Ws 3 part 2 ex 3

*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 09:39:51 -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/t1256053252cs9zhmwzab0oar5.htm/, Retrieved Tue, 20 Oct 2009 17:40:53 +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/t1256053252cs9zhmwzab0oar5.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

-16,8889 -16,8918 -16,8429 -16,838 -16,8985 -16,8175 -16,8165 -16,8093 -16,8213 -16,836 -16,7856 -16,8586 -16,8821 -16,819 -16,7909 -16,7688 -16,8056 -16,7792 -16,7548 -16,7898 -16,7724 -16,7706 -16,7724 -16,7839 -16,817 -16,7691 -16,7689 -16,7516 -16,8414 -16,7268 -16,7579 -16,7626 -16,7942 -16,8186 -16,8 -16,8331 -16,8526 -16,7894 -16,7464 -16,7392 -16,8382 -16,7205 -16,7836 -16,7576 -16,7467 -16,762 -16,7878 -16,7809 -16,8118 -16,7518 -16,7281 -16,7277 -16,8347 -16,7034 -16,7771 -16,7231 -16,7351 -16,7593 -16,7521 -16,7718 -16,8 -16,7362 -16,7295 -16,6836 -16,8168 -16,6815 -16,7085 -16,7051 -16,7306 -16,7542 -16,772 -16,7793

