Winsorized Mean ( 10 / 24 ) 17343.6712328767 492.866208352651 35.1894103084201 Winsorized Mean ( 11 / 24 ) 17245.5753424658 475.70645131489 36.2525572121161 Winsorized Mean ( 12 / 24 ) 17219.4383561644 465.987151635601 36.9526032975903 Winsorized Mean ( 13 / 24 ) 17198.9589041096 432.623032376282 39.7550699269069 Winsorized Mean ( 14 / 24 ) 17292.1643835616 409.703164540051 42.2065677793202 Winsorized Mean ( 15 / 24 ) 17362.6438356164 391.276448170142 44.3743647664336 Winsorized Mean ( 16 / 24 ) 17525.7123287671 364.677161953315 48.0581570693772 Winsorized Mean ( 17 / 24 ) 17623.9863013699 329.831694254334 53.4332709935994 Winsorized Mean ( 18 / 24 ) 17687.602739726 315.803185715348 56.0083100481098 Winsorized Mean ( 19 / 24 ) 17555.3835616438 291.402819753038 60.2443846511914 Winsorized Mean ( 20 / 24 ) 17374.8356164384 262.25803519045 66.2509181227598 Winsorized Mean ( 21 / 24 ) 17415.9726027397 253.908472025128 68.591537981514 Winsorized Mean ( 22 / 24 ) 17287.2876712329 232.827478802731 74.2493444507895 Winsorized Mean ( 23 / 24 ) 17328.5616438356 227.161058489404 76.283152398869 Winsorized Mean ( 24 / 24 ) 17336.4520547945 204.644984425079 84.7147664209744 Trimmed Mean ( 1 / 24 ) 17739.6478873239 615.454514645086 28.8236538447587 Trimmed Mean ( 2 / 24 ) 17657.347826087 595.038390526509 29.6743001917291 Trimmed Mean ( 3 / 24 ) 17575.5970149254 573.065000524143 30.6694650674011 Trimmed Mean ( 4 / 24 ) 17489.7076923077 546.916881131735 31.9787307645656 Trimmed Mean ( 5 / 24 ) 17439.380952381 529.793437332842 32.9173215889133 Trimmed Mean ( 6 / 24 ) 17387.6229508197 509.744408880238 34.1104731075232 Trimmed Mean ( 7 / 24 ) 17348.4406779661 490.627945584452 35.3596667986372 Trimmed Mean ( 8 / 24 ) 17327.2280701754 474.215738274293 36.5387031084851 Trimmed Mean ( 9 / 24 ) 17306.7272727273 455.692458946939 37.978963515704 Trimmed Mean ( 10 / 24 ) 17295.8113207547 436.928834344914 39.5849620377796 Trimmed Mean ( 11 / 24 ) 17288.9607843137 420.576976201051 41.1077204950206 Trimmed Mean ( 12 / 24 ) 17294.8367346939 404.018432750907 42.8070487203657 Trimmed Mean ( 13 / 24 ) 17304.5957446808 385.18120206857 44.9258573672562 Trimmed Mean ( 14 / 24 ) 17317.7777777778 369.066899972679 46.9231398943112 Trimmed Mean ( 15 / 24 ) 17320.8837209302 353.701009950467 48.9704106961862 Trimmed Mean ( 16 / 24 ) 17315.9268292683 337.987543770773 51.2324408056061 Trimmed Mean ( 17 / 24 ) 17291.3846153846 323.551670821644 53.4424210249757 Trimmed Mean ( 18 / 24 ) 17252.7837837838 312.532480318377 55.2031704551423 Trimmed Mean ( 19 / 24 ) 17202.4 300.358282414729 57.2729337166979 Trimmed Mean ( 20 / 24 ) 17161.303030303 290.280511814841 59.1197215514406 Trimmed Mean ( 21 / 24 ) 17136.1612903226 284.301351162165 60.2746389360216 Trimmed Mean ( 22 / 24 ) 17102.6206896552 277.009573796394 61.7401790676947 Trimmed Mean ( 23 / 24 ) 17079.9259259259 272.328907714545 62.7180054782474 Trimmed Mean ( 24 / 24 ) 17048.36 265.558222617941 64.1982004244978 Median 16438 Midrange 21421.5 Midmean - Weighted Average at Xnp 17138.0555555556 Midmean - Weighted Average at X(n+1)p 17252.7837837838 Midmean - Empirical Distribution Function 17252.7837837838 Midmean - Empirical Distribution Function - Averaging 17252.7837837838 Midmean - Empirical Distribution Function - Interpolation 17252.7837837838 Midmean - Closest Observation 17181.5 Midmean - True Basic - Statistics Graphics Toolkit 17252.7837837838 Midmean - MS Excel (old versions) 17252.7837837838 Number of observations 73

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295113933c093rf1w33zp3wz/1upzj1295114074.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/15/t1295113933c093rf1w33zp3wz/1upzj1295114074.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/15/t1295113933c093rf1w33zp3wz/20avb1295114074.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/15/t1295113933c093rf1w33zp3wz/20avb1295114074.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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