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 -16.7821361111111 0.00572225096662334 -2932.78575319358 Geometric Mean NaN Harmonic Mean -16.7819976984962 Quadratic Mean 16.7822053761401 Winsorized Mean ( 1 / 24 ) -16.7820722222222 0.00568911571737006 -2949.85601558131 Winsorized Mean ( 2 / 24 ) -16.7825416666667 0.00554481625347677 -3026.70835235406 Winsorized Mean ( 3 / 24 ) -16.7823291666667 0.00545585944995259 -3076.01933675409 Winsorized Mean ( 4 / 24 ) -16.7812125 0.00510978377324435 -3284.13358464778 Winsorized Mean ( 5 / 24 ) -16.7816291666667 0.00486501090776052 -3449.45355413224 Winsorized Mean ( 6 / 24 ) -16.7810375 0.00466826282122132 -3594.70709826267 Winsorized Mean ( 7 / 24 ) -16.7812513888889 0.0045795904448572 -3664.35636351149 Winsorized Mean ( 8 / 24 ) -16.7809958333333 0.00449813404084121 -3730.65713048317 Winsorized Mean ( 9 / 24 ) -16.7810208333333 0.0044853320925913 -3741.3106737518 Winsorized Mean ( 10 / 24 ) -16.7809375 0.00440386817693218 -3810.49950311862 Winsorized Mean ( 11 / 24 ) -16.7809069444444 0.00434151148037519 -3865.2222895871 Winsorized Mean ( 12 / 24 ) -16.7813902777778 0.00417517355056262 -4019.32759789505 Winsorized Mean ( 13 / 24 ) -16.7794583333333 0.00379134575332868 -4425.72622626188 Winsorized Mean ( 14 / 24 ) -16.7795944444444 0.00362977217524268 -4622.76794088945 Winsorized Mean ( 15 / 24 ) -16.7810111111111 0.00339120223000209 -4948.39587054081 Winsorized Mean ( 16 / 24 ) -16.7808333333333 0.00334365830501856 -5018.7046051167 Winsorized Mean ( 17 / 24 ) -16.7818722222222 0.00316404587757883 -5303.92822087142 Winsorized Mean ( 18 / 24 ) -16.7818722222222 0.00314950080639905 -5328.42290058328 Winsorized Mean ( 19 / 24 ) -16.7818722222222 0.00312651104139261 -5367.60369627456 Winsorized Mean ( 20 / 24 ) -16.78115 0.00284757948443727 -5893.12786235228 Winsorized Mean ( 21 / 24 ) -16.7805958333333 0.00271461545700697 -6181.5738173962 Winsorized Mean ( 22 / 24 ) -16.7803208333333 0.00243411455841533 -6893.80899322082 Winsorized Mean ( 23 / 24 ) -16.7786277777778 0.00216583879292205 -7746.94212358291 Winsorized Mean ( 24 / 24 ) -16.7790944444444 0.00210345297838408 -7976.92870573913 Trimmed Mean ( 1 / 24 ) -16.7819114285714 0.00545480984893345 -3076.53463518122 Trimmed Mean ( 2 / 24 ) -16.7817411764706 0.00517417874678307 -3243.36324617781 Trimmed Mean ( 3 / 24 ) -16.7813045454545 0.00493172189007219 -3402.72726636029 Trimmed Mean ( 4 / 24 ) -16.7809203125 0.00468143294124465 -3584.56919561011 Trimmed Mean ( 5 / 24 ) -16.7808354838710 0.00451465918136961 -3716.96617833733 Trimmed Mean ( 6 / 24 ) -16.780645 0.00439223083030330 -3820.52894037931 Trimmed Mean ( 7 / 24 ) -16.7805637931034 0.00429919638115661 -3903.18615512720 Trimmed Mean ( 8 / 24 ) -16.7804375 0.00420700603238142 -3988.68871849496 Trimmed Mean ( 9 / 24 ) -16.7803444444444 0.00411209093655368 -4080.7328202007 Trimmed Mean ( 10 / 24 ) -16.7802403846154 0.00399567003539962 -4199.6061326263 Trimmed Mean ( 11 / 24 ) -16.78014 0.00386802486115729 -4338.16756673572 Trimmed Mean ( 12 / 24 ) -16.7800354166667 0.00372029784323858 -4510.40108177451 Trimmed Mean ( 13 / 24 ) -16.7798586956522 0.00357040651292075 -4699.70537946546 Trimmed Mean ( 14 / 24 ) -16.7799090909091 0.00346870457048029 -4837.51462540544 Trimmed Mean ( 15 / 24 ) -16.7799476190476 0.00337192969234518 -4976.36343282626 Trimmed Mean ( 16 / 24 ) -16.77982 0.00329713200936506 -5089.21691710832 Trimmed Mean ( 17 / 24 ) -16.7797 0.00320490600097834 -5235.62937411511 Trimmed Mean ( 18 / 24 ) -16.7794444444444 0.00311911272600577 -5379.55691839699 Trimmed Mean ( 19 / 24 ) -16.7791588235294 0.00299969433275553 -5593.62287027292 Trimmed Mean ( 20 / 24 ) -16.7788375 0.00283378504859014 -5920.99866867029 Trimmed Mean ( 21 / 24 ) -16.77856 0.00268462030963349 -6249.88194412141 Trimmed Mean ( 22 / 24 ) -16.7783107142857 0.00250898564679286 -6687.28844094139 Trimmed Mean ( 23 / 24 ) -16.7780576923077 0.00234806744154833 -7145.47520885691 Trimmed Mean ( 24 / 24 ) -16.7779833333333 0.00220990578416351 -7592.17132855469 Median -16.77815 Midrange -16.79 Midmean - Weighted Average at Xnp -16.7804594594595 Midmean - Weighted Average at X(n+1)p -16.7794444444444 Midmean - Empirical Distribution Function -16.7804594594595 Midmean - Empirical Distribution Function - Averaging -16.7794444444444 Midmean - Empirical Distribution Function - Interpolation -16.7794444444444 Midmean - Closest Observation -16.7804594594595 Midmean - True Basic - Statistics Graphics Toolkit -16.7794444444444 Midmean - MS Excel (old versions) -16.7797 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053252cs9zhmwzab0oar5/1436y1256053186.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053252cs9zhmwzab0oar5/1436y1256053186.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053252cs9zhmwzab0oar5/2haef1256053186.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256053252cs9zhmwzab0oar5/2haef1256053186.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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